WO2023187623A1

WO2023187623A1 - A pre-processing method to generate a model for fluid-structure interaction simulation based on image data

Info

Publication number: WO2023187623A1
Application number: PCT/IB2023/053037
Authority: WO
Inventors: Yijin MAO; Chao Zhang; Qinghua Zhao; Chunliang WANG; Huiqiang YUE
Original assignee: Shenzhen Escope Tech Co., Ltd.
Priority date: 2022-03-28
Filing date: 2023-03-28
Publication date: 2023-10-05

Abstract

The present invention relates to a method and system to model an anatomical structure in its native environments. The present invention uses an image of an anatomical structure superimposed on a lattice structure to segment the image, then placing particles within each segment of the image. Particles are then moved to an optimized position to best reflect the anatomical structure in shape, size, and behavior in a native environment. A method and system to model two anatomical structures contacting each other are also provided.

Description

A PRE-PROCESSING METHOD TO GENERATE A MODEL FOR FLUIDSTRUCTURE INTERACTION SIMULATION BASED ON IMAGE DATA

BACKGROUND

[0001] Anatomical biomechanical simulation holds tremendous potential for functional anatomical analysis in the medical and diagnostics arenas. The ability to model and predict the hemodynamic behavior of, for example, blood vessels, or stress analysis in the myocardium has the potential to improve therapeutic outcomes, improve diagnostic conclusions and conduct prophylactic measures. The problem historically has been not only the ability to develop a proper functioning generic model, but one that is specifically applicable to a particular subject (including mammals and other species).

[0002] Medical imaging technologies such as nuclear magnetic resonance technology and computed tomography (CT) technology have improved diagnostic and therapeutic accuracy by providing static anatomical images to guide medical decisions. One problem with these technologies is their static nature, which provides precious little biomechanical information concerning what a surgeon will uncover when the portion of the anatomy is exposed during surgery, or the short- or long-term biomechanical effect of a surgical intervention.

[0003] There have been various attempts at recreating a portion of the anatomy to create a functional model based on MRI or CT images. Usually, the whole process follows a standard procedure, including creating anatomic geometry, cleaning anatomic geometry, setting up physical condition, running simulation, and displaying a result. Creating a properly representative geometry of the portion of the anatomy is an essential step, typically done via extracting an isosurface from an image. This aspect determines the overall error of the simulation. Due to the mathematical base of this process, to obtain a high geometry quality geometry involves the use and positioning of a number of small triangles to capture the details of the surface. This process, however, typically introduces a number of critical defects that fails the meshing process. Such defects may include, for example, a hole or gap in the surface, a silver triangle, flipped normals, intersecting/overlapping triangles, non-manifold edges, isolated body, etc. It is a highly manual and time-consuming process requiring highly skilled individuals to fix these errors. Typical processes may involve decomposing mesh sub-domains according to singularities, defining a mesh vertex distribution for each mesh sub-domain, and triangulation to produce mesh elements. And, even after all of this is complete, the model still suffers from the limitations of the individual artificial shapes used to produce it that often do not properly mimic real world aspects and environment of the portion of the anatomy it is supposed to model.

[0004] Fluid-structure interaction (FSI), which is a class of mechanics related problem with mutual dependence between fluid and structure parts, is an element of great importance in modeling anatomical parts. This is due to the fact that most anatomical parts in their native environment are in a constant interaction between fluid, such as blood, and structure, such as the blood vessel. A common method to model fluid-structure interaction is the grid base method. Grid base method has two approaches: the monolithic approach, which solves equations governing the fluid and the structure simultaneously, and the partitioned approach, which solves equations governing the fluid and the structure separately with two solvers. The first approach requires a program for each particular system, while the second approach is less accurate, and the algorithm usually faces problems in achieving robustness and stability.

[0005] In grid-based method, the method requires a pre-defined mesh. A mesh is required for each image and as the simulation moves along, a new mesh is required for a new image. In cases where the mesh deforms after each image, treating large deformation is very difficult due to mesh entanglement. Moreover, grid-based methods usually do not model large and complicated geometries and physics well.

[0006] Another method used in FSI is particle -level method, such as smooth particle hydrodynamics (SPH), material point method (MPM), moving particle semi-implicit (MPS), which are meshfree. Unlike traditional FEA (finite element analysis) commercial software that needs to build a model and then generate a grid, the SPH (smooth particle hydrodynamic) method can use points from the image to directly generate blood vessel walls, stents for arteries, and balloons for application in medicine. The points obtained from the image can be directly used as particles, which is much more convenient than generating a high-quality grid for the model. It is usually not a simple matter to obtain a high-quality grid. However, preparing a body-fitting particle-model for complex geometry is an issue hindering its wide application as a grid-based method.

[0007] There remains a need to accurately model FSI with better accuracy and less computational cost. The present invention addresses this and other related needs in the art. SUMMARY

[0008] According to frequently included embodiments, there is provided a computer operated method for optimization of a particle-based model based on image data, comprising:

(a) superimposing a mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(b) segmenting the image into a plurality of segments, each segment corresponding to a unit of the background;

(c) positioning one or more particles in one or more of the plurality of segments in an initial position;

(d) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and i. subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or ii. subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; and

(e) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero

[0009] Often according to embodiments described herein a method is provided as described herein, where the lattice structure is two-dimensional and comprises a plurality of pixels and each unit of the background corresponds to one or more pixel.

[0010] Frequently according to embodiments described herein a method is provided as described herein, wherein each of the plurality of pixels comprises a polygon and wherein the one or more particles are positioned at one or more comers of the polygon, the center of the polygon, or a combination thereof. [0011] Often according to embodiments described herein a method is provided as described herein, wherein the lattice structure is three-dimensional and comprises a plurality of voxels and each unit of the background corresponds to one or more voxel.

[0012] Frequently according to embodiments described herein a method is provided as described herein, wherein each of the plurality of voxels is a polyhedron and wherein the one or more particles are positioned at one or more comers of the polyhedron, at the center of the polyhedron, or a combination thereof.

[0013] Often according to embodiments described herein a method is provided as described herein, where adjusting the position of each particle comprises: calculating an acceleration for the particle; updating the particle to a new position using the acceleration and a time step; and modulating the new position, using one or more of a distance of the particle to the mask image, a spacing of the segments, and a normal vector of movement for the particle

[0014] Frequently according to embodiments described herein a method is provided as described herein, the method further comprising defining a critical distance.

[0015] Often according to embodiments described herein a method as described herein is provided and further comprises calculating a distance of each particle to the background in a final position and comparing the distance of each particle to the background in the final position to the critical distance.

[0016] Frequently according to embodiments described herein a method is provided as described herein, wherein a particle with the distance to the background smaller than the critical distance is classified as a solid type particle and a particle with the distance to the background larger than the critical distance is classified as a fluid type particle.

[0017] Often according to embodiments described herein a method is provided as described herein and further comprises: defining an open region on the mask image within an area circumscribed by a plurality of solid type particles; and classifying particles within the open region as fluid type particles. [0018] Frequently according to embodiments described herein a method is provided as described herein, wherein the mask image is an image of a biostructure or an anatomical portion in a native biological environment, in vitro environment, ex vivo environment or in situ environment.

[0019] Often according to embodiments described herein a method is provided as described herein, wherein the acceleration is the speed of change in particle position within a time period.

[0020] Frequently according to embodiments described herein a method is provided as described herein, wherein the updating step occurs if the acceleration is not 0.

[0021] Often according to embodiments described herein a method is provided as described herein, the method comprises repeating steps (c) through (e) for a different segment of the one or more of the plurality of segments.

[0022] Frequently according to embodiments described herein a method is provided as described herein, wherein a model is produced after the position of the one or more particles in each of the plurality of segments is adjusted.

[0023] Often according to embodiments described herein a method is provided as described herein, wherein one or more additional model is produced.

[0024] Frequently according embodiments described herein a method is provided as described herein, wherein one or more additional model is combined with the model to give a final model and an interface is provided between adjacent models, the interface connected by constraints mimicking a virtual spring force such that the final model operates as a single unit in a simulation.

[0025] Often according to embodiments described herein a method is provided as described herein, further comprising imposing a boundary condition on the classified particle

[0026] Frequently according embodiments described herein a method is provided as described herein, wherein the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[0027] Often according to embodiments described herein a method is provided as described herein, the method further comprises comprising imposing a boundary condition on each of the one or more particles in one or more of the plurality of segments before, during or after the position of the particle is adjusted.

[0028] Frequently according embodiments described herein a method is provided as described herein, wherein the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[0029] Frequently according embodiments described herein a method is provided as described herein, wherein the biostructure or an anatomical portion comprises a blood vessel, a heart or portion or structure thereof, a bone, a circulatory or lymph system or portion thereof, an organ, a limb, or another biostructure or anatomical portion of a mammalian body.

[0030] Frequently according embodiments described herein a method is provided as described herein, wherein one or more additional model is combined with the model such that the model and the one or more additional model operate as a single unit in a simulation.

[0031] Often according to embodiments described herein a method is provided as described herein, the method further comprises imposing a boundary condition on the classified particle.

[0032] Frequently according embodiments described herein a method is provided as described herein, wherein the background distance is the shortest distance between the segment and the background, and wherein the foreground distance is the shortest distance between the segment and the mask image.

[0033] Often according to embodiments described herein a method is provided as described herein, wherein the first algorithm comprises subtracting the foreground distance from the background distance, and/or wherein the second algorithm comprises subtracting the background distance from the foreground distance.

[0034] Frequently according to embodiments described herein a method is provided as described herein, wherein units closer to background have lower distance values and/or units closer to background have higher distance values.

[0035] Often according to embodiments described herein a system is provided as described herein, the system for generating a particle -based model based on image data, comprising a processor, wherein the processor is configured to: (a) superimpose a mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(b) segment the image into a plurality of segments, each segment corresponding to a unit of the background;

(c) position one or more particles in one or more of the plurality of segments in an initial position;

(d) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and

(i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or

(ii) subject the background distance and the foreground distance to an algorithm to obtain a foreground distance value and represent the distance value on the background to provide a foreground distance map; and

(e) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

[0036] Frequently according to embodiments described herein a system is provided as described herein, wherein the lattice structure is two-dimensional and comprises a plurality of pixels and each unit of the background corresponds to one or more pixel.

[0037] Often according to embodiments described herein a system is provided as described herein, wherein each of the plurality of pixels comprises a polygon and wherein the one or more particles are positioned at one or more comers of the polygon, at the center of the polygon, or a combination thereof.

[0038] Frequently according to embodiments described herein a system is provided as described herein, wherein the lattice structure is three-dimensional and comprises a plurality of voxels and each unit of the background corresponds to one or more voxel.

[0039] Often according to embodiments described herein a system is provided as described herein, wherein each of the plurality of voxels is a polyhedron and wherein the one or more particles are positioned at one or more comers of the polyhedron, at the center of the polyhedron, or a combination thereof.

[0040] Frequently according to embodiments described herein a system is provided as described herein, wherein the processor is configured to adjust the position of each particle by: calculating an acceleration for the particle; updating the particle to a new position using the acceleration and a time step; and modulating the new position, using one or more of a distance of the particle to the mask image, a spacing of the segments, and a normal vector of movement for the particle.

[0041] Often according to embodiments described herein a system is provided as described herein, wherein the system is further configured to define a critical distance.

[0042] Frequently according to embodiments described herein a system is provided as described herein, wherein the system is further configured to calculate a distance of each particle to the background in a final position and compare the distance of each particle to the background in the final position to the critical distance.

[0043] Often according to embodiments described herein a system is provided as described herein, wherein the system is further configured to classify a particle with the distance to the background smaller than the critical distance as a solid type particle and a particle with the distance to the background larger than the critical distance as a fluid type particle.

[0044] Frequently according to embodiments described herein a system is provided as described herein, wherein the system is further configured to: defining an open region on the mask image within an area circumscribed by a plurality of solid type particles; and classifying particles within the opening regions as fluid type particles.

[0045] Often according to embodiments described herein a system is provided as described herein, wherein the mask image is an image of a biostructure or an anatomical portion in a native biological environment, in vitro environment, ex vivo environment or in situ environment. [0046] Frequently according to embodiments described herein a system is provided as described herein, wherein the acceleration is the speed of change in particle position within a time period.

[0047] Often according to embodiments described herein a system is provided as described herein, wherein the updating step occurs if the acceleration is not 0.

[0048] Frequently according to embodiments described herein a system is provided as described herein, the system further comprises repeating steps (c) though (e) for a different segment of the one or more of the plurality of segments.

[0049] Often according to embodiments described herein a system is provided as described herein, wherein a model is produced after the position of the one or more particles in each of the plurality of segments is adjusted.

[0050] Frequently according to embodiments described herein a system is provided as described herein, the system includes wherein one or more additional model is produced.

[0051] Often according to embodiments described herein a system is provided as described herein, wherein the one or more additional model is combined with the model to give a final model and an interface is provided between adjacent models, the interface connected by constraints mimicking a virtual spring force such that the final model operates as a single unit in a simulation.

[0052] Frequently according to embodiments described herein a system is provided as described herein, the system is further configured to impose a boundary condition on the classified particle.

[0053] Often according to embodiments described herein a system is provided as described herein, wherein the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[0054] Frequently according to embodiments described herein a system is provided as described herein, the system is further configured to impose a boundary condition on each of the one or more particles in one or more of the plurality of segments before, during or after the position of the particle is adjusted. [0055] Often according to embodiments described herein a system is provided as described herein, wherein the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[0056] Frequently according to embodiments described herein a system is provided as described herein, wherein the biostructure or an anatomical portion comprises a blood vessel, a heart or portion or structure thereof, a bone, a circulatory or lymph system or portion thereof, an organ, a limb, or another biostructure or anatomical portion of a mammalian body.

[0057] Often according to embodiments described herein a system is provided as described herein, wherein the background distance is the shortest distance between the segment and the background, and wherein the foreground distance is the shortest distance between the segment and the mask image.

[0058] Frequently according to embodiments described herein a system is provided as described herein, wherein the first algorithm comprises subtracting the foreground distance from the background distance, and/or wherein the second algorithm comprises subtracting the background distance from the foreground distance.

[0059] Often according to embodiments described herein a system is provided as described herein, wherein units closer to background have lower distance values or units closer to background have higher distance values.

[0060] Frequently according to embodiments described herein a computer operated method for producing a model of an object comprised thin beams is provided, the method comprises: (a) obtaining a mask image of an object comprised on thin beams; (b) choosing one or more points on the beam and calculating the coordinate of the one or more points; (c) superimposing the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (d) segmenting the mask image into a plurality of segments, each segment corresponding to a unit of the background; (e) treating each one of the one or more points as a particle and positioning the one or more particles in one or more of the plurality of segments in an initial position; (f) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or (ii) subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; (g) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero; and (h) repeating steps (a) - (g) with each image of the thin beams to generate a model for the object.

[0061] Often according to embodiments described herein a method is provided as described herein, wherein the object is a stent made of thin wires and the wires are treated as thin beams.

[0062] Frequently according to embodiments described herein a method is provided as described herein, wherein the stent comprises multiple basic elements of the same size and shape, and wherein the method is applied to each of the multiple basic elements of the stent to generate a model for each of the multiple basic elements of the stent.

[0063] Often according to embodiments described herein a method is provided as described herein, the method further comprises splicing the models generated together to obtain a simulated model of the stent.

[0064] Frequently according to embodiments described herein a system for producing a model of an object comprised of thin beams is provided, the system comprises a processor, the processor is configured to: (a) obtain a mask image of an object comprised of thin beams; (b) choose one or more points on the beam and calculate the coordinate of the one or more points; (c) superimpose the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (d) segment the mask image into a plurality of segments, each segment corresponding to a unit of the background; (e) treat each one of the one or more points as a particle and position the one or more particles in one or more of the plurality of segments in an initial position; (f) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or (ii) subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; and (g) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero; and (h) repeat steps (a) - (g) with each image of the thin beams to generate a model for the object.

[0065] Often according to embodiments described herein a system is provided as described herein, the system includes the object is a stent made of thin wires and the wires are treated as thin beams.

[0066] Frequently according to embodiments described herein a system is provided as described herein, the system includes the stent comprises multiple basic elements of the same size and shape, and wherein the method is applied to each of the multiple basic elements of the stent to generate a model for each of the multiple basic elements of the stent.

[0067] Often according to embodiments described herein a system is provided as described herein, the system includes the processor is further configured to splice the models generated together to obtain a simulated model of the stent.

[0068] Frequently according to embodiments described herein a computer operated method for producing a model of an object comprised of thin walls is provided, the method comprises (a) obtaining a mask image of an object comprised of thin walls, disregarding the thickness of the walls; (b) superimposing the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (c) segmenting the mask image into a plurality of segments, each segment corresponding to a unit of the background; (d) positioning one or more particles in one or more of the plurality of segments in an initial position; (e) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or (ii) subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; and (f) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero. [0069] Often according to embodiments described herein a method is provided as described herein, wherein the object comprised of thin walls is an angioplasty balloon.

[0070] Frequently according to embodiments described herein a method is provided as described herein, wherein the object comprised of thin walls is a blood vessel.

[0071] Often according to embodiments described herein a system for producing a model of an object comprised thin beams is provided, the system comprises a processor, wherein the processor is configured to: (a) obtain a mask image of an object comprised of thin walls, disregarding the thickness of the walls; (b) superimpose the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (c) segment the mask image into a plurality of segments, each segment corresponding to a unit of the background; (d) position one or more particles in one or more of the plurality of segments in an initial position; (e) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or (ii) subject the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and represent the foreground distance value on the background to provide a foreground distance map; and (f) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

[0072] Frequently according to embodiments described herein a system is provided as described herein, the system includes the object comprised of thin walls is an angioplasty balloon.

[0073] Often according to embodiments described herein a system is provided as described herein, the system includes the object comprised of thin walls is a blood vessel.

[0074] Often according to embodiments described herein a computer operated method for producing a contact model between two bodies is provided, the method comprises (a) simulating a first body using the method as described herein, the first body having a first particle; (b) simulating a second body using the method as described herein, the second body having a second particle; and (c) simulating a contact between the first body and the second body, comprising: (i) contacting the first body and the second body such that the first particle comes into contact with the second particle; (ii) calculating a normal force acting on the first particle; (iii) calculating a time step tangential force acting on the first particle; (iv) calculating the contact force using the normal force and the tangential force; and (v) determining movement of the first body and/or the second body over the time step based on the calculated contact force.

[0075] Frequently according to embodiments described herein a method is provided as described herein, wherein the first body is a blood vessel and the second body is a stent implanted in the blood vessel.

[0076] Often according to embodiments described herein a system for producing a contact model between two bodies is provided, the system comprises a processor, wherein the processor is configured to: (a) simulate a first body using the method as described herein, the first body having a first particle; (b) simulate a second body using the method as described herein, the second body having a second particle; and (c) simulate a contact between the first body and the second body, comprising: (i) contact the first body and the second body such that the first particle comes into contact with the second particle; (ii) calculate a normal force acting on the first particle; (iii) calculate a time step tangential force acting on the first particle; (iv) calculate the contact force using the normal force and the tangential force; and (v) determine movement of the first body and/or the second body over the time step based on the calculated contact force.

[0077] Frequently according to embodiments described herein a system as described herein is provided, the system includes the first body is a blood vessel and the second body is a stent implanted in the blood vessel.

[0078] These and other embodiments, features, and advantages will become apparent to those skilled in the art when taken with reference to the following more detailed description of various exemplary embodiments of the present disclosure in conjunction with the accompanying drawings.

ABBREVIATIONS

[0079] CT: computed tomography

[0080] FEA: finite element analysis [0081] FEM: finite element method

[0082] FSE fluid structure interaction

[0083] FVM: finite volume method

[0084] MPM: material point method

[0085] MPS: moving particle semi-implicit

[0086] MRI: magnetic resonance imaging

[0087] NURBS: Non-Uniform Rational B-Splines

[0088] SPH: smooth particle hydrodynamics

BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The skilled person in the art will understand that the drawings, described below, are for illustration purposes only.

[0090] FIG. 1 depicts classical preprocessing workflow of image based numerical simulation.

[0091] FIG. 2 depicts a workflow for optimization-based particle generation using a lattice and distance map.

[0092] FIGS 3A-C depicts an example of two-dimensional particle generation and optimization.

[0093] FIG. 3D depicts placement of a mask image on a lattice, distance map generation, and placement of particle according to the example in FIG. 3A-C.

[0094] FIG. 3E is a close-up image of a comer of the mask image, which is the image at the top left comer of FIG. 3D.

[0095] FIG. 3F depicts relaxing of particles in a mask image.

[0096] FIG. 4A-C depict different methods to calculate the shortest distance from one point to another. [0097] FIG. 5A depicts an example of normal vector calculation to determine movement direction for particle i in a 2D environment.

[0098] FIG. 5B depicts 2D representation of unit cells in normal vector calculations.

[0099] FIG. 5C depicts the kernel function used in the algorithm to relax particles in a mask image.

[00100] FIG. 6A-C depicts an example of three-dimensional optimization-based particle generation.

[00101] FIGS. 7A and 7B depict exemplary structural lattices for initial particle positioning in a three-dimensional environment.

[00102] FIGS. 8A and 8B depict an example of the present embodiments in connection with a single blood vessel.

[00103] FIG. 9 depicts an example of the present embodiments in connection with an aorta and coronary tree.

[00104] FIG. 10 depicts an example of the present embodiments in connection with the mitral and aortic valves.

[00105] FIG. 11 depicts an example of the present embodiments in connection with a heart model.

[00106] FIG. 12 depicts an example of the present embodiments in connection with a left ventricle.

[00107] FIG. 13 depicts an example of the present embodiments in connection with a blood vessel system of a whole human body.

[00108] FIG. 14A and 14B depict extended applications of embodiments described herein.

[00109] FIG. 15 depicts using the present embodiments to generate a model with two types of particles, a calcified heart valve.

[00110] FIG. 16 depicts using the present embodiments to generate a model with two types of particles, a heart with an aortic valve.

[00111] FIG. 17 depicts the process steps in FIG. 16. [00112] FIG. 18 depicts a close-up view of the heart with an aortic valve in FIG. 14.

[00113] FIG. 19 depicts a close-up, cross section, top view of FIG. 14 at the heart/aortic valve connection.

[00114] FIG. 20 depicts a shell model according to Reissner-Mindlin theory in solid mechanical SPH.

[00115] FIG. 21 depicts a beam model according to Timoshenko beam theory in solid mechanical SPH.

[00116] FIG. 22 depicts a thin plate shell in Reissner-Mindlin theory.

[00117] FIG. 23 depicts an angioplasty balloon simulation using the method disclosed herein.

[00118] FIG. 24 depicts an artery simulation using the method disclosed herein.

[00119] FIG. 25 depicts a beam simulation under Timoshenko beam theory.

[00120] FIG. 26A depicts a stent in full.

[00121] FIG. 26B depicts a stent simulation using the method described herein.

[00122] FIG. 27A depicts a basis element of the stent in FIG. 26A.

[00123] FIG. 27B depicts a simulation of a basis element of the stent in FIG. 26A using the method described herein.

[00124] FIG. 28 depicts a contact model of particle simulation according to the method described herein.

[00125] FIG. 29 depicts a simulation of a blood vessel with a stent inside during blood flow using the method described herein.

DETAILED DESCRIPTION

[00126] For clarity of disclosure, and not by way of limitation, the detailed description of the invention is divided into the subsections that follow.

[00127] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as is commonly understood by one of ordinary skill in the art to which this invention belongs. All patents, applications, published applications and other publications referred to herein are incorporated by reference in their entirety. If a definition set forth in this section is contrary to or otherwise inconsistent with a definition set forth in the patents, applications, published applications and other publications that are herein incorporated by reference, the definition set forth in this section prevails over the definition that is incorporated herein by reference.

[00128] As used herein, “a” or “an” means “at least one” or “one or more.”

[00129] As used herein, the term “and/or” may mean “and,” it may mean “or,” it may mean “exclusive-or,” it may mean “one,” it may mean “some, but not all,” it may mean “neither,” and/or it may mean “both.”

[00130] As used herein, “subject” refers to a living or deceased organism. This organism may be or derived from, for example, Bacteria, Archaea, and/or Eukarya. Often a subject refers to mammal such as a human or other animal.

[00131] As used herein, “anatomy” refers to a body of a subject, including portions thereof.

[00132] As used herein “anatomical portion” refers to, without limitation, a portion of an anatomy, including whole organs, whole limbs, or portions of any such organ structure or limb.

[00133] As used herein, “biostructure” refers to, without limitation, a variety of structures within the anatomy, including structures within organs, cells, tissues, interfaces of different tissues or cells, among other things.

[00134] As used herein, “native biological environment” refers to, without limitation, the environment in which the anatomy, anatomical portion or biostructure typically exists or specifically exists in a specific subject.

[00135] As used herein, “force” refers to an external stimulus such as physical, pressure, temperature, acoustic, electromagnetic, magnetic, chemical, electric, electrochemical, gravimetric, etc.

[00136] As used herein “surface portion” refers to the portion of the image representing a surface of the anatomy, anatomical portion, or biostructure as shown in the image. A surface portion of a p-CT image may be the surface of a structure present below the surface of the image. [00137] Biomechanical simulation of human and animal anatomy, including portions thereof, is as a useful tool in the medical arena for diagnosis, prognosis and/or treatment planning. While external imaging via CT and MRI provides valuable static images of an internal aspect of the anatomy, the picture is incomplete from a therapeutic intervention standpoint since varied biomaterials have complex interactions and structural properties, and often varied formations from subject to subject. Once a physician exposes the area of the anatomy, often a different intervention is needed compared with what was thought to be required based on MRI and CT data alone. What is needed in the art is a tool that makes it possible to construct a three- dimensional model based on CT and/or MRI imaging data that is true to the original anatomy.

[00138] Areas of the anatomy that can be simulated are diverse, including circulatory system structures such as blood vessels, the heart, valves, and various components thereof. Typically, the process follows a standard procedure, including creating anatomic geometry, cleaning anatomic geometry, setting up one or more physical condition, running a simulation, and displaying a result. Creating a representative geometry of the part of interest, usually through extracting an isosurface from an image, is an essential step that determines the overall error of the simulation. At the same time, the meshing process is fraught with errors and manually tedious due to the discreet geometries involved in the anatomy. For example, to obtain a high geometry quality, a variety of known geometric shapes, such as a plurality of small triangles, are used to capture details of the surface through reverse engineering the image. However, introducing and using such geometric shapes generally introduces a number of critical defects which causes the meshing process to fail. Such defects may include, for example, a hole or gap in the surface, a sliver triangle, flipped normals, intersecting/overlapping triangles, non-manifold edges, isolated body, etc.. As such, excessive amounts of manual time must be spent cleaning/fixing the surface. A variety of tools exist that can be utilized to repair the surface of a geometry, such as Meshmixer, Meshlab, Magic, Blender, and Netfabb. Each of these tools carries at least the limitations and drawbacks noted above, among others.

[00139] Other image-based simulation methods such as finite cell method and immersed boundary method each involve specific procedures utilizing and embedded domain or cut cell methods. These concepts use small squares to represent a geometric model of interest. In an attempt to minimize error, this method applies high embedding at boundaries and imposes a high-order scheme for integration. This causes an excessive demand on hardware resources while slowing down the process and speed of convergence as a whole, even for static objects. For moving objects and anatomical structures the nrocess and performance is worse due to the requirement for dynamically releasing/reallocating hardware resources for either increasing or decreasing embedding levels intermittently at boundaries which have high variability in space.

[00140] Described herein are methods that eliminate, inter alia, the time-consuming step of surface cleaning. According to the present methods and systems, a user can import an image of whole or segmented anatomy into the system to generate a body-fit representative domain that is composed of particles.

[00141] FIG. 1 presents a typical preprocessing workflow of image-based simulation. According to this workflow imaging data such as MRI or CT image data is received. The image is processed and aspects of the image with complex geometries are segmented and meshed with a set of polygon faces. Using reverse engineering and Non-Uniform Rational B-Splines (NURBS), the mesh is refined to include thousands to millions of small polygon surfaces in an attempt to create a water-tight analysis model and also to mimic curved surfaces.

[00142] FIG. 2 presents a preprocessing workflow of image-based simulation according to the present systems and methods. According to this workflow imaging data such as MRI or CT image data is received. The image is processed and aspects of the image with complex geometries are segmented. Particles are placed on the segmented images and the position of these particles is optimized to match the shape of the real image. Optimizing these particles’ position takes the place of having to conduct meshing and provide a more accurate model of the original image.

[00143] As depicted in FIG. 3A, according to the presently described embodiments, an image is obtained (e.g., from MRI or CT imaging), then segmented and a mask 2D image is placed in a grid composed of a plurality of units, in this case pixels, on a 2D image (referred to herein as a lattice structure), each segment corresponds to a unit, in this case a pixel. This lattice structure can be of any geometric shape, wherein each pixel can be of any geometric shape, including square, triangle, diamond, or other polygon lattice structure. Most frequently, the lattice structure corresponds to a specific sector of the grid in which the mask 2D image is placed. The lattice structures are therefore positioned all about the mask image. In FIG. 3B, particles are then positioned in/on each of the lattice structures. Placement of the particles is according to a predefined particle placement location in/on the lattice structure. For example, a particle may be placed at a specific comer of the polygonal lattice structure at a specific location within the polygonal lattice structure, in the middle of the polygonal lattice structure, or a combination of the above. Overall, according to the present embodiments, the initial particle position can be arranged in multiple ways with the help of pre-defined or known lattice structure. In one basic embodiment, one particle is placed at each comer of the lattice structure, and optionally another particle in the center face of the 2D polygonal lattice structure. This means that in the example of a square or 4-sided 2D lattice structure, between 4 to 5 particles are often placed in/on each 2D lattice structure according to the present embodiments, with 4 particles at each comer of the square and optionally another 1 particle at the center of the square. In the example of a triangle lattice structure, between 3 to 4 particles are often placed in/on each 2D lattice structure according to the present embodiments, with 3 particles at each comer of the triangle and optionally another 1 particle at the center of the triangle. Each 2D lattice structure will carry other requirements that will vary based on the number of comers and sides in the lattice structure such that the number of particles may vary according to known or calculable formulae. The number of particles therefore corresponds to the number of lattice structures and the number of particles within/on each lattice structure.

[00144] In FIG. 3C, once the particles are placed, their positions are optimized based on a distance map. Optimization is a process wherein each particle is moved to a different location such that in their final position, the particles form a better model that resembles the image, which is an anatomical structure, and simulates the anatomical structure as it exists in its native environment. Optimization is conducted by determining the vector of movement and distance of movement for each particle, and the position where each particle should stop once movement is completed. Once all particles have completed their movement and arrived at their final locations, optimization is complete.

[00145] FIG. 3D depicts the detailed steps in using a mask image on a 2D lattice structure on which the mask image is imposed to generate a distance map from which particles are optimized. At the top left comer of FIG. 3D is a mask image, in this case resembling a circle, is placed on a lattice structure, in this case a grid with each cell being square, each side of the square is a spacing 103, and each square considered a segment or in this case a pixel of the mask image. The lattice is called the background 102 while the mask image is called the foreground 101. Background 102 is the static frame that serves as the reference frame, where other images can be compared with to analyze for movement and/or changes in subsequent images. Foreground 101 is the image of analysis interest, which is compared with the background 102 for analysis of movement, appearance, or disappearance of objects. [00146] The distance map, which is depicted in the upper, middle of FIG. 3D, is generated in step 2. From the mask image being placed on the lattice structure, the distance of each pixel to the background 102 is calculated and called background 102 distance. The background 102 is used as a reference point, therefore the distance to background 102 of a given pixel on the lattice not superimposed by the mask image is 0 pixel. FIG. 3E is a close-up image of a comer of the mask image being placed on the lattice structure, with a pixel not superimposed by the mask image 110 having a distance of 0 pixel, while a pixel superimposed by the mask image immediately adjacent to a pixel not superimposed by the mask image 109 having a distance of 1 pixel. For each pixel within the mask image, the distance from the pixel to the background 102 (the background distance) is calculated as the shortest Euclidean distance and given value Ii, and the distance from the pixel to the foreground 101 (the foreground distance) is calculated as the shortest Euclidean distance and given value L. Distance is calculated as Distance = Ii - h. Optionally, Distance is calculated as Distance = h - Ii. Apart from Euclidean method, other methods may be utilized to calculate Distance, such as Taxicab geometry, Chebyshev distance, Manhattan method, or another method. FIG. 4A-C depicts and explains these methods of calculation.

[00147] In the process of producing the distance map, black/white colors may be used to visualize the distance. If Distance = Ii — I2, then Distance < 0 and the inner of the distance map can be designated as positive while the outer is designative as negative. In this case, units closer to background 102 have lower distance values. If Distance = I2 - Ii, then Distance > 0 and the inner of the distance map can be designated as negative while the outer is designative as positive. In this case, units closer to the background 102 have higher distance values.

[00148] Returning to FIG. 3D, in step 2, for each pixel, a distinct Distance value is obtained. Then, each value of Distance is plotted into the lattice. In this example, the inner of the mask image is considered to be negative and the outer of the image is considered to be positive on the distance scale, which corresponds to Distance = L - Ii as discussed above. For pixels closer to the middle of the masked image, Distance is negative while Distance is positive. The scale 104, which is depicted at the upper right hand comer of FIG. 3D, shows the distance as represented by the color from white to black. White color represents negative Distance while black color represents positive Distance. Therefore, the distance map of the middle of the mask image as represented on the lattice is white while the outer edge of the mask image as represented on the lattice is black.

[00149] In a different event, step 1 is carried out, where the mask image after being imposed onto the lattice structure shall have particles placed on the various pixels within the mask image. The mask region shall be filled with particles such that all pixels within the mask imaged is filled. The mask image filled with particle is shown in the lower left comer of FIG. 3D. Placement of particles in this case can be at each comer of each pixel and optionally another particle at the center of the pixel. As an exemplary embodiment, in FIG. 3D, placement of particles in this case is by placing them at the center of the pixel.

[00150] With the mask image filled with particles, particles are now relaxed into their position. Relaxing means using the distance map generated in step 2 to move the particles in the particle -filled mask image generated in step 2, such that the particles reach their destinations, where the particles have achieved body-fitted configuration. Steps 3 and 4 represent this process.

[00151] FIG. 3F depicts the relaxing of the particles in the particle-filled mask image using the distance map generated in step 2. In FIG. 3F, the black dots represent the initial position of the particles after the particles have been placed into the mask image. The squares represent the positions where the particles would be after relaxing. The image on the left of FIG. 3F is the close-up look of the image on the right of FIG. 3F. The particles and the squares can be seen in this close-up image.

[00152] The position of each of the square is calculated as relative to the lattice structure. In other words, the position of each of the square shall be defined by its position on the lattice stmcture. Determining the position of the squares is by calculation, the position of the square is the final destination where the particle shall move to. From the initial position, i.e., the position where the particle is placed when the mask image is first superimposed onto the background 102, the particles shall be moved according to the particle acceleration. In order to determine whether a particle should stop, i.e., whether it has reached the square, each particle’s acceleration has reached 0.

[00153] For each particle, the particle acceleration cn shall be defined as:

[00155] Wherein: cn is particle acceleration

[00156] And, Fj is the volume of particle, calculated as

= — with r as mass of particle

Pi i and pt as density of particle i [00157] And, Vj i s the volume of particle, calculated as with mj as mass of particle

j and Pj as density of particle j, particle j being another particle within smoothing length, designated as h. Referring to FIG. 31, demonstrating the kernel function, particle j is within a domain that is defined by a radius (or within a sphere of radius h in a three-dimensional model).

[00158] And, p₀ is an empirical constant, named as the constant background pressure.

[00159] And, is the gradient along vector n of the kernel function

calculated as For clarity, FIG. 5C depicts the kernel function

W (r), with j = r, - n and h is the smoothing length.

[00160] To determine where the particle should move to, the following steps are carried out:

[00161] Step 1, calculating particle acceleration:

[00162] If a is not 0, the particle’s position is updated in step 2.

[00163] Step 2, update position of particle i

[00164] Wherein, r"is the initial position of particle /, At is timestep length, and up is the acceleration of particle i at the initial position.

[00165] Step 3, check to see if particle i is at the correct position using the equation: particle is at the correct position.

[00166] Wherein, Ax is spacing 103 of image (downsampled or upsampled)

[00167] 0, is the distance to interface at cell i

[00168] is the normal vector at position i.

[00169] FIGS. 5 A and 5B depicts the process of calculating vector N_t, where a close-up depiction of cell C (the center, where particle i is placed) relative to cell j (an adjacent cell) is shown.

[00170]

[00171] Wherein, N_C]=

, with s being a small value to avoid a division by 0 if 0_;-

reaches 0.

[00173] Wherein, w_Cj is the distance from cell C to cell j,

[00174] And, 0j is the distance to interface at position i,

[00175] And 0_Cj is the distance value stored at cell j.

[00176] In FIG. 5 A, close-up depiction of cell C to cell j, where normal vector for particle

1 can be calculated. In FIG. 5B, a 2D representation of unit cells in normal vector calculations is depicted, with left and right cells are used for gradient in x direction, and top and bottom cells are used for gradient in y direction.

[00180] In FIG. 5B, the center C of cell C is defined as a having coordinate C, C; representing the value on the x and y axis in a 2D model. Here, Ar is the spacing 103 along the x axis, with the left and right cells used for x direction, while Ay is the spacing 103 along the y axis, with the top and bottom cells used for y direction.

[00181] From there, N_C] can be calculated as and N_t is calculated as

=

[00182] For a 3D image, the method according to embodiments herein may be used to create a model. Step 1 and Step 2 above may be used to calculate the particle acceleration and updated position for particle i. In step 3, verifying particle position, the same method can be used but with the normal vector N_t calculated for a 3D model.

[00183] In the 3D case, the gradient is calculated as:

[00188] In a 3D unit cells, for normal vector calculations, left and right cells are used for gradient in x direction, top and bottom cells are used for gradient in y direction, and Az is the spacing 103 along the z axis, with the front and back cells used for z direction, “c” refers to the center of the cell while “z” refers to the arbitrary location in the image.

[00189] From there, N_C] can be calculated and N_t is calculated as

=

[00190] Once step 3 is completed, the particle moves according to vector N_t and is now at an updated position. Calculation will repeat at step 1, until a = 0. Once cu = 0, the particle has achieved a body-fitted configuration and the relaxing process is completed. These steps are performed for each particle in the mask image until all particles have achieved a body-fitted configuration.

[00191] Once the particles are relaxed, the optimization process is complete. The particles may then be categorized into solid type 105 or fluid type 106 to better define the structure’s outer limit. In FIG. 3D, step 5 depicts this categorization. A distance, D critical (Dent) may be defined. The critical distance could also be referred to as a thick layer that grows at zero-distance interface toward internal domain. After relaxing, for each particle, the distance between the particle (on the foreground 101 or the mask image) and the background 102 (lattice structure) is calculated. If such distance is smaller than Dent, then the particle is classified as a solid type 105 particle. If such distance is larger than Dcrit, then the particle is classified as a fluid type 106 particle.

[00192] To obtain better particle distribution, particle collision offset method can be applied to solid type particles, while particle collision shift method is applied to fluid type particles. The distance between each particle will be almost the same, which will lead to more accurate simulation results, especially for the total Lagrangian method. A high order kernel approximation is applied to the solid type particle on the boundary, which will lead to a more accurate normal vector.

[00193] The method may be applied to a 3D image with a lattice structure being a 3D lattice structure, where each unit is a 3D shape. Each unit is considered a voxel and may have the shape of a cube, a pyramid, a cuboid, diamond, or other polyhedron lattice structure.

[00194] On a 3D mask image, areas where material may pass through can be defined as open regions. Particles located at positions that are at the edge of a 3D mask image where other materials may pass through, either in or out, are also classified as fluid type particles. In step 5 of FIG. 3D, an inlet 107 and outlet 108 may be seen, for example, at the left and right of the mask image. This mimic various anatomy structures, such as an artery. In an artery model, particles simulating the wall of the artery are solid type, particles simulating the inner volume of the artery are fluid type, particles at the entrance or exit of the artery are also fluid type. This classification allows for imposing boundary conditions. In some cases, boundary conditions may be used to create models of different anatomy structures and/or biological implant connected together.

[00195] As depicted in FIG. 6A-C, according to the presently described embodiments, an image is obtained (e.g., from MRI or CT imaging), optionally segmented and a mask 3D image is placed in a grid composed of a plurality of voxels (referred to herein as a collection of lattice structures). This lattice structures (or individual - lattice structure) can be of any 3D geometric shape, including cube, cuboid, pyramid, diamond, or other polyhedron lattice structure. Most frequently, the lattice structure corresponds to a specific sector of the grid in which the mask 3D image is placed. The lattice structures are therefore positioned all about the mask image. One or more different 3D geometric shapes may be used in a single model, in a manner suitable to the production of the most accurate model. Particles are then positioned in/on each of the lattice structures. Placement of the particles is according to a predefined particle placement location in/on the lattice structure. For example, a particle may be placed at a specific comer of the polyhedron lattice structure or at a specific location within the polyhedron lattice structure. Overall, according to the present embodiments, the initial particle position can be arranged in multiple ways with the help of pre -defined or known lattice structure. In one basic embodiment, one particle is placed at each comer of the lattice stmcture, and optionally another particle in the center of each face of the 3D polyhedron lattice structure (FIG. 7B). In another basic embodiment, one particle is placed at each comer of the lattice structure, and optionally another particle in the center of the 3D polyhedron lattice structure (FIG. 7A). In another basic embodiment, one particle is placed at each comer of the lattice structure, and optionally another particle in the center of the 3D polyhedron lattice stmcture, and optionally another particle in the center of each face of the 3D polyhedron lattice stmcture. This means that in the example of a cube or cuboid polyhedron lattice stmcture, between 8 to 14 or 15 particles are often placed in/on each 3D polyhedron lattice stmcture according to the present embodiments. In the example of a 3-sided pyramid lattice stmcture, between 4 to 7 or 8 particles are often placed in/on each 3D polyhedron lattice stmcture according to the present embodiments. In the example of a 4-sided pyramid lattice stmcture, between 5 to 9 or 10 particles are often placed in/on each 3D polyhedron lattice stmcture according to the present embodiments. Each 3D polyhedron lattice stmcture will carry other requirements that will vary based on the number of comers and faces in the lattice stmcture such that the number of particles may vary according to known or calculable formulae. The number of particles therefore corresponds to the number of lattice structures and the number of particles within/on each lattice stmcture.

[00196] FIGS. 6A-C depict the same process as in FIGS. 3A-C, but in a 3D environment. As depicted in FIG. 6C, after the particles are initialized in FIG. 6B, the positions of the particles are optimized to the geometry of the image. This means that the position of one or more of the particles is relaxed/adjusted to fit the geometry of the image. So, the position of one or more of the particles within the lattice stmcture is thereby altered/relaxed to move toward a specific part of the geometry of the image so that, within the lattice stmcture framework where the particle resides, the particle is relaxed as much as possible (or in a predefined manner) relative to (i.e., moved toward) the closest aspect of the geometry of the image. This process will involve varied movements of each particle, even including particles within a single lattice stmcture. For example, some particles will be relaxed/adjusted to fit the geometry of the image and thereby be prompted to move a distance that is different than other particles for the same image, even in close proximity to the specific geometry. For another example, some particles will be relaxed/adjusted to fit the geometry of the image and thereby be prompted to move in a direction that is different than other particles for the same image, even in close proximity to the specific geometry. For yet another example, some particles will be relaxed/adjusted to fit the geometry of the image and thereby be prompted to move a distance and direction that is different than other particles for the same image, even in close proximity to the specific geometry. An exemplary difference in particle position/movement during particle optimization is depicted in FIGS. 6B to FIG. 6C, which position can be viewed relative to particle positioning during particle initialization. The particles are relaxed to better fit the geometry of the image without the use of a mesh.

[00197] Since the present systems are adapted for use in biological systems or to simulate portions of the anatomy in a biological system, the parameters guiding optimization, or the movement of particles in FSI simulation, are important. Such parameters account for tissue type and composition, tissue elasticity, fluid flows on, in, through or around the tissue and related pressures, tissue structures and connections, and other parameters. These parameters are accounted in the mathematical function utilized for optimization. Overall, the result provides for placement of particles relative to the selected domain (e.g., boundary) in a manner that behaves in a manner identical, similar or correlative with the tissue it is simulating. This is done in the absence of meshing and without the need for the use of placement of a large amount of geometric shapes (e.g., triangles) in a highly manual effort to recreate the tissue. In other words, the resulting particle model behaves in an environment (e.g., in a biological system) in a manner that mimics or predicts how the corresponding real-world tissue would behave, with extremely small spatial tolerances for variability. This is a largely or entirely automated process. Prior methods take longer, involve a much greater use of human and digital resources, and in the end do not produce models with the accuracy of the present methods and systems.

[00198] The systems and procedures described herein are provided to prepare particlebased models for use in simulating real-world applications across a variety of fields. Most frequently the field contemplated herein is the medical field and the particle-based models are provided to simulate the anatomy, a portion of the anatomy, an organ, a portion of an organ, a biological system. To best simulate fluid structure interaction, particle properties need to be assigned. Such properties may include density, mass, volume, acceleration, elasticity, velocity, force, pressure, Young Modulus, shear modulus, viscosity, among other properties. Assignment of particle properties is necessary for particle level simulation by solving mass/momentum/energy conservation equations.

[00199] FIGS. 8A-B and 9-13 present particle models of a variety of portions of the anatomy. For example, FIGS. 8A-B present an example of a particle model created according to the present methods and systems for a single blood vessel. FIG. 8A and 8B provide a mask image and post-particle placement, respectively. FIG. 9 presents an example of a particle model created according to the present methods and systems for the aorta and coronary tree. FIG. 10 presents an example of a particle model created according to the present methods and systems for the mitral valve and aortic valve. FIG. 11 presents an example of a particle model created according to the present methods and systems for a human heart. FIG. 12 presents an example of a particle model created according to the present methods and systems for a left ventricle. FIG. 13 presents an example of a particle model created according to the present methods and systems for the blood vessel system of whole human body.

[00200] While the present systems and methods are particularly suitable for creating accurate models for anatomical structures, the utility is not so limited. For example, particle models according to the present systems and methods can utilize porous structure images obtained using microtomography (p-CT) to prepare corresponding models of those porous structures. These structures may be biostructures or other structures. FIG. 14A-B depicts one such example, where a porous structure is imaged using microtomography (p-CT). A particle model for the porous structure is then prepared using the systems and methods described herein.

[00201] FIG. 15 depicts an exemplary embodiment where particle placement and classification are used to model a heart with a calcified valve 111. Mask image of each of the valve and of a calcium structure having similar image as the valve are provided. The two mask images are combined to give the mask image of a calcified valve 111. The method as described herein is used to produce a 3D model of the calcified valve 111. Classification is used to classify the particles on the calcified valve 111 as solid type. At the same time, when the heart model with the calcified valve 111 at the top is also generated by this method, particle classification will allow the identification of the boundary between the calcified valve 111 and the soft tissue of the heart 112, which is the interface. In simulation of a beating heart, this model allows for imposing a virtual spring-like constrain between paired particles at the interface.

[00202] Virtual spring is a mathematical model simulating behavior of physical springs. Classic Hooke’s law on spring force dictates: F = -k Ax, wherein F is the force, k is a constant that is the spring coefficient, and Ax is the distance to inert position, Ax = x_c - Xi, with x_c being the current position and Xi being the inert position.

[00203] In image modeling, the distance between paired particles is x_c. Subtracting inert distance value (x) from x_c gives Ax. Spring coefficient is large if the spring is stiff and small if the spring is flexible. This value can be imposed to mimic the spring force in physical condition, but it is to constrain the movement of paired particles. Depending on the nature of the tissue being modeled and the condition in vivo of the tissue, spring force can correlate linearly or nonlinearly to tissue material properties. The spring force can correlate in a straight line with a tissue material property, such as elasticity, or it could correlate in a non-straight line. Time or distance can serve as a constant in the linear or nonlinear correlation. The spring force can also correlate linearly and nonlinearly with distance between the paired particles and/or time.

[00204] For an example, with two paired particles, the spring force can be calculated using Hooke’s law:

[00206] Wherein, F is the spring force vector, k is material property equivalent to the spring coefficient, L is the distance vector between the two particles, and Lo is equilibrium distance. The formulae of calculating spring force could be in other form of mathematical function where polynomial, algebraic, power, exponential, trigonometric function, etc., could be involved.

[00207] Adding a virtual spring between paired particles at the interface allows movement of two different models to be in sync, such that modeling of the overall part or organ best mimics the in vivo appearance and/or movement of parts or organs.

[00208] FIG. 16 depicts another example of an application of this method and system. In this case, the heart and the aortic valve are modeled using separate mask images. Upon completion of relaxing of the particles in the heart model, particles on the outside wall of the heart model will be classified as solid type particles while particles inside the heart model are classified as fluid type. The same modeling is performed for a mask image of the aortic valve within the heart, with particles forming the valve being classified as solid type. When the aortic valve model is integrated into the heart model, particles within the heart model were previously classified as fluid type but are now in the mask region corresponding to the aortic valve are now classified as solid type. In FIG. 16, the mask image of aortic valve can be seen separated from the mask image of the heart before being integrated into the mask image of the heart. FIG. 17 describes this process in a workflow diagram.

[00209] This classification and re-classification allow the valve particles 114 and the heart particles to be distinguished. FIG. 18 is a close-up view of the finished model generated in this example. Valve particles 114 are distinguishable from the wall particles 115 of the heart . FIG. 19 is the cross section, top view of the same model, with the aortic valve inside the heart model, the particles representing each of them have been optimized and relaxed into their positions. To better simulate the movement of the heart/valve structure in a biological environment, a virtual spring may be placed at a location 113 between valve particles 114 and heart particles, such that when one moves in a simulation, then other moves as well.

[00210] Unlike traditional FEA (finite element analysis) commercial software that needs to build a model and then generate a grid, the method described herein can use points from the image to directly generate blood vessel walls, stents for arteries, and balloons for use in angioplasty. The points obtained from the image can be directly used as particles, which is much more convenient than generating a high-quality grid for the model, which is usually not a simple matter to obtain a high-quality grid. The method described herein is thus more user friendly, in particular in clinical settings and medical environment.

[00211] Simulation of objects with thin walls can be achieved using the method described herein with a single layer of SPH particles. In classic solid mechanicals SPH, a solid body usually has a thickness and a width. To simulate a solid body, there should be at least four (4) layers of particles along the thickness or width direction of the solid body for simulation. To achieve accurate simulation results, the number of the particles along the two directions are at least 10. Figure 20 illustrates a particle model of a shell-like structure, with four layers of particles along the thickness of the shell. Figure 21 illustrates a particle model of a beam, with the thickness and width direction both have more than four layers of particles.

[00212] For three-dimensional shell-like structures undergoing large deformation, the Lagrangian SPH method has been used to simulate such shell structures. Under the Reissner- Mindlin theory, the stress along the thickness of a shell model is the same. A shell model under this theory can be seen in Figure 22. Applying the Reissner-Mindlin theory, a shell-like structure can be simulated using only one layer of particles. Thin wall, shell-like objects, such as arteries and balloon used in angioplasty, can be modeled using one layer of particles. The method described herein, with one layer of particles, can simulate angioplasty balloons and arteries. Figure 23 illustrates an angioplasty balloon model and Figure 24 illustrates an artery model generated using the method described herein applied to one layer of particles under the Reissner- Mindlin theory.

[00213] Under the Timonshenko beam theory, the distribution of stress and strain along the thickness and width of a beam can be ignored. With this theory, a beam in a particle model can be represented by a series of particles. Figure 25 illustrates a series of particles simulating a beam under the Timonshenko beam theory.

[00214] Simulating objects of beam-like structure can be achieved using the method described herein under the Timonshenko beam theory. An example is simulating a stent for blood vessel. A stent 300 is illustrated in Figure 26A, which comprises constraints, hinges, and fixed links and is generally tubular with a cross section along the width of the stent 300 being a circle, which can be simulated as beams using the method described herein (SPH).

[00215] For different objects made of generally thin beams, the Timonshenko beam theory can be applied for each component to simulate the thin beams according to the method described herein. Stents are examples of objects made of generally thin beams, i.e. the thin wires of the stents. An example for an object simulated by the method described herein, wherein the object’s components, generally thin beams, are treated under the Timonshenko beam theory. Note that the following example is only an illustration, and other equations may be needed to ascertain the coordinates of various points on an object. However, application of the method described herein can be carried out once the coordinates are determined.

[00216] Figure 27A illustrates one basic element 301 of the stent 300 in Figure 26A, which is the enlarged imaged of the part in the circle in Figure 26A. The first step in simulating the stent 300 is simulating the basic element 301. On a three-dimensional plane consisting of axes x, y, and z, each point on the basic element 301 has a coordinate of (x, y, z), with: x = A * sin(u) y = A * cos (a) z = B * sin (6a)

[00217] With A being the length of the basic element 301, B being the radius of the stent 300, and a being number between 0 and 2K, since the stent 300 is tubular and the cross section of the stent 300 is a circle. Applying the method described herein, treating each point as a particle, a model simulating the basic element 301 of the stent 300 is achieved, which is illustrated in Figure 27B.

[00218] Once each and every basic element 301 of the stent 300 has been simulated, the models can be splice together to form a model of a complete stent 300. Due to the nature of the method described herein, which is SPH in nature, neighbor particles in the neighbor domain will make the connection automatically, enabling easy spicing. In SPH, each particle has a neighborhood region, calculating as an area with a radius of at least three initial particle distance (3 A x). The variable of a particle can be calculated in the summation way of their neighbor particles. This relationship between particles can be seen as an automatic connection, which enables easy splicing. A simulated model of a stent 300 generated from the method described herein is illustrated in Figure 26B.

[00219] When there are more than one simulated model and the simulated models come into contact with each other, a contact force can be obtained using the method illustrated in Figure 28. On the left of Figure 28 is a collision between two (2) bodies, body A 201 and body B 202, both bodies being simulated by the method described herein. On the right is the enlarged image of the square marked on the left of Figure 28. Body A 201 as simulated comprises of particles coming into contact with body B 202 as simulated also comprises of particles. At the contact point, particle a 203a of body A 201 comes into contact with particle b 203b on body B 202. The force acting on particle a 203a of body A 201 due to the interaction with the particle b 203b of body B 202 can be resolved into normal and tangential component. The normal force (F ¹) on particle a 203a due to the interaction with the particles b of body B 202 is computed as:

[00220] Here, the overlap 5“_c = Ax — d_a. where d_a is the normal distance between body A 201 and body B 202, Ax is the initial particle distance between particle a 203a and particle b. k_r is the normal spring stiffness coefficient, and n_a ^c is the normal direction of body A 201.

[00221] The tangential force is history dependent, as below.

[00222] With t"⁺¹ being the tangential direction, kf being the tangential spring stiffness coefficient, A/„ ¹ is a tangential spring in each time step,

¹ is the relative velocity between particle a 203a of body A 201 and particle b 203b of body B 202, and At is the time step. The contact force can be obtained with the normal force and the tangential force as described above. The contact friction force is proportional to the tangential displacement and depends on the material involved. For each particle involved in a contact event, the normal force and tangential force will be imposed together. Using this contact force, models simulating contact between simulated models can be obtained. For example, a blood vessel, a stent, and blood flow in the vessel can be simulated into models. Contact between these models can also be simulated as above to give a time dependent shape and location model, thereby simulating the behavior of a stent 300 implanted in a blood vessel with blood flowing through the blood vessel.

[00223] Fluid-solid coupling between blood flow and stent can be done directly using the method disclosed herein. Traditionally, simulation of liquid flow, such as blood flow in a blood vessel uses the Finite Volume Method (FVM), while simulation of a solid structure’s movement uses the Finite Element Method (FEM). To correctly simulate a stent’s movement in a blood vessel with blood flow in the blood vessel, an exchange of data between the two methods, FVM and FEM, is needed. In particular, data generated from the FVM simulating blood flow is supplied to the FEM simulating stent movement, such that accurate stent movement can be simulated, and vice versa.

[00224] FIG. 29 illustrates a simulation of a blood vessel 401 with a stent 300 implanted inside and their movement and interaction in the presence of blood flow 404 in the blood vessel 401. A model of blood vessel, stent and blood flow can be simulated by the method disclosed herein using the pressure exerted by the blood flow, stent, and blood vessel on each other. In Figure 29, the simulation shows blood enters blood vessel inlet 402 in the direction of blood flow and flows towards the stent 300, then exits the blood vessel 401 at blood vessel outlet 403. Since the simulations for blood movement, stent 300, and blood vessel 401 are by the same method, there is no need to exchange data between different methods. This reduces computational time.

[00225] It is observed that the models produced using the herein described systems and methods are often outputted by a computing device, e.g., in form of a file, on a screen and/or via a printing device. The output being an image created by particles organized in a manner that closely depicts and simulates the behavior of an anatomical structure in its environment. The present systems and methods require only information embodying or about the MRI or CT (or other suitable image data) image as input. In addition, user input regarding particle placement, lattice structure or particle initialization, and/or parameters affecting the distance map and/or specific regions of the image and model as it is being built may be provided. In simulation concerning multiple models and their interactions with each other, such as illustrated in Figure 29, additional inputs by users are contemplated. Such inputs include, but are not limited to, blood flow velocity, blood viscosity, and/or other parameters affecting contact models between two bodies. [00226] Further, the present systems and methods are conducted using a computing device, optionally including one or more processors. Further, the computing device may comprise memory, e.g., transitory memory such as RAM and/or non-transitory memory in the form of a hard disk or flash memory. The computing device may be local or virtual through the use of cloud computing resources. In addition, often an output device such as a screen, display or printer may be operably connected to the computing device. The computing device also often includes an input device such as a keyboard, a mouse and/or a touch sensitive screen. Further, the computing device is often adapted for communication, such as through the use of any known or readily available means of wired, wireless, or cloud-based communication known in the art, including but not limited to a LAN connection, a WLAN connection, a Bluetooth connection, a WiFi connection, a thunderbolt connection, a USB connection, among many others.

[00227] In a first embodiment, a computer operated method for optimization of a particlebased model based on image data is provided, the method comprising: (a) superimposing a mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (b) segmenting the image into a plurality of segments, each segment corresponding to a unit of the background; (c) positioning one or more particles in one or more of the plurality of segments in an initial position; (d) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or (ii) subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; and (e) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

[00228] In a second embodiment, the first embodiment includes a two-dimensional lattice structure comprising a plurality of pixels and each unit of the background corresponds to one or more pixel.

[00229] In a third embodiment, the first or second embodiment includes a two- dimensional lattice structure comprising a plurality of pixels, each of the plurality of pixels comprises a polygon, and the one or more particles are positioned at one or more comers of the polygon, the center of the polygon, or a combination thereof.

[00230] In a fourth embodiment, the first through third embodiment includes a three- dimensional lattice structure comprising a plurality of voxels and each unit of the background corresponds to one or more voxel.

[00231] In a fifth embodiment, the first through fourth embodiment includes a three- dimensional lattice structure comprising a plurality of voxels, each unit of the background corresponds to one or more voxel, each of the plurality of voxels is a polyhedron, and the one or more particles are positioned at one or more comers of the polyhedron, at the center of the polyhedron, or a combination thereof.

[00232] In a sixth embodiment, each of the first to fifth embodiments includes adjusting the position of each particle comprising: calculating an acceleration for the particle; updating the particle to a new position using the acceleration and a time step; and modulating the new position, using one or more of a distance of the particle to the mask image, a spacing of the segments, and a normal vector of movement for the particle.

[00233] In a seventh embodiment, each of the first to sixth embodiments comprises defining a critical distance.

[00234] In an eighth embodiment, the first through seventh embodiments comprises calculating a distance of each particle to the background in a final position and comparing the distance of each particle to the background in the final position to the critical distance.

[00235] In a ninth embodiment, the first through eighth embodiment includes classifying a particle with the distance to the background smaller than the critical distance as a solid type particle and a particle with the distance to the background larger than the critical distance as a fluid type particle.

[00236] In a tenth embodiment, the first through ninth embodiment comprises defining an open region on the mask image within an area circumscribed by a plurality of solid type particles; and classifying particles within the open region as fluid type particles.

[00237] In an eleventh embodiment, the first through tenth embodiment includes a mask image of a biostructure or an anatomical portion in a native biological environment, in vitro environment, ex vivo environment or in situ environment. [00238] In a twelfth embodiment, the first to sixth embodiment includes the acceleration being the speed of change in particle position within a time period.

[00239] In a thirteenth embodiment, the first to sixth embodiment includes conducting the updating step if the acceleration is not 0.

[00240] In a fourteenth embodiment, the first through thirteenth embodiment comprises repeating steps (c) through (e) for a different segment of the one or more of the plurality of segments.

[00241] In a fifteenth embodiment, the first through fourteenth embodiment includes producing a model after the position of the one or more particles in each of the plurality of segments is adjusted.

[00242] In a sixteenth embodiment, each of the first to fifteenth embodiments includes producing one or more additional model.

[00243] In seventeenth embodiment, each of the eleventh to fifteenth embodiments includes producing one or more additional model, the one or more additional model is combined with the model to give a final model and an interface is provided between adjacent models, the interface connected by constraints mimicking a virtual spring force such that the final model operates as a single unit in a simulation.

[00244] In an eighteenth embodiment, the first through seventeenth embodiment comprises imposing a boundary condition on the classified particle.

[00245] In a nineteenth embodiment, the first through eighteenth embodiment includes imposing a boundary condition on the classified particle, the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[00246] In a twentieth embodiment, the first through seventeenth embodiment comprises imposing a boundary condition on each of the one or more particles in one or more of the plurality of segments before, during or after the position of the particle is adjusted.

[00247] In the twenty first embodiment, the first through twentieth embodiment includes imposing a boundary condition on the classified particle, wherein the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image. [00248] In the twenty second embodiment, the first through eleventh embodiment includes the biostructure or an anatomical portion comprising a blood vessel, a heart or portion or structure thereof, a bone, a circulatory or lymph system or portion thereof, an organ, a limb, or another biostructure or anatomical portion of a mammalian body.

[00249] In the twenty third embodiment, the first through twenty second embodiment includes a background distance, the background distance is the shortest distance between the segment and the background, and a foreground distance, the foreground distance is the shortest distance between the segment and the mask image.

[00250] In the twenty fourth embodiment, the first through twenty third embodiment includes the first algorithm comprising subtracting the foreground distance from the background distance, and/or the second algorithm comprising subtracting the background distance from the foreground distance.

[00251] In the twenty fifth embodiment, the first through twenty fourth embodiment includes units closer to background have lower distance values and/or units closer to background have higher distance values.

[00252] In the twenty sixth embodiment, a system for generating a particle-based model based on image data, comprising a processor is provided, wherein the processor is configured to: (a) superimpose a mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (b) segment the image into a plurality of segments, each segment corresponding to a unit of the background; (c) position one or more particles in one or more of the plurality of segments in an initial position; (d) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or (ii) subject the background distance and the foreground distance to an algorithm to obtain a foreground distance value and represent the distance value on the background to provide a foreground distance map ; and (e) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero. [00253] In the twenty seventh embodiment, the twenty sixth embodiment includes a two- dimensional lattice structure, and the two-dimensional lattice structure comprises a plurality of pixels and each unit of the background corresponds to one or more pixel.

[00254] In the twenty eighth embodiment, each of the twenty sixth to twenty seventh embodiment includes each of the plurality of pixels comprises a polygon and wherein the one or more particles are positioned at one or more comers of the polygon, at the center of the polygon, or a combination thereof.

[00255] In the twenty ninth embodiment, the twenty sixth embodiment comprises a lattice structure, the lattice structure is three-dimensional and comprises a plurality of voxels and each unit of the background corresponds to one or more voxel.

[00256] In the thirtieth embodiment, each of the twenty sixth to twenty ninth embodiment includes each of the plurality of voxels is a polyhedron and wherein the one or more particles are positioned at one or more comers of the polyhedron, at the center of the polyhedron, or a combination thereof.

[00257] In the thirty first embodiment, each of the twenty sixth to thirtieth embodiment comprises the processor is configured to adjust the position of each particle by: calculating an acceleration for the particle; updating the particle to a new position using the acceleration and a time step; and modulating the new position, using one or more of a distance of the particle to the mask image, a spacing of the segments, and a normal vector of movement for the particle.

[00258] In the thirty second embodiment, the twenty sixth embodiment includes the system is further configured to define a critical distance.

[00259] In the thirty third embodiment, each of the twenty sixth to the thirty second embodiment includes the system is further configured to calculate a distance of each particle to the background in a final position and compare the distance of each particle to the background in the final position to the critical distance

[00260] In the thirty fourth embodiment, each of the twenty sixth to the thirty third embodiment includes the system is further configured to classify a particle with the distance to the background smaller than the critical distance as a solid type particle and a particle with the distance to the background larger than the critical distance as a fluid type particle. [00261] In the thirty fifth embodiment, each of the twenty sixth to the thirty fourth embodiment comprises the system is further configured to: defining an open region on the mask image within an area circumscribed by a plurality of solid type particles; and classifying particles within the opening regions as fluid type particles.

[00262] In the thirty sixth embodiment, each of the twenty sixth to the thirty fifth embodiment includes the mask image is an image of a biostructure or an anatomical portion in a native biological environment, in vitro environment, ex vivo environment or in situ environment.

[00263] In the thirty seventh embodiment, each of the twenty sixth to thirty first embodiment comprises the acceleration is the speed of change in particle position within a time period.

[00264] In the thirty eighth embodiment, each of the twenty sixth to thirty first embodiment comprises the updating step occurs if the acceleration is not 0.

[00265] In the thirty ninth embodiment, each of the twenty sixth to thirty eighth embodiment comprises repeating steps (c) though (e) for a different segment of the one or more of the plurality of segments.

[00266] In the fortieth embodiment, each of the twenty sixth to thirty ninth embodiment comprises a model is produced after the position of the one or more particles in each of the plurality of segments is adjusted.

[00267] In the forty first embodiment, each of the twenty sixth to fortieth embodiment includes one or more additional model is produced.

[00268] In the forty second embodiment, each of the twenty sixth to forty first embodiment includes the one or more additional model is combined with the model to give a final model and an interface is provided between adjacent models, the interface connected by constraints mimicking a virtual spring force such that the final model operates as a single unit in a simulation.

[00269] In the forty third embodiment, each of the twenty sixth to thirty fourth embodiment comprises imposing a boundary condition on the classified particle.

[00270] In the forty fourth embodiment, each of the twenty sixth to thirty fourth embodiment and the forty third embodiment includes the boundary condition correlates to a real- world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[00271] In the forty fifth embodiment, each of the twenty sixth to forty second embodiment comprises imposing a boundary condition on each of the one or more particles in one or more of the plurality of segments before, during or after the position of the particle is adjusted.

[00272] In the forty sixth embodiment, each of the twenty sixth to forty second and forty fifth embodiment comprises the boundary condition correlates to a real-world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

[00273] In the forty seventh embodiment, each of the twenty sixth to thirty sixth embodiment includes the biostructure or an anatomical portion comprises a blood vessel, a heart or portion or structure thereof, a bone, a circulatory or lymph system or portion thereof, an organ, a limb, or another biostructure or anatomical portion of a mammalian body.

[00274] In the forty eighth embodiment, each of the twenty sixth to forty seventh embodiment comprises the background distance is the shortest distance between the segment and the background, and the foreground distance is the shortest distance between the segment and the mask image.

[00275] In the forty ninth embodiment, each of the twenty sixth to forty eighth embodiment includes the first algorithm comprises subtracting the foreground distance from the background distance, or the second algorithm comprises subtracting the background distance from the foreground distance.

[00276] In the fiftieth embodiment, each of the twenty sixth to forty ninth embodiment includes units closer to background have lower distance values and/or units closer to background have higher distance values.

[00277] In the fifty first embodiment, a computer operated method for producing a model of an object comprised of thin beams is provided, the method comprises: (a) obtaining a mask image of an object comprised of thin beams; (b) choosing one or more points on the thin beams and calculating the coordinate of the one or more points; (c) superimposing the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (d) segmenting the mask image into a plurality of segments, each segment corresponding to a unit of the background; (e) treating each one of the one or more points as a particle and positioning the one or more particles in one or more of the plurality of segments in an initial position; (f) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or (ii) subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; (g) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero; and (h) repeating steps (a) - (g) with each image of the thin beams to generate a model for the object.

[00278] In the fifty second embodiment, the fifty first embodiment includes the object is a stent made of thin wires and the wires are treated as thin beams.

[00279] In the fifty third embodiment, the fifty second embodiment includes the stent comprising multiple basic elements of the same size and shape, and the method is applied to each of the multiple basic elements of the stent to generate a model for each of the multiple basic elements of the stent.

[00280] In the fifty fourth embodiment, the fifty third embodiment further includes splicing the models generated together to obtain a simulated model of the stent.

[00281] In the fifty fifth embodiment, a system for producing a model of an object comprised of thin beams is provided, the system comprises a processor, and the processor is configured to: (a) obtain a mask image of an object comprised of thin beams; (b) choose one or more points on the thin beams and calculate the coordinate of the one or more points; (c) superimpose the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (d) segment the mask image into a plurality of segments, each segment corresponding to a unit of the background; (e) treat each one of the one or more points as a particle and position the one or more particles in one or more of the plurality of segments in an initial position; (f) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or (ii) subject the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and represent the foreground distance value on the background to provide a foreground distance map; and (g) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero; and (h) repeat steps (a) - (g) with each image of the thin beams to generate a model for the object.

[00282] In the fifty sixth embodiment, the fifty fifth embodiment includes the object is a stent made of thin wires and the wires are treated as beams.

[00283] In the fifty seventh embodiment, the fifty sixth embodiment includes the stent comprises multiple basic elements of the same size and shape, and wherein the method is applied to each of the multiple basic elements of the stent to generate a model for each of the multiple basic elements of the stent.

[00284] In the fifty eighth embodiment, the fifty seventh embodiment includes the processor is further configured to splice the models generated together to obtain a simulated model of the stent.

[00285] In the fifty ninth embodiment, a computer operated method for producing a model of an object comprised of thin walls is provided, the method comprises (a) obtaining a mask image of an object comprised of thin walls, disregarding the thickness of the walls; (b) superimposing the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (c) segmenting the mask image into a plurality of segments, each segment corresponding to a unit of the background; (d) positioning one or more particles in one or more of the plurality of segments in an initial position; (e) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or (ii) subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; and (f) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

[00286] In the sixtieth embodiment, the fifty ninth embodiment includes the object comprised of thin walls is an angioplasty balloon.

[00287] In the sixty first embodiment, the fifty ninth embodiment includes the object comprised of thin walls is a blood vessel.

[00288] In the sixty second embodiment, a system for producing a model of an object comprised of thin walls is provided, the system comprises a processor, wherein the processor is configured to (a) obtain a mask image of an object comprised of thin walls, disregarding the thickness of the walls; (b) superimpose the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape; (c) segment the mask image into a plurality of segments, each segment corresponding to a unit of the background; (d) position one or more particles in one or more of the plurality of segments in an initial position; (e) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or (ii) subject the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and represent the foreground distance value on the background to provide a foreground distance map; and (f) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

[00289] In the sixty third embodiment, the sixty second embodiment includes the object comprised of thin walls is an angioplasty balloon.

[00290] In the sixty fourth embodiment, the sixty second embodiment includes the object comprised of thin walls is a blood vessel.

[00291] In the sixty fifth embodiment, a computer operated method for producing a contact model between the two bodies is provided, the method comprises (a) simulating a first body using the method described herein, the first body having a first particle; (b) simulating a second body using the method described herein, the second body having a second particle; and (c) simulating a contact between the first body and the second body, comprising: (i) contacting the first body and the second body such that the first particle comes into contact with the second particle; (ii) calculating a normal force acting on the first particle; (iii) calculating a time step tangential force acting on the first particle; (iv) calculating the contact force using the normal force and the tangential force; and (v) determining movement of the first body and/or the second body over the time step based on the calculated contact force.

[00292] In the sixty sixth embodiment, the sixty fifth embodiment includes the first body is a blood vessel and the second body is a stent implanted in the blood vessel.

[00293] In the sixty seventh embodiment, a system for producing a contact model between two bodies is provided, the system comprises a processor, wherein the processor is configured to: (a) simulate a first body using the method described herein, the first body having a first particle; (b) simulate a second body using the method described herein, the second body having a second particle; and (c) simulate a contact between the first body and the second body, comprising: (i) contact the first body and the second body such that the first particle comes into contact with the second particle; (ii) calculate a normal force acting on the first particle; (iii) calculate a time step tangential force acting on the first particle; (iv) calculate the contact force using the normal force and the tangential force; and (v) determine movement of the first body and/or the second body over the time step based on the calculated contact force.

[00294] In the sixty eighth embodiment, the sixty seventh embodiment includes the first body is a blood vessel and the second body is a stent implanted in the blood vessel.

[00295] Other features and advantages of the invention will be apparent from the following detailed description, and from the claims.

[00296] The above examples are included for illustrative purposes only and are not intended to limit the scope of the invention. Many variations to those described above are possible. Since modifications and variations to the examples described above will be apparent to those of skill in this art, it is intended that this invention be limited only by the scope of the appended claims.

Claims

CLAIMS We claim:

1. A computer operated method for optimization of a particle -based model based on image data, comprising:

(e) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

2. The method of claim 1, wherein the lattice structure is two-dimensional and comprises a plurality of pixels and each unit of the background corresponds to one or more pixel.

3. The method of claim 2, wherein each of the plurality of pixels comprises a polygon and wherein the one or more particles are positioned at one or more comers of the polygon, the center of the polygon, or a combination thereof.

4. The method of claim 1, wherein the lattice structure is three-dimensional and comprises a plurality of voxels and each unit of the background corresponds to one or more voxel.

5. The method of claim 4, wherein each of the plurality of voxels is a polyhedron and wherein the one or more particles are positioned at one or more comers of the polyhedron, at the center of the polyhedron, or a combination thereof.

6. The method of claim 1, wherein adjusting the position of each particle comprises: calculating an acceleration for the particle; updating the particle to a new position using the acceleration and a time step; and modulating the new position, using one or more of a distance of the particle to the mask image, a spacing of the segments, and a normal vector of movement for the particle.

7. The method of claim 1, further comprising defining a critical distance.

8. The method of claim 7, further comprising calculating a distance of each particle to the background in a final position and comparing the distance of each particle to the background in the final position to the critical distance.

9. The method of claim 8, further comprising classifying a particle with the distance to the background smaller than the critical distance as a solid type particle and a particle with the distance to the background larger than the critical distance as a fluid type particle.

10. The method of claim 9, further comprising: defining an open region on the mask image within an area circumscribed by a plurality of solid type particles; and classifying particles within the open region as fluid type particles.

11. The method of any of claims 1 to 10, wherein the mask image is an image of a biostructure or an anatomical portion in a native biological environment, in vitro environment, ex vivo environment or in situ environment.

12. The method of claim 6, wherein the acceleration is the speed of change in particle position within a time period.

13. The method of claim 6, wherein the updating step occurs if the acceleration is not 0.

14. The method of claim 1, further comprising repeating steps (c) through (e) for a different segment of the one or more of the plurality of segments.

15. The method of claim 14, wherein a model is produced after the position of the one or more particles in each of the plurality of segments is adjusted.

16. The method of claim 15, wherein one or more additional model is produced.

17. The method of claim 16, wherein one or more additional model is combined with the model to give a final model and an interface is provided between adjacent models, the interface connected by constraints mimicking a virtual spring force such that the final model operates as a single unit in a simulation.

18. The method of claim 9, further comprising imposing a boundary condition on the classified particle.

19. The method of claim 18, wherein the boundary condition correlates to a real- world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

20. The method of claim 18, further comprising imposing a boundary condition on each of the one or more particles in one or more of the plurality of segments before, during or after the position of the particle is adjusted.

21. The method of claim 20, wherein the boundary condition correlates to a real- world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

22. The method of claim 11, wherein the biostructure or an anatomical portion comprises a blood vessel, a heart or portion or structure thereof, a bone, a circulatory or lymph system or portion thereof, an organ, a limb, or another biostructure or anatomical portion of a mammalian body.

23. The method of any of claims 1 to 10 and 12 to 22, wherein the background distance is the shortest distance between the segment and the background, and wherein the foreground distance is the shortest distance between the segment and the mask image.

24. The method of any of claims 1 to 10 and 12 to 22, wherein the first algorithm comprises subtracting the foreground distance from the background distance, and wherein the second algorithm comprises subtracting the background distance from the foreground distance.

25. The method of any of claims 1 to 10 and 12 to 22, wherein units closer to background have lower distance values or units closer to background have higher distance values.

26. A system for generating a particle-based model based on image data, comprising a processor, wherein the processor is configured to:

(a) superimpose a mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(d) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and (i) subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or

27. The system of claim 26, wherein the lattice structure is two-dimensional and comprises a plurality of pixels and each unit of the background corresponds to one or more pixel.

28. The system of claim 27, wherein each of the plurality of pixels comprises a polygon and wherein the one or more particles are positioned at one or more comers of the polygon, at the center of the polygon, or a combination thereof.

29. The system of claim 26, wherein the lattice structure is three-dimensional and comprises a plurality of voxels and each unit of the background corresponds to one or more voxel.

30. The system of claim 29, wherein each of the plurality of voxels is a polyhedron and wherein the one or more particles are positioned at one or more comers of the polyhedron, at the center of the polyhedron, or a combination thereof.

31. The system of any of claims 26 to 30, wherein the processor is configured to adjust the position of each particle by: calculating an acceleration for the particle; updating the particle to a new position using the acceleration and a time step; and modulating the new position, using one or more of a distance of the particle to the mask image, a spacing of the segments, and a normal vector of movement for the particle.

32. The system of claim 26, wherein the system is further configured to define a critical distance.

33. The system of claim 32, wherein the system is further configured to calculate a distance of each particle to the background in a final position and compare the distance of each particle to the background in the final position to the critical distance.

34. The system of claim 33, wherein the system is further configured to classify a particle with the distance to the background smaller than the critical distance as a solid type particle and a particle with the distance to the background larger than the critical distance as a fluid type particle.

35. The system of claim 34, wherein the system is further configured to: defining an open region on the mask image within an area circumscribed by a plurality of solid type particles; and classifying particles within the opening regions as fluid type particles.

36. The system of any of claims 26 to 30 and 32 to 35, wherein the mask image is an image of a biostructure or an anatomical portion in a native biological environment, in vitro environment, ex vivo environment or in situ environment.

37. The system of claim 31 , wherein the acceleration is the speed of change in particle position within a time period.

38. The system of claim 31, wherein the updating step occurs if the acceleration is not 0.

39. The system of any of claims 26 to 30 and 32 to 35 and 37 to 38, further comprising repeating steps (c) though (e) for a different segment of the one or more of the plurality of segments.

40. The system of claim 39, wherein a model is produced after the position of the one or more particles in each of the plurality of segments is adjusted.

41. The system of claim 40, wherein one or more additional model is produced.

42. The system of claim 41, wherein the one or more additional model is combined with the model to give a final model and an interface is provided between adjacent models, the interface connected by constraints mimicking a virtual spring force such that the final model operates as a single unit in a simulation.

43. The system of claim 34, further comprising imposing a boundary condition on the classified particle.

44. The system of claim 43 , wherein the boundary condition correlates to a real -world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

45. The method of any of claims 26 to 30, 32 to 35, 37 to 38, and 40 to 42, further comprising imposing a boundary condition on each of the one or more particles in one or more of the plurality of segments before, during or after the position of the particle is adjusted.

46. The system of claim 45 , wherein the boundary condition correlates to a real -world boundary condition for a corresponding portion of a composition or structure represented by the mask image.

47. The system of claim 36, wherein the biostructure or an anatomical portion comprises a blood vessel, a heart or portion or structure thereof, a bone, a circulatory or lymph system or portion thereof, an organ, a limb, or another biostructure or anatomical portion of a mammalian body.

48. The system of any of claims 26 to 30, 32 to 35, 37 to 38, 40 to 44, and 46 to 47, wherein the background distance is the shortest distance between the segment and the background, and wherein the foreground distance is the shortest distance between the segment and the mask image.

49. The system of any of claims 26 to 30, 32 to 35, 37 to 38, 40 to 44, and 46 to 47 wherein the first algorithm comprises subtracting the foreground distance from the background distance, and wherein the second algorithm comprises subtracting the background distance from the foreground distance.

50. The system of any of claims 26 to 30, 32 to 35, 37 to 38, 40 to 44, and 46 to 47, wherein units closer to background have lower distance values or units closer to background have higher distance values.

51. A computer operated method for producing a model of an object comprised of thin beams, comprising:

(a) obtaining a mask image of an object comprised of thin beams;

(b) choosing one or more points on the thin beams and calculating the coordinate of the one or more points;

(c) superimposing the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(d) segmenting the mask image into a plurality of segments, each segment corresponding to a unit of the background;

(e) treating each one of the one or more points as a particle and positioning the one or more particles in one or more of the plurality of segments in an initial position;

(f) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and i. subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or ii. subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map;

(g) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero; and (h) repeating steps (a) - (g) with each image of the thin beams to generate a model for the object.

52. The method of claim 51, wherein the object is a stent made of thin wires and the wires are treated as thin beams.

53. The method of claim 52, wherein the stent comprises multiple basic elements of the same size and shape, and wherein the method is applied to each of the multiple basic elements of the stent to generate a model for each of the multiple basic elements of the stent.

54. The method of claim 53, further comprising splicing the models generated together to obtain a simulated model of the stent.

55. A system for producing a model of an object comprised of thin beams, comprising a processor, wherein the processor is configured to:

(a) obtain a mask image of an object comprised of thin beams;

(b) choose one or more points on the thin beams and calculate the coordinate of the one or more points;

(c) superimpose the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(d) segment the mask image into a plurality of segments, each segment corresponding to a unit of the background;

(e) treat each one of the one or more points as a particle and position the one or more particles in one or more of the plurality of segments in an initial position;

(f) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and i. subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or ii. subject the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and represent the foreground distance value on the background to provide a foreground distance map; (g) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero; and

(h) repeat steps (a) - (g) with each image of the thin beams to generate a model for the object.

56. The system of claim 55, wherein the object is a stent made of thin wires and the thin wires are treated as thin beams.

57. The system of claim 56, wherein the stent comprises multiple basic elements of the same size and shape, and wherein the method is applied to each of the multiple basic elements of the stent to generate a model for each of the multiple basic elements of the stent.

58. The system of claim 57, wherein the processor is further configured to splice the models generated together to obtain a simulated model of the stent.

59. A computer operated method for producing a model of an object comprised of thin walls, comprising:

(a) obtaining a mask image of an object comprised of thin walls, disregarding the thickness of the walls;

(b) superimposing the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(c) segmenting the mask image into a plurality of segments, each segment corresponding to a unit of the background;

(d) positioning one or more particles in one or more of the plurality of segments in an initial position;

(e) for each of the segment, calculating a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and i. subjecting the foreground distance and the background distance to a first algorithm to obtain a background distance value and representing the background distance value on the background to provide a background distance map; or ii. subjecting the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and representing the foreground distance value on the background to provide a foreground distance map; and

(f) adjusting the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

60. The method of claim 59, wherein the object comprised of thin walls is an angioplasty balloon.

61. The method of claim 59, wherein the object comprised of thin walls is a blood vessel.

62. A system for producing a model of an object comprised of thin walls, comprising a processor, wherein the processor is configured to:

(a) obtain a mask image of an object comprised of thin walls, disregarding the thickness of the walls;

(b) superimpose the mask image on a background, the background being a lattice structure comprising a plurality of units, each unit comprising a geometric shape;

(c) segment the mask image into a plurality of segments, each segment corresponding to a unit of the background;

(d) position one or more particles in one or more of the plurality of segments in an initial position;

(e) for each of the segment, calculate a distance between the segment and the background to obtain a background distance and a distance between the segment and the mask image to obtain a foreground distance, and i. subject the foreground distance and the background distance to a first algorithm to obtain a background distance value and represent the background distance value on the background to provide a background distance map; or ii. subject the background distance and the foreground distance to a second algorithm to obtain a foreground distance value and represent the foreground distance value on the background to provide a foreground distance map; and

(f) adjust the position of the one or more particles in each of the plurality of segments to an adjusted position, wherein the adjusted position has a distance value of zero.

63. The system of claim 62, wherein the object comprised of thin walls is an angioplasty balloon.

64. The system of claim 62, wherein the object comprised of thin walls is a blood vessel.

65. A computer operated method for producing a contact model between two bodies, comprising:

(a) simulating a first body using the method of claim 1, the first body having a first particle;

(b) simulating a second body using the method of claim 1, the second body having a second particle; and

(c) simulating a contact between the first body and the second body, comprising:

(i) contacting the first body and the second body such that the first particle comes into contact with the second particle;

(ii) calculating a normal force acting on the first particle;

(iii) calculating a time step tangential force acting on the first particle;

(iv) calculating the contact force using the normal force and the tangential force; and

(v) determining movement of the first body and/or the second body over the time step based on the calculated contact force.

66. The method of claim 65, wherein the first body is a blood vessel and the second body is a stent implanted in the blood vessel.

67. A system for producing a contact model between two bodies, comprising a processor, wherein the processor is configured to:

(a) simulate a first body using the method of claim 1, the first body having a first particle;

(b) simulate a second body using the method of claim 1, the second body having a second particle; and

(c) simulate a contact between the first body and the second body, comprising: (i) contact the first body and the second body such that the first particle comes into contact with the second particle;

(ii) calculate a normal force acting on the first particle;

(iii) calculate a time step tangential force acting on the first particle;

(iv) calculate the contact force using the normal force and the tangential force; and

(v) determine movement of the first body and/or the second body over the time step based on the calculated contact force.

68. The system of claim 67, wherein the first body is a blood vessel and the second body is a stent implanted in the blood vessel.