CN116629075A - Irreversible electroporation tissue ablation finite element model optimization method and system based on Nelder-Mead algorithm - Google Patents
Irreversible electroporation tissue ablation finite element model optimization method and system based on Nelder-Mead algorithm Download PDFInfo
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Abstract
The invention discloses a method and a system for optimizing irreversible electroporation tissue ablation finite element model based on a Nelder-Mead algorithm, wherein the method comprises the steps of establishing a tumor tissue three-dimensional geometric model according to a medical diagnosis image of a patient; selecting optimized parameters of a treatment scheme, and establishing an irreversible electroporation tissue ablation parameterized finite element model; carrying out scheme optimization through a Nelder-Mead algorithm, constructing an initial simplex according to initial parameters, calculating values of an objective function and a constraint function under each group of parameters, sequencing peaks of the simplex according to the objective function values, carrying out deformation operations such as reflection, expansion, contraction and the like, and outputting optimal treatment scheme parameters under iteration termination conditions; the invention has the advantage that the arrangement position of the electrode needle can be accurately determined by taking the irregularity of tumor tissues and the accurate positioning of the electrode needle into consideration. The treatment scheme is optimized through the optimization algorithm, so that the ablation effect of tumor tissues can be ensured, and the damage to healthy tissues can be reduced to the greatest extent.
Description
Technical Field
The invention relates to the field of treatment scheme optimization of irreversible electroporation tissue ablation, in particular to an optimization method and system of an irreversible electroporation tissue ablation finite element model based on medical images and a Nelder-Mead algorithm.
Background
The irreversible electroporation tumor ablation technology establishes a high-strength electric field in a target area by applying high-voltage microsecond pulse on an electrode needle, destroys the cell membrane structure of tumor cells in the target area to form irreversible destruction, induces apoptosis of the tumor cells and finally achieves the aim of ablating tumor tissues.
The prediction of the pre-operative therapeutic effect of irreversible electroporation tissue ablation can be accomplished by building and solving a finite element model thereof. The existing method generally idealizes the tumor shape into a regular geometric figure, such as a sphere or ellipsoid, so as to calculate the sphere or ellipsoid of maximum diameter that can be ablated by a particular treatment parameter, and considers that the volume of the tumor area is smaller than the volume of the sphere or ellipsoid, thus achieving complete ablation of the tumor area.
Although the method can realize the ablation of the tumor tissue in the target area, the geometrical irregularity of the tumor tissue is ignored in the process of predicting the ablation effect, and the relative position of the electrode needle and the tumor is not strictly restrained, namely the geometrical position of the electrode needle cannot be clearly given.
The above method is not accurate enough for the tumor ablation area of irreversible electroporation tissue ablation and the prediction of the ablation area of healthy tissue due to the ambiguous electrode needle arrangement position caused by the idealization of the tumor tissue in the actual clinical process.
Disclosure of Invention
The invention aims at solving the problem that the current irreversible electroporation tissue ablation finite element model ignores the geometric irregularity of tumors, and provides an irreversible electroporation tissue ablation finite element model optimizing method and system based on a medical image and a Nelder-Mead algorithm.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the irreversible electroporation tissue ablation finite element model optimization method based on the Nelder-Mead algorithm comprises the following steps of:
(1) And establishing a three-dimensional geometric model of tumor tissue according to the medical diagnostic image of the patient.
(2) And selecting the treatment parameters and the range thereof which need to be optimized, and establishing an irreversible electroporation tissue ablation parameterized finite element model by utilizing a three-dimensional geometric model of the tumor.
(3) An initial treatment parameter is selected, and an initial simplex is determined based on the initial parameter.
(4) The objective function value and constraint function value of the simplex vertex are calculated. And sorting the vertexes of the simplex according to the order of the objective function values from small to large.
(5) And (3) carrying out reflection, expansion and contraction operation on the simplex according to the sequencing result in the step (4).
(6) And (3) judging whether the optimization algorithm meets the iteration termination condition, returning to the step (4) if the optimization algorithm does not meet the iteration termination condition, stopping iteration if the optimization algorithm meets the iteration condition, namely the maximum iteration number of the iteration number or the convergence of the objective function to the minimum value, and outputting an optimal solution.
Specifically, the medical diagnostic image in the step (1) may be a CT image or an MRI image, and the three-dimensional geometric model of the tumor may be established after the segmentation by the professional imaging physician, wherein positive directions of an x axis, a y axis and a z axis in the three-dimensional geometric model of the tumor respectively represent l, p and s directions of a human anatomy coordinate system, and an origin of the coordinate system is a centroid of the geometric model of the tumor.
Specifically, the treatment parameters in the step (2) include the coordinates (x, y, z) of the electrode needle set, the rotation angles of the electrode needle set around the x-axis, the y-axis and the z-axis of the local coordinate system, and any combination of the distance d between the anode and the cathode of the electrode needle and the pulse amplitude amp. And selecting part of parameters or adding other parameters to be optimized according to actual requirements for optimization. Upper and lower limits of parameters to be optimizedAccording to the actual requirements.
The finite element model in the step (2) is used for calculating the application on the electrode needleWhen pulsed, the electric field inside the tissue is distributed. The nonlinear conductivity of healthy tissue is expressed as: sigma (sigma) h (|E|)＝σ h0 (1+A·fl2chs(|E|-E del ,E range)) wherein ,σh0 Represents the initial conductivity of normal tissue, A is the tissue conductivity increase coefficient after electroporation, E del and Erange Determines the electric field intensity of the tissue after electroporation and electroporation saturation, E represents the electric field intensity in the tissue, sigma h (|E|) describes the process from non-electroporation to electroporation saturation of normal tissue under the influence of an electric field from the point of change in conductivity, fl2chs represents a smooth step function with a continuous second derivative.
The electrical conductivity of tumor tissue is expressed as:
wherein ,E 0 indicating the electric field strength at which electroporation of tumor tissue begins to occur, E 1 Represents the electric field strength, sigma, at irreversible electroporation saturation of tumor tissue t0 Represents the electrical conductivity, σ, of tumor tissue without electroporation t1 Represents the electrical conductivity after electroporation saturation of tumor tissue.
Constraint c (x)>0.95，Wherein c (x) represents the percentage of the volume of the tumor tissue region where irreversible electroporation occurs to the total volume of the tumor tissue, v tire Represents the region in tumor tissue where irreversible electroporation occurred.
The objective function f (x) is: wherein ,vhire Representing the region in normal tissue where irreversible electroporation occurs, the objective function also requires the addition of a penalty function due to the constraints, so the final objective functionF (x) =f (x) +μc (x), where μ is the penalty function coefficient.
Specifically, in the step (5), the reflection is performed by calculating the symmetry point of the current worst vertex, firstly, calculating the central symmetry point of the worst vertex about the rest of vertices, then proceeding along the direction for a distance, if the objective function value of the reflection point is between the objective function values of the next best and next best vertices, the reflection point will be accepted and replace the worst vertex, and if the objective function value of the reflection point is smaller than the current best vertex, performing the expansion operation; the expansion operation is to further extend along the reflection direction, calculate an expansion point, the position of which is in the extension direction of the reflection point, if the objective function value of the expansion point is smaller than that of the current optimal vertex, the expansion point will replace the worst vertex, if the objective function value of the reflection point is larger, or the expansion operation does not significantly improve the objective function value, then the contraction operation is performed; the contraction operation is to approach the worst vertex to the current optimal vertex by a certain distance, calculate a contraction point, the position of which is between the worst vertex and the current optimal vertex, and approach the current optimal vertex, if the objective function value of the contraction point is smaller than that of the worst vertex, the contraction point will replace the worst vertex.
In the above step (6), the termination condition of the optimization algorithm includes the following cases. Objective function value convergence: when the objective function changes sufficiently little within a certain number of iterations, i.e. reaches the convergence threshold, the iterative process of the algorithm is terminated. Simplex vertex convergence: when the relative position of the simplex vertex changes sufficiently small within a certain iteration number, the iteration process of the algorithm can be terminated. Up to the maximum number of iterations: in order to avoid infinite loop of the optimization algorithm, setting the maximum iteration number as a termination condition, stopping iteration and returning to the current optimal solution when the maximum iteration number is reached.
The invention also provides an irreversible electroporation tissue ablation finite element model optimization system based on the Nelder-Mead algorithm, which comprises the following steps:
the geometric model construction module is used for establishing a three-dimensional geometric model of tumor tissues according to the medical diagnosis image of the patient;
the finite element model construction module is used for selecting treatment parameters and the range thereof which need to be optimized, and establishing an irreversible electroporation tissue ablation parameterized finite element model by utilizing a three-dimensional geometrical model of a tumor;
the optimization problem construction module is used for selecting initial treatment parameters, determining an initial simplex according to the initial parameters, and calculating an objective function value and a constraint function value of a simplex vertex;
the simplex deforming module is used for sequencing the vertexes of the simplex according to the order of the objective function values from small to large, and carrying out reflection, expansion and contraction operations on the simplex according to the sequencing result;
and the output module is used for judging whether the optimization algorithm meets the condition of ending iteration and outputting an optimal solution.
A medical system comprising the irreversible electroporation tissue ablation finite element model optimization system based on the Nelder-Mead algorithm.
The invention has the beneficial effects that: according to the invention, firstly, by establishing a three-dimensional geometric model of tumor tissue, geometric irregularity of the tumor tissue is brought into the consideration range of the irreversible electroporation tissue ablation finite element model, and the irreversible electroporation tissue ablation effect of the irregular tumor can be estimated more accurately. Secondly, in the process of carrying out parameter optimization by adopting a Nelder-Mead algorithm, aiming at geometric irregularities of tumor tissues, the degree of freedom of the electrode needle set in a Cartesian coordinate system is further introduced, namely, the coordinates of the electrode needle set and the rotation angle around the shaft are taken as optimization parameters, and the arrangement position of the electrode needle set in the actual application of irreversible electroporation tissue ablation is more accurately given. Finally, the optimized treatment parameters can reduce the damage to healthy tissues to the greatest extent while guaranteeing the ablation effect of the tumor tissues.
Drawings
FIG. 1 is a flow chart of an irreversible electroporation tissue ablation treatment protocol optimization of the present invention;
FIG. 2 is a medical diagnostic image of a patient in an embodiment;
FIG. 3 (a) is a 3-dimensional geometric model of a tumor in an example, and FIG. 3 (b) is an irreversible electroporation tissue ablation geometric model;
FIG. 4 is an iterative plot of tumor volume percent of tumor ablation zone volume versus algorithm during analysis using the method of the present invention;
FIG. 5 is an iterative plot of normal tissue ablation zone volume versus algorithm during analysis using the method of the present invention;
fig. 6 (a) is a cross-sectional view of an ablation region under initial treatment parameters, and fig. 6 (b) is a cross-sectional view of an ablation region under optimal treatment parameters after optimization.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
As shown in fig. 1, the irreversible electroporation tissue ablation finite element model optimization method based on the medical image and the Nelder-Mead algorithm comprises the following steps:
(1) And establishing a three-dimensional geometric model of tumor tissue according to the medical diagnostic image of the patient.
Specifically, the medical diagnostic image of the patient can be CT or MRI, the three-dimensional geometric model of the tumor tissue can be built by dividing the tumor region of the image by an imaging physician, when the 3-dimensional geometric model of the tumor tissue is built, the L axis of the human anatomy coordinate system is selected as the x axis of the cartesian coordinate system in the geometric model, the p axis of the anatomy coordinate system is selected as the y axis of the cartesian coordinate system, the s axis of the anatomy coordinate system is selected as the z axis of the cartesian coordinate system, and the centroid of the tumor is selected as the origin of the model cartesian coordinate system.
(2) According to application requirements, a parameter x to be optimized is selected, wherein the parameter x comprises coordinates (x, y, z) of an electrode needle set, rotation angles of the electrode needle set around x-axis, y-axis and z-axis of a local coordinate system of the electrode needle set, a distance d between the anode and the cathode of the electrode needle and a pulse amplitude amp. And selecting part of parameters or adding other parameters to be optimized according to actual requirements for optimization. Upper and lower limits of parameters to be optimizedAccording to the actual requirementsAnd (5) setting. And selecting the treatment parameters and the range thereof which need to be optimized, and establishing an irreversible electroporation tissue ablation parameterized finite element model by utilizing a three-dimensional geometric model of the tumor.
Specifically, the geometric schematic of the irreversible electroporation tissue ablation parameterized finite element model is shown in fig. 3 (b), including external normal tissue, internal tumor tissue, and electrode pins. Whereas parametric modeling is advantageous in reducing the time required to later modify the model parameter settings, where the model parameters include geometrical parameters and electromagnetic parameters of the material.
The tissue irreversible electroporation parameterized finite element model is the basis of a treatment protocol optimization algorithm. In the optimization algorithm, the values of the objective function and the constraint function under specific treatment parameters are calculated by a finite element model.
Specifically, the electrical conductivity of healthy tissue in the finite element model is nonlinear electrical conductivity, and the expression is: sigma (sigma) h (|E|)＝σ h0 (1+A·fl2chs(|E|-E del ,E range ))。
wherein ,σh0 Represents the initial conductivity of normal tissue, A is the tissue conductivity increase coefficient after electroporation, E del and Erange The electric field strength after the tissue begins to generate electroporation and electroporation saturation is determined. E represents the electric field intensity in the tissue, σ h (|E|) describes the process from non-electroporation to electroporation saturation of normal tissue under the influence of an electric field from the point of change in conductivity, fl2chs represents a smooth step function with a continuous second derivative.
Likewise, the electrical conductivity of tumor tissue is also nonlinear, and the expression is:
wherein ,σt0 Represents the electrical conductivity, σ, of tumor tissue without electroporation t1 Represents the electrical conductivity after electroporation saturation of tumor tissue.E 0 Indicating the electric field strength at which electroporation of tumor tissue begins to occur, E 1 Represents the electric field strength at which irreversible electroporation of tumor tissue is saturated.
The constraint function is calculated by a finite element model, and the constraint condition is c (x)>0.95, meaning that the percentage value of the ablated area of tumor tissue must be greater than 95%, whereinWherein c (x) represents the percentage of the volume of the tumor tissue region where irreversible electroporation occurs to the total volume of the tumor tissue, v tire Representing the region in the tumor tissue where irreversible electroporation occurs, i.e. the electric field strength E in the tumor tissue>E 1 V of (v) t The method is characterized in that a tumor area is represented, the electric field intensity distribution E in tumor tissues and healthy tissues can be obtained by solving Laplace equation through a finite element model, the volume of the tumor tissues can be calculated through integration, and the area of irreversible electroporation of the tumor tissues is generated. Further, at a known treatment parameter x i The value of the constraint condition under the parameter can be calculated by the finite element model.
Similarly, the value of the objective function is also calculated by a finite element model, and the objective function f (x) refers to the ablation volume of normal tissue calculated by irreversible electroporation finite element model ablation, and the expression is:, wherein ,vhire Indicating the region of normal tissue where irreversible electroporation occurs, i.e. the E > E electric field strength del +E range Is a region of (a) in the above-mentioned region(s). Furthermore, the objective function also requires the addition of a penalty function due to the existence of constraints, so the final objective function is F (x) =f (x) +μc (x), where μ is the penalty function coefficient.
(3) Given the initial parameters, an initial simplex, i.e., a set of parameters of number n+1, where n is the variable dimension of the optimization problem, is selected based on the initial parameters. Values of the objective function and the constraint function under each set of initial parameters are calculated.
The initial parameters are the parameters x to be optimized i I=1, 2, initial value of n (n is the number of parameters to be optimized), upper and lower limits of parameters to be optimizedI.e., the search space of the Nelder-Mead algorithm. i xRepresenting the minimum value of the parameter to be optimized,representing the maximum value of the parameter to be optimized.
(4) The vertices of the simplex are ordered in order of decreasing objective function values, so that the worst vertex can be selected from the simplex.
(5) And (3) carrying out reflection, expansion, contraction and compression deformation operation on the simplex according to the sequencing result in the step (4).
Reflection is performed by calculating the symmetry point of the current worst vertex. First, the central symmetry point of the worst vertex with respect to the remaining vertices is calculated, and then proceeds a distance along the direction. If the objective function value of the reflection point is between the objective function values of the second best and second best vertices, the reflection point will be accepted and replace the worst vertex. If the objective function value of the reflection point is smaller than the current optimal vertex, an expansion operation may be attempted. The expansion operation is further extended along the reflection direction in order to obtain better results. An expansion point is calculated whose position is in the extending direction of the reflection point and which extends farther than the reflection point. If the objective function value of the extension point is smaller than the objective function value of the current optimal vertex, the extension point will replace the worst vertex. If the objective function value of the reflection point is large or the expansion operation does not significantly improve the objective function value, then a contraction operation may be attempted. The contraction operation is to approach the worst vertex to the current optimal vertex by a certain distance. A pinch point is calculated that is positioned between the worst vertex and the current optimal vertex and is close to the current optimal vertex. If the objective function value of the contraction point is smaller than the objective function value of the worst vertex, the contraction point will replace the worst vertex.
Specifically, in an iteration process of the Nelder-Mead optimization algorithm, multiple deformation operations of different simplex are usually performed, and each deformation operation can be judged whether to enter the next iteration or continue the deformation operation by adopting the current simplex vertex according to the result of the objective function.
In the simplex deformation operation, reflection means the pass-through formula x r ＝x c +a(x c -x w ) Modifying simplex worst vertex x w Wherein x is r Is a reflection point for replacing the worst vertex x w Form a new simplex, x c Refers to the center point of the remaining vertices after the simplex removes the worst vertex, α being the reflection coefficient.
The formula of the expansion operation is: x is x e ＝x c +γ*(x r -x c ). Wherein x is r Is the reflection point, x γ Is the expansion coefficient (usually greater than 1), x e Representing the apex after expansion. The expansion coefficient y determines the extent of the expansion point in the reflection direction relative to the center point. A larger gamma value would move the extension point away from the center point, continuing to explore the possible solution space in larger steps.
The formula for the shrink operation is: x is x s ＝x c +β*(x w -x c ) Wherein x is s Is the shrinkage point and β is the shrinkage factor (typically between 0 and 1).
Unlike the contraction operation, the compression operation changes the coordinates of all vertices of the simplex by the formula: x is x m ＝x b +δ*(x m -x b ) Wherein x is m Is each vertex of a simplex, x b Is the optimal vertex of the simplex, delta is the compression coefficient (typically between 0 and 1).
(6) And (3) judging whether the optimization algorithm meets the iteration termination condition, returning to the step (4) if the iteration termination condition is not met, and outputting an optimal solution if the iteration termination condition is met.
The termination conditions for the optimization algorithm include the following. Objective function value convergence: when the objective function changes sufficiently little within a certain number of iterations, i.e. reaches the convergence threshold, the iterative process of the algorithm is terminated. Simplex vertex convergence: when the relative position of the simplex vertex changes sufficiently small within a certain iteration number, the iteration process of the algorithm can be terminated. Up to the maximum number of iterations: in order to avoid infinite loop of the optimization algorithm, setting the maximum iteration number as a termination condition, stopping iteration and returning to the current optimal solution when the maximum iteration number is reached.
Specifically, the maximum number of iterations: and setting a maximum iteration number, and stopping the algorithm when the iteration number reaches the value, so that infinite iteration of the algorithm can be prevented. Convergence of objective function values: monitoring the change of the objective function value and setting a threshold value e, when the change of the objective function value is smaller than the threshold value, the algorithm is considered to be converged, the iteration can be terminated, |f (x i )-F(x i-1 )|＜＝∈。
Examples
Tumor diagnostic images of a patient are shown in fig. 2, and the method of the present invention is used to optimize an irreversible electroporation treatment.
The normal tissue surrounding the tumor is liver tissue, whereby the values of the relevant parameters in the nonlinear conductivity of the normal tissue are: a=0.9, σ h0 ＝0.23S/m，E del ＝1200V/cm，E range ＝350V/cm。
The values of the relevant parameters in the nonlinear conductivity expression of tumor tissue are: σ 0 ＝0.8S/m，σ 1 ＝0.83S/m，E 0 ＝470V/cm，E 1 ＝955V/cm。
in the example, parameters to be optimized are the distance d between positive and negative electrode pins, the amplitude amp of pulse voltage applied by the electrode pins, and the rotation angle θ of the electrode pin set around the y-axis, and the initial parameter x 0 ＝[d 0 ,amp 0 ,θ 0 ] T ＝[6,2000,30] T . Upper and lower limits of parameters to be optimizedRespectively ([ 6, 14)],[1500,3000],[0,360]) T 。
In this embodiment, the constraint function, that is, the change of the percentage value of the irreversible ablation area of the tumor tissue to the tumor area along with the iteration number is shown in fig. 4, and it can be seen that when the convergence condition is reached, the optimal treatment scheme can meet the requirement that the percentage value of the irreversible ablation area of the tumor reaches 95%.
In this example, after optimization by the Nelder-Mead algorithm, the objective function, i.e., the volume of the ablated region of healthy tissue, was 481.1mm from the initial treatment plan 3 Reduced to 151mm 3 。
In this embodiment, the maximum iteration number is 1000, and the optimization algorithm finds the optimal solution after 218 iterations. Therefore, the optimal treatment regimen is: distance d=11 mm between positive and negative electrode pins, amplitude amp=1986v of pulse voltage applied by the electrode pins, and rotation angle θ=149° of the electrode pins around y axis.
As can be seen from fig. 4 and 5, the method of the present invention can optimize the treatment scheme of irreversible electroporation tissue ablation, and can minimize the damage to healthy tissue while ensuring the ablation effect of the tumor area.
FIG. 6 depicts the electric field distribution in the xOz plane in a tissue irreversible electroporation ablation system, wherein dark gray areas represent areas having an electric field strength greater than 1550V/cm. In the figure, two circles are projections of the electrode needle on the xOz plane, the irregular geometric figure is a projection of the tumor geometry on the xOz plane, the inside of the irregular geometric figure is a tumor tissue area, and the outside of the irregular geometric figure is a normal tissue area. Comparing fig. 6 (a) and fig. 6 (b), it can be seen that the area of normal tissue where irreversible electroporation occurs is significantly reduced after the treatment parameters are optimized.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (10)
1. The irreversible electroporation tissue ablation finite element model optimization method based on the Nelder-Mead algorithm is characterized by comprising the following steps of:
(1) Establishing a three-dimensional geometric model of tumor tissue according to the medical diagnosis image of the patient;
(2) Selecting treatment parameters and the range thereof which need to be optimized, and establishing an irreversible electroporation tissue ablation parameterized finite element model by utilizing a three-dimensional geometric model of a tumor;
(3) Selecting initial treatment parameters, and determining an initial simplex according to the initial parameters;
(4) Calculating an objective function value and a constraint function value of the simplex vertex, and sequencing the simplex vertex according to the order of the objective function value from small to large;
(5) According to the sequencing result in the step (4), carrying out reflection, expansion and contraction operation on the simplex;
(6) And (3) judging whether the optimization algorithm meets the iteration termination condition, returning to the step (4) if the optimization algorithm does not meet the iteration termination condition, stopping iteration if the optimization algorithm meets the iteration condition, namely the maximum iteration number of the iteration number or the convergence of the objective function to the minimum value, and outputting an optimal solution.
2. The irreversible electroporation tissue ablation finite element model optimization method based on the Nelder-Mead algorithm of claim 1, wherein: the medical diagnosis image is a CT image or an MRI image, positive directions of an x axis, a y axis and a z axis in the three-dimensional geometrical model of the tumor tissue respectively represent l, p and s directions of a human anatomy coordinate system, and an origin of the coordinate system is the centroid of the tumor geometrical model.
3. The irreversible electroporation tissue ablation finite element model optimization method based on the Nelder-Mead algorithm of claim 1, wherein: the treatment parameters comprise the coordinates (x, y, z) of the electrode needle set, the rotation angles of the electrode needle set around the x axis, the y axis and the z axis of the local coordinate system of the electrode needle set, and any combination of the distance d between the anode and the cathode of the electrode needle and the pulse amplitude amp.
4. A method of irreversible electroporation tissue ablation finite element model optimization based on the Nelder-Mead algorithm according to claim 1 or 3, characterized in that: the irreversible electroporation tissue ablation parameterized finite element model comprises:
the conductivity of healthy tissue is expressed as: sigma (sigma) h (|E|)＝σ h0 (1+A·fl2chs(|E|-E del ,E range ) Wherein σ h0 Represents the initial conductivity of normal tissue, A is the tissue conductivity increase coefficient after electroporation, E del And E is range Determining the electric field strength of the tissue after electroporation and electroporation saturation, E representing the electric field strength in the tissue, fl2chs representing a smooth step function with a continuous second derivative;
the electrical conductivity of tumor tissue is expressed as:
wherein,E 0 indicating the electric field strength at which electroporation of tumor tissue begins to occur, E 1 Represents the electric field strength, sigma, at irreversible electroporation saturation of tumor tissue t0 Represents the electrical conductivity, σ, of tumor tissue without electroporation t1 Represents the conductivity of tumor tissue after electroporation saturation;
constraint c (x)>0.95，Wherein c (x) represents the percentage of the volume of the tumor tissue region where irreversible electroporation occurs to the total volume of the tumor tissue, v tire Represents the region in the tumor tissue where irreversible electroporation occurred,
the objective function f (x) is:wherein v is hire Representing the region in normal tissue where irreversible electroporation occurs, the objective function also requires the addition of a penalty function due to the presence of constraints, so the final objective function is F (x) =f (x) +μc (x), where μ is the penalty function coefficient.
5. The irreversible electroporation tissue ablation finite element model optimization method based on the Nelder-Mead algorithm of claim 1, wherein: the step (5) specifically comprises the following steps:
the reflection is carried out by calculating the symmetry point of the current worst vertex, firstly, calculating the central symmetry point of the worst vertex relative to the rest vertexes, then continuing to advance for a distance along the direction, if the objective function value of the reflection point is between the objective function values of the inferior good and inferior poor vertexes, the reflection point is accepted and replaces the worst vertex, and if the objective function value of the reflection point is smaller than the current optimal vertex, the expansion operation is carried out; the expansion operation is to further extend along the reflection direction, calculate an expansion point, the position of which is in the extension direction of the reflection point, if the objective function value of the expansion point is smaller than that of the current optimal vertex, the expansion point will replace the worst vertex, if the objective function value of the reflection point is larger, or the expansion operation does not significantly improve the objective function value, then the contraction operation is performed; the contraction operation is to approach the worst vertex to the current optimal vertex by a certain distance, calculate a contraction point, the position of which is between the worst vertex and the current optimal vertex, and approach the current optimal vertex, if the objective function value of the contraction point is smaller than that of the worst vertex, the contraction point will replace the worst vertex.
6. Irreversible electroporation tissue ablation finite element model optimization system based on Nelder-Mead algorithm, characterized in that it comprises:
the geometric model construction module is used for establishing a three-dimensional geometric model of tumor tissues according to the medical diagnosis image of the patient;
the finite element model construction module is used for selecting treatment parameters and the range thereof which need to be optimized, and establishing an irreversible electroporation tissue ablation parameterized finite element model by utilizing a three-dimensional geometrical model of a tumor;
the optimization problem construction module is used for selecting initial treatment parameters, determining an initial simplex according to the initial parameters, and calculating an objective function value and a constraint function value of a simplex vertex;
the simplex deforming module is used for sequencing the vertexes of the simplex according to the order of the objective function values from small to large, and carrying out reflection, expansion and contraction operations on the simplex according to the sequencing result;
and the output module is used for judging whether the optimization algorithm meets the condition of ending iteration and outputting an optimal solution.
7. The irreversible electroporation tissue ablation finite element model optimization system based on the Nelder-Mead algorithm of claim 6, wherein: the treatment parameters are the coordinates (x, y, z) of the electrode needle set, the rotation angles of the electrode needle set around the x axis, the y axis and the z axis of the local coordinate system, and the arbitrary combination of the distance d between the anode and the cathode of the electrode needle and the pulse amplitude amp.
8. The irreversible electroporation tissue ablation finite element model optimization system based on the Nelder-Mead algorithm of claim 6, wherein: the irreversible electroporation tissue ablation parameterized finite element model comprises:
the conductivity of healthy tissue is expressed as: sigma (sigma) h (|E|)＝σ h0 (1+A·fl2chs(|E|-E del ,E range ) Wherein σ h0 Represents the initial conductivity of normal tissue, A is the tissue conductivity increase coefficient after electroporation, E del And E is range Determining the electric field strength of the tissue after electroporation and electroporation saturation, E representing the electric field strength in the tissue, fl2chs representing a smooth step function with a continuous second derivative;
the electrical conductivity of tumor tissue is expressed as:
wherein,E 0 indicating the electric field strength at which electroporation of tumor tissue begins to occur, E 1 Represents the electric field strength, sigma, at irreversible electroporation saturation of tumor tissue t0 Represents the electrical conductivity, σ, of tumor tissue without electroporation t1 Represents the conductivity of tumor tissue after electroporation saturation;
constraint c (x)>0.95，Wherein c (x) represents the percentage of the volume of the tumor tissue region where irreversible electroporation occurs to the total volume of the tumor tissue, v tire Represents the region in tumor tissue where irreversible electroporation occurred.
The objective function f (x) is:wherein v is hire Representing the region in normal tissue where irreversible electroporation occurs, the objective function also requires the addition of a penalty function due to the presence of constraints, so the final objective function is F (x) =f (x) +μc (x), where μ is the penalty function coefficient.
9. The irreversible electroporation tissue ablation finite element model optimization system based on the Nelder-Mead algorithm of claim 6, wherein: the operation in the simplex deformation module comprises the steps of calculating the central symmetry point of the worst vertex relative to the rest vertexes, continuing to advance for a distance along the direction, accepting the reflection point and replacing the worst vertex if the objective function value of the reflection point is between the objective function values of the second best vertex and the second best vertex, and performing expansion operation if the objective function value of the reflection point is smaller than the current optimal vertex; the expansion operation is to further extend along the reflection direction, calculate an expansion point, the position of which is in the extension direction of the reflection point, if the objective function value of the expansion point is smaller than that of the current optimal vertex, the expansion point will replace the worst vertex, if the objective function value of the reflection point is larger, or the expansion operation does not significantly improve the objective function value, then the contraction operation is performed; the contraction operation is to approach the worst vertex to the current optimal vertex by a certain distance, calculate a contraction point, the position of which is between the worst vertex and the current optimal vertex, and approach the current optimal vertex, if the objective function value of the contraction point is smaller than that of the worst vertex, the contraction point will replace the worst vertex.
10. A medical system comprising the irreversible electroporation tissue ablation finite element model optimization system based on the Nelder-Mead algorithm of any one of claims 6-8.
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| US12076071B2 (en) | 2020-08-14 | 2024-09-03 | Kardium Inc. | Systems and methods for treating tissue with pulsed field ablation |
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| CN117675961A (en) * | 2023-11-28 | 2024-03-08 | 江苏慧铭信息科技有限公司 | Communication transmission data management method and system |
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