CN103995989B - The adjust automatically of the particular patient of boundary condition for tip vascular tree - Google Patents
The adjust automatically of the particular patient of boundary condition for tip vascular tree Download PDFInfo
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Abstract
The present invention relates to the adjust automaticallies of the particular patient of the boundary condition for tip vascular tree.For specific user to being modeled for the boundary condition of tip vascular tree（24）And adjustment（26）.Measurement from patient is used to find the reference compliance and resistance of the root for tip vascular tree-model.It is used to such as adjust by iteratively solving attribute in the compliance and resistance of mating structure tree-model and the reference compliance of particular patient and with reference to resistance while with reference to compliance and resistance（26）The attribute of structuring tree-model.Then, the structuring tree of adjustment is used to calculate（28）Boundary condition, to calculate（30）The flow of the vascular of the scanning of patient.
Description
Related application
This patent document is required on 2 15th, 2013 U.S. Provisional Patent Applications submitted（Sequence number No.61/765,
165）The equity of submission date at 35 U.S.C. § 119 (e) is incorporated herein by the following way herein hereby.
Technical field
The present invention relates to a kind of adjust automaticallies of the particular patient of the boundary condition for tip vascular tree.
Background technology
The present embodiment is related to the calculating of the blood flow in the vascular of patient.In particular, being adjusted in arteries and veins for special patient
The boundary condition in the exit of pipe is to calculate vascular flow.
Outlet for the vascular for calculating its flow, it has been proposed that be used for three-dimensional, the one-dimensional or more ruler of tip vascular tree
Spend several export boundary conditions of model.Simple method is directly with flow velocity rate or pressure, but for particular patient
Geometry, this method is determined by the flow velocity rate of measurement or the availability of amount of pressure.In addition, pressure boundary condition may
Lead to the physiological error result for the vessel geometry with multiple exit.
In another method, three element elastic chamber models use the simulation with circuit.Boundary condition is in exit
Tip vascular tree resistance and compliance.Resistance is modeled as two concatenated resistors, and compliance is modeled as electricity
Perhaps energy stores.Although elastic cavity boundary condition is only by three components（For example, two resistance and a capacitance）It constitutes, still
Elastic chamber model may be adjusted so that matching particular patient quantity.
The not physiology aspect modelings to downstream vasculature or tip vascular tree of the two methods.Especially when wave passes
It, can not be in the tip portion of cycle according to the boundary condition of these methods when being of interest in calculating research in terms of broadcasting
（That is, being combined as in the region of export boundary condition based on model）Capture wave propagation phenomenon.
In another method that can be modeled to the wave propagation effects of the tip of artificial outlet, structuring tree by with
To determine boundary condition.Tip vascular system is modeled as with multiple simplified simple geometric structures for assuming to obtain.These are assumed
The analytical Calculation for allowing the impedance of structuring tree, is then imposed in the exit of geometrical model as periodic boundary condition.So
And it is adjusted for particular patient calculating in structuring tree method and wants much more difficult.
In order to obtain in the proximal part of structuring tree（That is, in exit）Desired time-varying flow velocity rate and pressure
Profile, tip domain or in tip domain drag overall, total compliance, wave propagation effects and wave reflection effect are used as out
The attribute of mouth boundary condition.For elastic cavity boundary condition, can be by three parameter adjustment the first two in terms of, but wave propagate and
Reflection effect cannot be adjusted.Structuring tree boundary condition naturally models wave propagation effects, but is difficult to adjust knot
The parameter of structureization tree is to obtain the value of specific priori specified drag overall and compliance.
Invention content
By introducing, preferred embodiment described below includes the boundary condition for automatically adjusting tip vascular tree
Method, computer-readable medium and system.Measurement from patient is used for finding suitable for the reference of the root of tip vascular tree
Answering property and resistance.With reference to compliance and resistance be used to such as by the compliance and resistance for making structuring tree-model with it is specific
Patient iteratively solves attribute with reference to compliance and while matching with reference to resistance to adjust the attribute of structuring tree-model.So
Afterwards, the structuring tree of adjustment is used to calculation of boundary conditions, to calculate the flow in patient's vascular of scanning.
In the first aspect, the method for providing the boundary condition for automatically adjusting tip vascular tree.It obtains and indicates
The scan data of one or more outlets of patient's vascular and vascular.Structuring tree-model is each in one or more outlets
It is a that tip vessel tree structure is modeled.Each in structuring tree-model is adjusted to one or more characteristics of patient
With the matched function of one or more characteristics of structuring tree-model.Determine one for corresponding one or more outlets
Or multiple boundary conditions.The blood flow of patient's vascular is calculated as the function of boundary condition and is shown.
In second aspect, non-transient computer-readable storage media has been stored therein that indicate can be by programming
The data for managing the instruction that device executes, automatically to adjust the boundary condition for tip vascular tree.Storage medium includes being used for
Following instructions：Generating structure tree-model, wherein compliance and Resistance Value are configured to the value obtained from patient, according to structure
Change tree-model calculation of boundary conditions, boundary condition is counted in compliance and the characteristic of the structuring tree-model of Resistance Value according to response
It calculates, and the Hemodynamics attribute of patient's vascular is determined as to the function of boundary condition.
In a third aspect, the system for automatically adjusting the boundary condition for tip vascular tree is provided.Scanning
Instrument is configured to the vascular of scanning patient.Processor is configured to construct the boundary condition for determining vascular, root according to structuring tree
According to match that determination structuring tree constructs the of second characteristic of one or more and the value specific to patient of structuring tree construction
One characteristic, and determine with boundary condition the discharge characteristic of vascular.
The present invention is defined by the below claims, and in the portion anything is all not to be construed as to those
The limitation of claim.The more aspects and advantage of the present invention are discussed with reference to preferred embodiment, and later can be only
It is claimed on the spot or in combination.
Description of the drawings
Component and attached drawing not necessarily to scale, but focus on and illustrate in the principle of the present invention.Moreover, in the figure
Similar reference number indicates the corresponding part throughout different views.
Fig. 1 illustrates the vasculars of the sample scan with corresponding outlet tree-model；
Fig. 2 is the flow of one embodiment of the method for automatically adjusting the boundary condition for tip vascular tree
Figure；
Fig. 3 is the flow chart of one embodiment of the method for the compliance for calculating structuring tree；
Fig. 4 is one embodiment of the method for the attribute for iteratively solving structuring tree in being adjusted in particular patient
Flow chart；And
Fig. 5 is the block diagram of one embodiment of the system for automatically adjusting the boundary condition for tip vascular tree.
Specific implementation mode
The blood flow calculating of particular patient can be executed according to the patient data of such as medical imaging data.Fig. 1 is shown
Vascular 40 with two outlets 42 and a bifurcated that are indicated by patient data.Outlet be in the edge of scanning area or
The edge of scanning area（Such as it is disabled at position in the scan data from patient）Vascular artificial end.For
The part for the vascular tree that explanation does not indicate in patient data, in the end of represented vascular 40（For example, outlet 42）Place
Boundary condition be to be determined according to the model 44 of tip vascular tree.It, can be in order to more precisely compute the flow in vascular 40
Model 44 and corresponding boundary condition are automatically adjusted for particular patient.
Structuring tree boundary condition is adjusted to realize the desired value of drag overall and compliance.It finds and is used for structuring tree boundary
The parameter value of condition is to obtain the system that the inverse problem of desired integrity attribute is formulated as nonlinear equation
Solution.Measured value is matched by the respective value of structuring tree-model, in the hope of other attributes of solution structure tree-model.
Fig. 2 shows for automatically method of the adjustment for the boundary condition of tip vascular tree.Method is by medical diagnosis
Imaging system, examination station, work station, computer, picture archive and communication system（PACS）It stands, server, a combination thereof, Huo Zheyong
Implement in other devices of image procossing medical diagnosis data.For example, system, computer-readable medium shown in Fig. 5 and/
Or processor implements the method, but other systems can be used.
In the order presented or different order implements this method.Additional, different or less action can be executed.
For example, not executing action 30 and/or 32.In another example, it provides for scanning, the data of scanning is stored, by vascular
Location segment and/or the action for shifting result.
In real time（Such as during surgical procedures）Execute the action.Execution during the process allows clinical doctor
Life is diagnosed and/or treated based on the flow information calculated according to scan data.In other embodiments, as diagnosis
A part, the action execute after the procedure the procedure（For example, the part as examination executes）, or in order to plan in the process
It executes before.This method can be repeated to provide comparison information over time, or stream is provided for different vasculars
Measure information.
The action is automatically carried out by processor.User keeps patient scanned, or is obtained from previous scanning for suffering from
The scan data of person.User can activate program and input the information of particular patient, the radius of the outflow of such as scanned vascular,
Threshold value vascular tip dimensions, the measurement of pressure and/or the measurement of flow.As long as being activated, this method is in no any user
In the case of input（Such as in the case of not to the user test of the different attribute of structuring tree）It is performed.Alternatively
Ground, user assist in automanual program, and such as user indicates possible attribute value.It is defeated that other users can be provided
Enter, such as changing modeling parameters value, correction output and/or confirmation accuracy.
In action 20, the one or more outlets for the scan data and vascular for indicating patient's vascular are obtained.By sweeping
Patient is retouched to obtain data.Any kind of medical imaging data can be used.For example, obtaining computerized tomography（CT）, C arms x
Ray, Standard x-ray, similar CT（CT-like）, magnetic resonance（MR）Or ultrasound data, for indicating vascular and outlet.It can be with
Use any scanning sequency or method.
In the alternative embodiment, data are obtained by being loaded from memory.It will be from previously having executed to patient's
The data of scanning are stored in memory（Such as picture archive and communication system（PACS）Database）In.Number is selected from the database
According to.The data can be by such as being obtained by network or the transfer on portable memory devices.
Data indicate volume.Data are organized as or are formatted as frame, a data set, multiple data sets or other collection
It closes to indicate volume.Data indicate the position being distributed in three-dimensional.The volume includes one or more vasculars 40.Single branch or
Multiple branch vessel structures are expressed.Vascular 40 may include any number of outlet（For example, one or more）, and suffering from
Extend in the cardiac system of person or any range of vascular structure.
In one embodiment, the data sectional that will such as obtain.It is quasi- using threshold value, edge detection, contrasting detection, shape
Conjunction, flow detection, a combination thereof or other programs identify position associated with the vascular relative to other dissections.Scanning
Or the type of detection can cause such as to obtain number from vascular rather than other dissections by contrasting detection and/or flow detection
According to.Vascular can be represented as the outside of the tissue of blood vessel wall, the boundary of vascular tissue with blood and/or blood column.It can
Alternatively, acquired data are handled so that vascular 40 to be segmented.
In action 22, generating structure tree-model 42.In the figure 2 example, processor by action 24 in will be last
Tip vessel modeling automatically adjusts the tree construction to generate for tree construction and in action 26 based on the information from particular patient
Structuring tree-model.Additional, different or less action can be provided.The action is dividually executed or executes together, it is all
Such as adjust the part as modeling.
It creates structuring tree by processor and calculates the characteristic of structuring tree and generate structuring tree-model 42.Alternatively
Ground is pre-calculated and is stored from the associated multiple and different structuring tree of different root radius.In the arteries and veins of given patient
In the case of the radius of pipe, structuring tree is generated by loading pre-determined model appropriate.Because different from only passing through outlet
Radius and model is adjusted to particular patient, so scheduled structuring tree-model can be changed by the adjustment.Alternatively
Ground, the action for calculating structuring tree-model from the beginning are adjusted also based on other patient specific informations.In another reality
It applies in example, scheduled structuring tree-model is provided for the various combinations of possible patient specific information, to be directed to given patient
Given outlet identify and load the structuring tree-model appropriate precalculated.
Structuring tree-model 42 indicates tip vessel tree structure attachment outlet.To the blood flow and/or geometric form more than outlet
Shape is modeled.The general shape and material properties of structuring tree influence blood flow at the root of structuring tree-model 42 and right
The boundary condition answered.Because the patient scan data for the tip tree construction are disabled or are not used, make
Tip tree construction and corresponding flow are modeled or emulated with assuming.
Separated structuring tree-model is generated for each outlet.Because except through what is be available for its scan data
Other than vascular, each outlet is independent or not connected, so creating separated structuring tree-model.
Any structuring tree-model can be used.Known information can be used to generate model.For example, larger radius
Outlet is more likely to be connected with the tip tree construction of bigger, so the size of the radius of outlet can be used to the length to bifurcated
It is modeled with number.The root of structuring tree-model has radius identical with the outlet for being connect with outlet modeling, but
There can be different radiuses.It assume that the bifurcated other than three tunnels or more branch.It is every before next bifurcated
The length of a branch can be based on the radius for being attributed to the branch.For bifurcated, each tip branch can be assumed to have
Smaller radius.Radius reduces can be between branch in proportion, and such as a branch is more than another.Each branch is not with
The equal factor scales down, and creates asymmetric binary tree, wherein each branch since immediate branch on a radius
Reduce.Alternatively, Liang Ge branches radius is all identical, but is reduced with the factor.The factor that radius reduces can be sample plot
It is determining or hypothesis.
Model indicates entire tip tree construction or only a part.For example, using radius threshold（For example, 0.05 μm）.For
With any branch less than the radius of threshold value, model terminates.This creates terminal end with the given radius in structuring tree.
More than these terminal ends, there is no modeling, and the boundary condition at terminal end is assumed to be or as one of adjustment
Divide and is solved.In other embodiments, it is that vascular models entire tip tree, is terminated at artery.
In one embodiment of action 24, " the Numerical simulation and in Olufsen et al. have been used
experimental validation of blood flow in arteries with structured-tree
outflow conditions,” Annals of Biomedical Engineering, vol. 28, pp. 1281–
" the Boundary Conditions for Hemodynamics of 1299,2000 or Cousins et al.: The
Structured Tree Revisited,” Journal of Computational Physics, Vol. 231, pp.
One of structuring tree-model disclosed in 6086-6096,2012 and corresponding boundary condition.
Structuring tree is asymmetrical binary tree, wherein each vascular is axisymmetric and has constant radius.Dividing
Power law is used at fork, to describe the radius of two sub- vasculars：
(1)
Wherein, subscriptp, d 1Withd 2Respectively refer to godfather's vascular and two sub- vasculars.Power law assume for blood flow and
It is minimum to maintain the required energy of vascular system（For example, for laminar flow ξ=3.0）.Other values, such as base can be used
In the value of father's radius.For example, ξ=3.0 are used for big vascular coronarius, and smaller value is used for other vasculars.
It can determine the type of the flow for patient, and based on each section assigned value that the type is tree or tree（For example, ξ
2.33（For turbulent flow）With 3.0（For laminar flow）Between interval in change）.Value can depend on the heart system being just modeled
The part of system, such as 2.73 for coronary artery bifurcated.
For structuring tree boundary condition, bifurcated is considered asymmetrical, and therefore the radius of sub- vascular is to pass through
It is determined based on the radius of father's vascular using two parameters：
(2)
Wherein, α and β is two scale parameters between zero and one.Other ratios can be used.Scale parameter is predetermined
Or calculating.In order to calculate, the two additional parameters introduced the following definitions respectively, i.e. area ratio and dissymmetry ratio：
(3)。
Parameter ξ, η and γ are complementary by following relationship：
(4)。
Two scale parameters can be calculated as：
(5)。
From given root radius（For example, exit radius）Start, structuring tree is with regard to bifurcated until the radius of vascular becomes small
Until least radius.The length of each vessel branchings is expressed according to the radius of each vascular.For example, length and radius ratiol rr
It is 50, but other values can be used.
Once it is determined that the branched structure of structuring tree-model（That is, geometry）, just to the flow of tree, material and/or
Other attributes are modeled.Any modeling of the non-geometrically characteristic of structuring tree-model can be used.In one embodiment
In, use Young's model（Young's model）.Young's model includes a variety of materials attribute.Because parteriole by with main artery
The organizational composition of same type, so can also be used for for aortic relationship based on the best fit to experimental data
The wall attribute of the structuring tree down to minimum vascular indicated in structuring tree.One example expression provides as follows：
(6)
Wherein, x is the distance along branch, r0It is the radius of branch, k1-3Material properties, and E be Young's modulus and
H is the thickness of blood vessel wall.Table 1 shows the Example Parameters Values of the structure and attribute of definition structureization tree.
These values are example or initial value.For given patient, value can be different due to adjusting to patient.Value
One or more of be used as not adjusted and the constant that changes, such as ξ, γ, η, α, β,l rr And/or k2。
The governing equation that blood flow is used in structuring tree is to receive to tie up Stokes from axial symmetry（Navier-Stokes）Side
Journey exports, but can use other modelings of flow.Because in parteriole viscosity effect than the inertia effect more much more significant, institute
To ignore nonlinear inertial item.If flow and pressure are periodic, analytic solutions can be determined in frequency domain：
(7)
(8)
Wherein, Q is flow, and P is pressure, and ρ is density,cIt is velocity of wave propagation, andF J Depending on Bessel function
（Bessel function）, and manage number using Butterworth（Womersley number）To be calculated.C A It is that area is complied with
Property, and can be determined that：
(9)
Wherein, A is area of section.
The root impedance of structuring tree is recursively calculated using following formula：
(10)
Wherein, It is the impedance of the inlet in vessel segment or branch, and
AndIt is the impedance in the exit in vessel segment or branch.Then, it is export boundary condition root impedance to be applied, and is indicated
For：
(11)。
By applying inverse Fourier transform,It is converted intoAnd use convolution theorem by equation（11）Weight
It is written as：
(12)
WhereinTIt is the period.
In action 26, the structure of material properties, discharge characteristic and/or structuring tree-model is adjusted to specific trouble
Person.The value of one or more parameters of the adjustment or appointment structuring tree-model, leads to different boundary conditions.Adjustment
Wherein each structuring tree-model.
Not instead of randomly assigned value is not with determination boundary condition appropriate, by by the one or more of structure tree-model
One or more characteristics match of characteristic and patient adjust structuring tree.For example, structuring tree-model can be used to calculate
Resistance and/or compliance in root or exit.Resistance and/or compliance for reference in matching can be according to patients
Pressure or the measurement of flow calculate.Then, by the drag overall of structuring tree and/or total compliance and in the patient in exit
Resistance and/or compliance match.The Matching and modification structuring tree boundary condition.
Change each attribute of structuring tree to provide matching.By for solving compliance and/or resistance boundary condition
Match come the combination of the attribute or characteristic that determine structuring tree-model.
Any adjustment, such as adjustment suitable for Hemodynamics emulation can be used.In one embodiment, by structuring
The determination of tree parameter is formulated as the solution with the system of the nonlinear equation of root, herein the category of the calculating of structuring tree
Property and reference values match.It is directed to one group of parameter value in order to determinex i Object function：f(x i )Residual error（residual）Value, be
Structuring tree calculation equation（10）In zero frequency impedance, and determine total compliance.This group of parameter valuex i It is to change or ask
Solution is one of to be adjusted or multiple attributes or characteristic.
Nonlinear system is solved using broken line trust region methodf(x i )=0 is pseudo-Newtonian algorithm（quasi-
Newton method）, but other optimizations can be used.The performance of this method for undated parameter is independently of really joining
Difference in number and target function value.However, because the absolute value of drag overall and total compliance usually differs by more than six quantity
Grade, so as described below, both parameter and target residual have been necessarily to scale using representative value.
The nonlinear system of equation can be formulated as：
(13)
Wherein,R term It is the terminal resistance forced in each exit of structuring tree（For example, due to the model of threshold value
The terminal resistance of the minimum bifurcation of end）,R comp It is the calculating resistance of structuring tree,R ref It is the reference resistance from patient,C comp It is calculating compliance, andC ref It is the reference compliance from patient.In this example, RtermAnd k3It is to change or solve
To provide matching（For example, homodyne is different）Structuring tree two attributes or characteristic.It can be in solution using additional, different
Or less characteristic.
Reference value is obtained from patient（For example,C ref WithR ref ）.Measure some aspect of the cardiac system of patient.For example, with
Cuff（cuff）Or ultrasonic measurement pressure or the difference between systolic pressure and diastolic pressure.As another example, with ultrasound
The other aspects of wave measurement volume flow, flow velocity rate or flow.Therefore for any two patient, this aspect is generated not
Same or identical value.
The pressure of measurement, flow of measurement or both are used to calculate the reference compliance and/or resistance of patient.It can be with
Use the estimation for carrying out any currently known of the pressure of measurement and/or the compliance of flow or resistance or developing later.Example
Such as, pulse-pressure method can be used to estimation compliance, while can be according to the ratio between pressure and flow velocity rate estimated resistance.Pressure
Power and flow velocity rate invasive ground or can non-invasively measure, or be estimated according to physiological mode or scaling rule
Meter.
In order to iteratively solve the nonlinear equation for structuring tree-model, the drag overall and always of structuring tree is calculated
Compliance.In order to determine the material properties of structuring tree-model（For example, k3）With terminal resistance（For example, Rterm）, calculating causes
The combination for the value matched.The adjustment makes structuring tree be suitable for given patient, is being exported then to calculate（For example, structuring tree
The root of model is total）The boundary condition at place.
The corresponding adjustment of drag overall and drag overall is the function in the terminal resistance of the end of structuring tree.In order to adjust
The resistance at the terminal vascular of structuring tree is assigned in drag overall.All terminal resistances are considered equal, this is reasonable
It is assumed that because all terminal vasculars have almost the same radius.In other embodiments, terminal resistance can pass through end position
It sets to change.The drag overall of structuring tree is equal to equation（10）In zero frequency determine impedance.
Any method for making the drag overall by structure tree representation adapt to can be used.In a method, modification exists
The least radius that structuring tree is terminated at it.The drag overall of calculating matches during being used for iterative solution with reference value.Modification
Tip radius can be provided in only discrete space, and the adjustment in discrete space so that the perfect matching with particular value
It is less likely.In addition, if drag overall is very high, then least radius becomes very small, causes to determine at the root of structuring tree
Sizable increase of calculating cost required by impedance.For forcing for the resistance in each end.
In another method, force resistance at each terminal vascular of structuring tree.Specific drag overall passes through multiple
It exports to divide, and forces result at the terminal sites of structuring tree.The resistance of vascular only inside structuring tree with
Terminal resistance is compared to being negligible, then this method can just lead to desired result.The hypothesis is only applicable to main artery, without
Drop to the parteriole of the structuring tree of parteriole level suitable for bifurcated.
Such as another method, matching can be used to calculate resistance.Matching, which solves, will be applied to one of each end
Terminal resistance, or solution will be applied to the different terminal resistances of corresponding end.Desired matched iterative solution is provided
Solve the terminal resistance of structuring tree.
The compliance of structuring tree is determined using any method.By adjusting one or more such as equations（6）'s
k1And k3Material properties make to match with reference to total compliance and total compliance of structuring tree.
It is vascular by calculating the institute in structuring tree in a method of the compliance for calculating structuring tree
The summation of volume compliance analytically calculates total complianceC an .The appearance of given branch is determined using following area compliance
Product complianceC anb ：
(14)
Wherein,l rr It is the ratio between the length introduced and radius.
1 He of tablerIt is the radius of corresponding vascular.Such as equation（9）In give, CAIt is the elasticity of the wall of vascular.
In another method, pulse method calculates total compliance of structuring tree with being used for numerical value.Fig. 3 is shown
The estimation of total compliance of structuring tree boundary condition based on the pulse method.First, using asymmetric Gaussian function
It counts to calculate resolution flow rate profileq(t).It is calculated according to the root radius of the mean blood flow velocity value of 20cm/s and structuring tree
The mean flow rate of time-varying profile.The empirically determined stream rate profile for giving radius can be used.Alternatively, it uses
The flow velocity rate of measurement.It is next determined that the impedance z (t) of structuring tree boundary condition（Referring to equation（10））.Then, pass through
Force the stream rate profile being previously calculated in the inlet of structuring tree to calculate to run.As a result, obtain pressure outline, by with
To calculate the resistance of structuring tree（）And pulsePP ST .Finally, structure is calculated using pulse method
Change the equivalent compliance of treeC PPM .Pulse method is based on the average and pulse at time-varying flow velocity rate, the position in arterial tree
Pressure estimates the compliance in the downstream of the position in arterial tree.It is to be based on two element elastic chamber models, and the resistance of model
Power directly basis enters data to calculate and only compliance is unknown.
Last compliance value is to be substantially independent of selected mean blood flow velocity（For example, difference is 10-8 cm4∙
s2The magnitude of/g）, and numerical value the resistance that calculates be substantially equivalent to equation（10）In zero frequency impedance（For example, poor
It is different 10-5 g/(cm4S) magnitude）.
In order to be used in matching solution, the method applied several times that will be shown in Fig. 3, until for structuring tree boundary condition
Until adjustment process restrains.The fact that this respect and pulse method are iterative process causes for reducing total execution time
Pulse method inside high-efficiency search method application.One exemplary search method is broken line trust region method.It should
Broken line trust region method is not only applicable to adjustment structuring tree parameter, and applied to determining complianceC PPM , cause to refer to
PulsePP ST 。
Volume compliance and computationally faster than pulse method.Pulse method can provide more accurate
Or effective result.The other methods for the total compliance for calculating structuring tree can be used.
Using for reference to and structuring tree compliance and resistance calculating, the nonlinear system of equation can using
With solving.By between the compliance measured from patient and the compliance of structuring tree-model difference and survey from patient
Difference between the resistance and the resistance of structuring tree-model of amount minimizes.Any optimization, such as trust region side can be used
Method.
Fig. 4 is the flow chart of a method for adjustment.The adjustment solves the attribute of structuring tree using matching
Or characteristic.Additional, different or less action can be provided.Action is executed by the order or different order that show,
The execution action 42 such as before action 40.
In the example of fig. 4, trust region method be used to optimize.Finding the root of the nonlinear system of equation can use
Formula is expressed as optimization application.In order to apply trust region method, it is formulated merit function, is used for determining residual error function
Practical reduction how to show as to prediction reduction it is related.Any merit function can be used, such as：
(15)
Wherein, operatorRefer to Euclid norm.Another aspect pattern function is based on around current pointx i 'sg (x)Taylor series expansion：
(16)
Wherein,J i Bex i Placef(x) Jacobian, andsIt is taken to minimize merit function
Stepping.x i It is the attribute for the part for being adapted to adjustment or the collection of characteristic, such as k3And Rterm。
In action 40, the least radius of the end of structuring tree is initialized before iterative solution.The initialization
Ensure the resistance of structuring tree-model be it is positive to with reference to impedance match.Exemplary algorithm is provided below to will at which
The least radius initialization that structuring tree is terminated.
Algorithm 1. initializes least radius
Set r min = 0.005 cm
while(true)
Compute total resistance (R comp ) using r min and R term = 0.0
if R comp < R ref
break
else
r min = r min + 0.001
end(if)
end(while)
Other algorithms can be used.
Using 50 μm of initial value, the beginning of parteriole level is nearly corresponded to, but other initial values can be used.Such as
The drag overall for the calculating that fruit is obtained with zero terminal resistanceR comp Less than reference value, then algorithm termination, otherwise algorithm is incrementally increased
Least radius is until the drag overall of calculating becomes less than reference value.Algorithm 1 ensures to need positive terminal resistance to obtain
With reference to resistance.
In action 42, the material properties of initialisation structuresization tree before iterative solution.The initialization ensures structure
The compliance for changing tree is positive being matched with reference to compliance.The material properties set for initialisation structuresization are provided below
Exemplary algorithm.
Algorithm 2. initializes wall attribute
Set k1 = , k3 = 0
while(true)
Compute total compliance (C comp )
if C comp < C ref
break
else
k1 = k1 -
end(if)
end(while)。
In this example, the parameter by Young's model is initializedk 1The material properties of expression.The value being displayed in Table 1 is to use
In k1First value.k 3It is arranged to 0.Total compliance of structuring tree is calculated using these settings or value.It has used and calculation
Similar method in method 1, whereink 1Value become less than by the compliance for being incrementally decreased until calculating and be with reference to compliance
Only.
Use k1Value and least radius, execute for adjustment trust region optimization.It is used to adjust in one embodiment
Whole solution uses Jacobian matrix and broken line trust region, but can use for optimization, merit function and/or step size computation
Other solutions.In action 44, initial Jacobian is calculated（J）.In action 46, typical step value is determined, so as to
It being capable of update and parameter value of the bi-directional scaling for parameter（For example, k3And Rterm）The two Jacobian matrix.Using from
The gradient information of Jacobian estimation selects certain representative values for target residualf typAnd it determines and is used for each parameter
Typical step-length：
(17)
Whereinn eq It is the number of equation, is 2 in this case（Referring to equation 13）.Initially, using aroundR term =
104 g/cm4S andk 3 = 5∙104Value or the central difference formulas of other initial values calculate JacobianJ.Target
The representative value of function is selected as the 1/50 of reference value, but can be calculated using other representative values or Heuristics.
In action 48, fixed point methods are used to find the finite difference Jacobian determined using typical step-length,
It is consistent with the representative value of selected target residual.The component that Jacobian is approached is calculated as follows：
(18)
Wherein use equation（17）To calculate, ande i Withe j Indicate the unit on i-th of direction and j-th of direction
Vector.As long as this is by correspondingWithIt is worth Euclid's model of the difference of standardized two continuous Jacobians
Number is less than 10-6Or the iterative process that another value just terminates in action 50.The typical step value determined by the iterative process
It is standardized with the amount that will be used for broken line trust region algorithm with being used in together with typical target residual error in following action.
In action 52, broken line trust region method is initialized using the value of table 2 or other values.
In action 54, target residual is calculated in trust region algorithmf(x i ), and execute convergence in action 56 and survey
Examination.If each of residual error function is less than 1/100 or corresponding typical residual values（）Other factors, then action 58
Middle algorithm terminates.Otherwise new Jacobian is calculated in action 60J i (x i ), and act 62 middle polyline algorithms by with
To determine next step values i .In action 62 stepping is calculated by finding the approximate solution of subproblems i ：
It obeys
Wherein, Δ is trust region radius.
In the case where giving specific trust region, broken line algorithmic notation Cauchy（Cauchy）Stepping（Along under steepest
The path of drop determines）With the combination between newton stepping.Therefore, Cauchy's point is calculated as：
(19)
Wherein
(20)
Newton stepping is calculated using following formula：
(21)。
Newton stepping is introduced to improve the convergence rate especially in the terminal stage of search process.Trust region method
Ability（power）It is that can manage transformation from the steepest descent with its good global property to Newton method wherein
Complexity.
In one embodiment, fold-line method is implemented as：
3. fold-line method of algorithm
Compute
if
else
Compute
where τ is the largest value in [0,1] such that
end(if)
It can implement fold-line method using other algorithms.
The ratio between in action 64, each iterative calculation for trust region is practical and prediction reduces.The ratio has estimated two
Merit function is approached in the secondary much degree of model, and is represented as：
(22)。
If ratio ρ i Less than ρlow, then ω is useddownTo update trust region radius.If ratio is more than ρhigh, then
Use ωupTo update trust region.If ratio is more than ρ0, then receive steppings i 。
In one embodiment, the update of trust region radius is implemented as：
4. trust region method of algorithm
It is calculated using fold-line methods i
It uses（22）To calculate ρ i
if ρ i < ρlow
Δ = ωdownΔ
else
if ρ i > ρhigh and = Δ
Δ = ωupΔ
end(if)
end(if)
if ρ i > ρ0
x i+1 = x i + s i
end(if)。
Other algorithms can be used to implement the update of trust region radius.The test for acting 66 is incorporated by this method
Step value or update x are recalculated in action 68i+1, and back in the calculating for acting the target residual in 54.
With reference to figure 2, the structuring tree according to corresponding adjustment is that each of outlet determines one or more boundary conditions.Root
Carry out calculation of boundary conditions according to the structuring tree-model such as adjusted to particular patient.In the characteristic that structuring tree-model can be used
Any one.For example, using the impedance calculated for structuring tree come according to equation（7）With（8）It determines on the cardiac cycle
Flow or pressure outline（Referring to equation（11）With（12））.The k determined by the solution of tree construction1And k3Value be used to
Find the area compliance used in determining these boundary conditions.Other examples boundary condition can be partially in response to end
End resistance RtermPressure outline, the terminal resistance RtermIt is solved by creating structuring tree.The tree knot of adjustment can be used
The characteristic of structure（Such as, any one of Young's model or navier stokes equations characteristic）Other information is determined as side
Boundary's condition.It can be according to one or more material properties and by adjusting the terminal resistance solved to particular patient by pressure wheel
Wide and/or time-varying flow velocity rate is calculated as boundary condition.
For finding the characteristic response of boundary condition in compliance and resistance.By patient spy during the establishment of structuring tree
Fixed compliance and/or resistance is used as adjusting to patient with reference to by structuring tree.It can be according to the adjustment for given outlet
Tree calculate any boundary condition.
In action 30, one or more blood flow are calculated for vascular 40.Boundary condition, which is used in, to be calculated in the amount.Resistance
Power, compliance, wave propagation, wave reflection, a combination thereof, or other characteristics of total tip vascular tree for given outlet can be by
For determine volume flow, pressure or in vascular flow other quantizations.It is based on tip vascular to flow part in vascular
The characteristic of tree, is illustrated by boundary condition.Any Hemodynamics attribute of the vascular of patient can be determined that boundary condition
Function.
In action 32, blood flow is shown.Image is presented with blood flow on screen or display device.Image is the amount
's.Other information can also be presented, such as by the description of the vascular of scan data（rendering）, about vascular geometry believe
Breath, the attribute of structuring tree, boundary condition are beneficial to the other information diagnosed to patient.For example, from given view
Vascular is shown by three-dimensional describe of scan data.Such as the blood flow of the flow velocity rate of time and/or pressure is shown as
It is adjacent to and describes or be covered in curve graph, block diagram or numerical value on describing（For example, the average value or variance in each period）.
The method that known arterial tree can be used to test chart 2-4, to adjust total resistance of structuring tree boundary condition
Power and total compliance.Specifically, the drag overall of the export boundary condition in known arterial tree and total compliance value are used as joining
Value is examined, and is dividually that each of any one of various vasculars go out portal canal adjustment structuring tree boundary condition.In table 3
In show the result of adjustment process.For some arteries, the least radius that structuring tree terminates at which is more than 0.005cm.
Under those circumstances, even if not having terminal resistance, total initial resistance is also greater than reference value.
The drag overall value given in table 3 corresponds to resting state.If will be emulated to physical training condition, drag overall
With smaller and it can use the least radius of bigger.In general, the terminal resistance forced at the terminal sites of structuring tree
Three to five orders of magnitude higher than the drag overall of structuring tree.
About the adjustment of total compliance, as a result show that the compliance of analytical Calculation is significantly different than based on pulse
The compliance of method.Pulse method may be more accurate.Aboutk 1, algorithm 2 changes the value, shows and usually requires to compare table
The initial value shown in 1 is smallerk 1Value, to be directed tok 3Obtain the reference compliance with positive value.
Although calculating compliance to numerical value at each adjustment iteration, it is used to adjust each knot on a personal computer
The execution time of structureization tree can be less than 10 seconds.The adjustment proposed is computationally efficient.Convergence can only be needed
3-10 iteration.Broken line trust region method is applied not only to the adjustment of structuring Pterostyrax property, and is applied to as pulse
Pressure method and the search process executed.
It is physiological with reference to resistance and compliance value, allows the successful application of adjustment process.Equation（13）It can
Can not have solution, if any with unpractical value in two reference parameters.For example, if too with reference to compliance value
Height, then may require fork 1Negative value, transfer to lead to unstable structuring tree impedance.
Structuring tree boundary condition is automatically adjusted to carry out Hemodynamics calculating.Adjust structuring tree perimeter strip
The parameter of part is to obtain the particular reference value for drag overall and total compliance.Initially make two parameters（Structuring tree at which
The least radius and constant of terminationk 1）It adapts to, to determine starting point, leads to the positive value for practical adjusting parameter.Two
Parameter is suitable for adjusting two attributes of structuring tree：Terminal resistance（It is equal at all end places）, and determine wall attribute
Constant（k 3）.Other initial and/or adaptability attributes can be used.
Adjustment is executed using broken line trust region method, is efficient method, it is only necessary to 3-10 iteration.It can go out
The iteration of existing other numbers.One advantage of the method proposed is not need initial searching algorithm, is obtained by algorithm 1 and 2
Initial starting point be the good enough initial solution for trust region method.
Method can be easily incorporated into the adjustment algorithm of the higher order calculated for Hemodynamics, be hit by a bullet
Property chamber boundary condition is used to match certain particular patient Hemodynamics attributes.Be not at each iteration direct use by more
The given elastic cavity parameter value of high order adjustment algorithm, but the structuring tree for using structuring tree boundary condition, and adjusting
It is used to regulation and refers to resistance and compliance value.Alternatively, the parameter for directly adjusting structuring tree boundary condition, without the use of
Resistance and compliance are as intermediate quantity.
The system that Fig. 5 shows the boundary condition for adjust automatically tip vascular tree.System includes medical image system
11, processor 12, memory 14 and display 16.Processor 12 and memory 14 are shown as dividing with medical image system 11
It opens, it is associated with the computer of separate medical image system 11 or work station in this way.In other embodiments, processor 12 and/
Or memory 14 is a part for medical image system 11.In the alternative embodiment, system is for adjusting boundary condition simultaneously
According to the data obtained in real time by the system separated or using the particular patient data stored in memory previously obtained come
Calculate work station, computer or the server of blood flow.For example, providing the medical imaging for obtaining the data for indicating volume
System 11, and provide separated database, server, work station and/or computer for being adjusted and calculating.It can
To use additional, different or less component.
The calculating unit, device or machine of such as system of medical image system 11 and/or processor 12 are by hardware, software
And/or it is configured for the design for executing calculating or other actions.Calculating unit separately or combined in being operated each other, to hold
Any given action of the action of row such as Fig. 2-4.Action is by another in one in machine element, calculating unit
Or the combination of calculating unit executes.Other components can by calculating unit using or control scan or execute other work(
Energy.
Medical image system 11 is the form for scanning any currently known of patient or developing later.Medical imaging system
System 11 scans patient for vascular regions.For example, using C arm X-ray systems（For example, the DynaCT from Siemens）, it is similar
CT system or CT system.Other forms include MR, x-ray, angiography, fluoroscopy, PET, SPECT or surpass
Sound wave.Medical image system 11 is configured as obtaining the medical imaging data for indicating one or more vasculars.Data by using
The transmitting carried out by scanner scans patient and/or is obtained by receiving signal from patient.The type or pattern of scanning can be with
Lead to the data for only receiving vascular.Alternatively, receive the data of volume area, and according to the information of other dissections come by
Vessel information is divided.
Memory 14 is buffer, caching, RAM, removable media, hard disk drive（hard drive）, magnetic, light, number
According to library or memory that is other currently known or developing later.Memory 14 is single device or two or more dresses
The group set.Memory 14 in system 11, a part for computer with processor 12, or in the outside of other components or
Far from other components.
14 storage organization tree of memory, the characteristic of structuring tree, intermediate solution data, patient measurement characteristic, scanning
Data or other vasculars or flow information.Memory 14 stores the data obtained from process described herein, such as stores
Constant, initial value, the value of adjustment or other attributes.
Memory 14 is additionally or alternatively the non-transient computer-readable storage media for having process instruction.Storage
Device 14 stores the data for indicating instruction, and described instruction can be executed by the processor 12 programmed automatically to adjust for tip arteries and veins
The boundary condition of Guan Shu.Provided on computer readable storage medium or memory for implement process described herein,
It is the instruction of method and/or technology, the computer readable storage medium or all cachings in this way of memory, buffer, RAM, removable
Except medium, hard disk drive or other computer readable storage mediums.Computer readable storage medium includes various types of easy
The property lost and non-volatile memory medium.Illustrated in figure or functions described in this article, action or task are in response to being stored in meter
One or more instruction set among or on calculation machine readable storage medium storing program for executing execute.Function, action or task are independently of specific
Instruction set, storage medium, processor or the processing strategy of type, and can be by software, hardware, integrated circuit, firmware, micro- generation
Code etc. executes, and is either individually or in combination operated.Similarly, processing strategy may include multiprocessing, it is multitask, parallel
Processing etc..In one embodiment, instruction is stored on removable media device with so that Local or Remote system is read.
In other embodiments, instruction is stored in remote location, to be shifted by computer network or by telephone wire.
In another embodiment, instruction is stored in given computer, in CPU, GPU or system.
Processor 12 is general processor, digital signal processor, three-dimensional data processor, graphics processing unit, special
Integrated circuit, field programmable gate array, digital circuit, analog circuit, a combination thereof or for handling the other of medical data
Device that is currently known or developing later.Processor 12 is single device, multiple devices or network.For more than one device,
The in parallel or sequentially division of processing can be used.The different devices of composition processor 12 can execute different functions, such as
The calculating of the adjustment and the boundary conditions and/or flow that are carried out by another device that carried out by a device.Implement at one
In example, processor 12 is the control processor of medical image system 11 or other processors.Instruction of the processor 12 according to storage
It is operated to execute various actions described herein.
Processor 12 be configured as the one or more of the other characteristic constructed according to structuring tree with specific to the value of patient
Matching come determine structuring tree construct characteristic.For example, the terminal resistance and material properties of structuring tree construction are according to knot
Total compliance of structureization tree construction and drag overall come with the compliance in the exit of the vascular in given patient and the matching of resistance
It determines.The structuring tree construction created by processor 12 indicates the vascular tree of vascular tip, obtained for it scan data and
Execute calculating.
Processor 12 is configured as constructing the one or more boundary conditions for determining vascular according to structuring tree.In vascular
The discharge characteristic in exit is boundary condition.Structuring tree characteristic is used to calculation of boundary conditions.The characteristic itself can be
Boundary condition.
Processor 12 is configured as determining the discharge characteristic of vascular with boundary condition.In part with for tip vascular
Boundary condition come determine the flow in vascular some aspect.
Processor 12 is configurable to generate image.Image includes the amount of the calculating of flow in vascular.Image may include arteries and veins
The expression of pipe and/or structuring tree-model.
Display 16 is CRT, LCD, plasma, projecting apparatus, printer or other outputs dress for showing image
It sets.Display 16 shows the one or more amounts calculated using boundary condition.The amount can be displayed in chart, curve graph
And/or on the image.
Although describing the present invention by reference to various embodiments above, but it is to be understood that, do not departing from this
Many changes and modifications can be done in the case of the range of invention.Therefore it is considered as example to be intended to aforementioned detailed description
Property and not restrictive, and it should be understood that following claim includes being intended to limit the spirit and scope of the present invention
All equivalents.
Claims (20)
1. one kind is for automatically adjusting（26）The method of the boundary condition of tip vascular tree, the method includes：
It obtains（20）Indicate one of the vascular of patient and the vascular in the edge of the scanning area for scan data
Or the scan data of multiple outlets；
Tip vessel tree structure is modeled for each in one or more outlets of the vascular（24）, the end
Tip vascular structure models the vascular system extended from one or more of outlets of the vascular；
Function as one or more characteristics match with the patient adjusts（26）The modeling（24）, one or more
A characteristic includes the resistance and compliance of the root of the tip vascular tree-model；
Based on the relationship between the flow and pressure in the exit of the vascular according to the adjustment（26）It determines（28）For
One or more boundary conditions of corresponding one or more outlets；
For the vascular of the patient, calculate（30）The blood flow of function as the boundary condition；And
It is shown in real time to clinician（32）The blood flow.
2. method described in claim 1, wherein modeling（24）Including modeling（24）For structuring tree-model, and wherein adjust
（26）Including adjustment（26）The structuring tree-model.
3. method described in claim 1, wherein modeling（24）Include being built with the radius of the bi-directional scaling for bifurcated
Mould（24）, the length of the branch between bifurcated is the function of corresponding radius and root radius is based on according to scan data
Outlet radius.
4. method described in claim 1, wherein adjusting（26）Including：As the resistance that is measured from the patient and described
Compliance and the modeling（24）The resistance and the matched function of the compliance be adjusted（26）.
5. the method described in claim 4, wherein the resistance and the compliance that are measured from the patient include from described
Patient measures pressure or flow, and according to pressure or flow rate calculation（30）The resistance and the compliance.
6. the method described in claim 4, wherein adjusting（26）Include the nonlinear system that equation is solved with the matching, institute
State matching include will be in the compliance that is measured from the patient and the modeling（24）The compliance between difference
And in the resistance measured from the patient and the modeling（24）The resistance between difference minimize.
7. method of claim 6, wherein it includes executing trust region optimization to solve.
8. the method described in claim 4, wherein the modeling（24）The resistance be arranged in the end of structuring tree
The function of the terminal resistance at place, and the wherein described adjustment（26）Including initializing the least radius for the end so that
The resistance of the structuring tree be it is positive to the impedance match from the patient.
9. the method described in claim 4, wherein the modeling（24）The compliance be determined according to pulse method.
10. the method described in claim 4, wherein modeling（24）Including being modeled to attribute with Young's model（24）, described
Young's model includes the first material properties, and is wherein adjusted（26）Including executing the function as first material properties
The matching.
11. method according to any one of claims 10, wherein adjusting（26）The second material properties including initializing the Young's model,
Make the modeling（24）The compliance be positive being matched with the compliance from the patient.
12. method described in claim 1, wherein adjusting（26）Including：It is carried out as the function of end resistance and material properties
Adjustment（26）.
13. method described in claim 1, wherein adjusting（26）Including：Letter as Jacobian matrix and broken line trust region
Number is adjusted.
14. method described in claim 1, wherein determining（28）One or more of boundary conditions include that basis is such as adjusted
The modeling（24）To determine（28）Time-varying flow velocity rate and pressure outline for the primary outlet in the outlet.
15. method described in claim 1, wherein calculating（30）The blood flow include as the boundary condition function into
Row calculates（30）, the boundary condition includes resistance, compliance and wave and reflection effect, and is wherein shown（32）Including with
The blood flow is shown（32）Image.
16. a kind of non-transient computer-readable storage media（14）, wherein storing the data for indicating instruction, described instruction can be by
The processor of programming（12）It executes automatically to adjust（26）For the boundary condition of tip vascular tree, the storage medium packet
It includes for following instructions：
It generates（22）The structuring tree-model of the vascular system extended from the outlet of vascular, the structuring tree-model are utilized and are set
Be set to the value obtained from patient compliance and Resistance Value and generate；
It is calculated according to the structuring tree-model（28）The boundary condition of the outlet, the boundary condition is according to response in described
The characteristic of the structuring tree-model of compliance and Resistance Value calculates；
Function as the boundary condition determines（30）The Hemodynamics attribute of the vascular of the patient；And to clinic
Doctor shows the Hemodynamics attribute of the vascular.
17. the non-transient computer-readable storage media described in claim 16（14）, wherein generating（22）The structuring tree
Model includes generating（22）The structuring tree-model of root radius with the vessel radius for being configured to the patient, and
Described in being solved with the compliance and the Resistance Value and as the matching of the described value obtained from the patient with reference to value
The characteristic of structuring tree-model, the reference value obtained from the patient are the pressure measured from the patient, the stream of measurement
The function of amount or the pressure and flow that measure.
18. the non-transient computer-readable storage media described in claim 16（14）, wherein generating（22）Including iteratively asking
Nonlinear equation of the solution for structuring tree-model, it is described to solve material properties and the end for providing the structuring tree-model
End resistance, and the calculating of wherein boundary condition（28）Including calculating（28）As the material properties and the terminal resistance
Pressure outline, time-varying flow velocity rate or the two of function.
19. one kind is for automatically adjusting（26）The system of the boundary condition of tip vascular tree, the system comprises：
Scanner（11）, it is configured to the vascular of scanning patient；
Processor（12）, it is configured to determine the perimeter strip of the vascular according to the structuring tree of the outlet of vascular construction
Part, what it is according to structuring tree construction includes second characteristic of one or more of total compliance and drag overall and described in being included in
The matching of the compliance in the exit of vascular and the value specific to the patient of resistance determines what the structuring tree constructed
First characteristic of terminal resistance and material properties as structuring tree construction, and described in boundary condition determination
The discharge characteristic of vascular；And
Display is configured as showing the discharge characteristic of the vascular.
20. the system described in claim 19, wherein structuring tree construction indicates the vascular tree of the vascular tip.
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| US14/167,120 US20140236547A1 (en) | 2013-02-15 | 2014-01-29 | Patient-specific automated tuning of boundary conditions for distal vessel tree |
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| Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions;Mette S.Olufsen;《Annals of Biomedical Engineering》;20001231;第28卷(第11期);第1281-1299页 * |
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