CN103995989B - The adjust automatically of the particular patient of boundary condition for tip vascular tree - Google Patents

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

Patient-specific automatic adjustment of boundary conditions for the peripheral vascular tree

related application

This patent document claims the benefit of the filing date of U.S. Provisional Patent Application (Serial No. 61/765,165) filed February 15, 2013 under 35 U.S.C. §119(e), which is hereby incorporated herein by reference.

technical field

The invention relates to a patient-specific automatic adjustment of boundary conditions for the peripheral vascular tree.

Background technique

This embodiment relates to the calculation of blood flow in a patient's vasculature. In particular, the boundary conditions at the outlet of the vessel are adjusted for the particular patient in order to calculate the vessel flow.

For the outlet of a vessel whose flow is calculated, several outlet boundary conditions have been proposed for three-dimensional, one-dimensional or multi-scale models of the peripheral vascular tree. A simple approach is to use flow rate or pressure directly, but for a particular patient geometry, this approach depends on the availability of flow rate or pressure quantities via measurements. Furthermore, pressure boundary conditions may lead to physiologically incorrect results for vessel geometries with multiple outlets.

In another approach, a three-element elastic cavity model uses simulations with electrical circuits. The boundary conditions are the resistance and compliance of the peripheral vascular tree at the outlet. Resistance is modeled as two resistors connected in series, and compliance is modeled as capacitance or energy storage. Although the elastic chamber boundary condition consists of only three components (for example, two resistors and a capacitor), the elastic chamber model can be tuned to match a specific patient population.

Neither of these approaches models the physiological aspects of the downstream vasculature or the terminal vascular tree. Especially when wave propagation aspects are of interest in computational studies, boundary conditions according to these methods are not able to capture wave propagation phenomena in the distal part of the loop (i.e. in the region where the model-based grouping together is the outlet boundary condition) .

In another approach capable of modeling wave propagation effects at the tip of an artificial outlet, a structured tree is used to determine boundary conditions. The peripheral vasculature was modeled as a simple geometry obtained with several simplifying assumptions. These assumptions allow the analytical calculation of the impedance of the structured tree, which is then imposed as periodic boundary conditions at the exit of the geometric model. However, tuning for a specific patient calculation is much more difficult in a structured tree approach.

To obtain the desired time-varying flow rate and pressure profile in the proximal portion of the structured tree (i.e., at the outlet), the total resistance, total compliance, wave propagation effects, and The wave reflection effect can be used as a property of the exit boundary condition. For elastic cavity boundary conditions, the first two aspects can be tuned by three parameters, but wave propagation and reflection effects cannot be tuned. Structured tree boundary conditions naturally model wave propagation effects, but it is difficult to tune the parameters of the structured tree to obtain specific a priori specified values of total resistance and compliance.

Contents of the invention

By way of introduction, the preferred embodiments described below include methods, computer readable media, and systems for automatically adjusting boundary conditions of a peripheral vascular tree. Measurements from the patient are used to find the reference compliance and resistance for the root of the peripheral vascular tree. The reference compliance and resistance are used to adjust the properties of the structured tree model, such as by iteratively solving the properties while matching the compliance and resistance of the structured tree model to the specific patient reference compliance and reference resistance. The adjusted structured tree is then used to compute boundary conditions for computing flow in the scanned patient vessel.

In a first aspect, a method for automatically adjusting boundary conditions of a peripheral vascular tree is provided. Scan data representing a vessel of the patient and one or more outlets of the vessel is acquired. The structured tree model models the distal vessel tree structure for each of the one or more outlets. Each of the structured tree models is adjusted as a function of a match of one or more characteristics of the patient to one or more characteristics of the structured tree model. One or more boundary conditions are determined for the corresponding one or more outlets. Blood flow in the patient's vessels is calculated as a function of boundary conditions and displayed.

In a second aspect, a non-transitory computer readable storage medium has stored thereon data representing instructions executable by a programmed processor to automatically adjust boundary conditions for a peripheral vascular tree. The storage medium includes instructions for generating a structured tree model in which the compliance and resistance values are set to values obtained from the patient, computing boundary conditions from the structured tree model, the boundary conditions being defined in response to the compliance and resistance values The properties of the structured tree model of the model are computed, and the hemodynamic properties of the patient's vessels are determined as a function of the boundary conditions.

In a third aspect, a system for automatically adjusting boundary conditions for a peripheral vascular tree is provided. The scanner is configured to scan a vessel of a patient. The processor is configured to determine a boundary condition of the vessel from the structured tree construction, determine a first property of the structured tree construction from a match of one or more second properties of the structured tree construction to a patient-specific value, and use The boundary conditions determine the flow characteristics of the vessel.

The invention is defined by the following claims, and nothing in this section should be taken as a limitation on those claims. Further aspects and advantages of the invention are discussed below in conjunction with preferred embodiments and may be claimed later on independently or in combination.

Description of drawings

The components and drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Also, in the figures, like reference numerals designate corresponding parts throughout the different views.

Figure 1 illustrates a vessel with an example scan of a corresponding outlet tree model;

Figure 2 is a flowchart of one embodiment of a method for automatically adjusting boundary conditions for a peripheral vascular tree;

Figure 3 is a flowchart of one embodiment of a method for computing compliance of a structured tree;

4 is a flowchart of one embodiment of a method for iteratively solving properties of a structured tree in patient-specific adjustments; and

5 is a block diagram of one embodiment of a system for automatically adjusting boundary conditions for a peripheral vascular tree.

Detailed ways

Patient-specific blood flow calculations may be performed from patient data, such as medical imaging data. FIG. 1 shows a vessel 40 with two outlets 42 and one bifurcation represented by patient data. An exit is an artificial end of a vessel within or at the edge of the scan area, such as at a location where scan data from the patient is not available. To account for portions of the vascular tree not represented in the patient data, boundary conditions at the ends of the represented vessels 40 (eg, outlet 42 ) are determined from a model 44 of the distal vascular tree. For a more accurate calculation of the flow in vessel 40, model 44 and corresponding boundary conditions can be automatically adjusted for a particular patient.

Adjust the structured tree boundary conditions to achieve desired values for total resistance and compliance. The inverse problem of finding parameter values for the boundary conditions of the structured tree in order to obtain the desired global properties is formulated as the solution to a system of nonlinear equations. Measured values are matched by corresponding values of the structured tree model to solve for other properties of the structured tree model.

Fig. 2 shows a method for automatically adjusting boundary conditions for a peripheral vascular tree. The method is implemented by a medical diagnostic imaging system, inspection station, workstation, computer, picture archiving and communication system (PACS) station, server, combination thereof, or other means for image processing medical diagnostic data. For example, the system, computer readable medium, and/or processor shown in FIG. 5 implement the method, although other systems may be used.

The methods are performed in the order shown or in a different order. Additional, different, or fewer acts may be performed. For example, actions 30 and/or 32 are not performed. In another example, acts for scanning, storing scanned data, segmenting vessel locations and/or transferring results are provided.

This action is performed in real time, such as during a surgical procedure. Execution during this procedure allows a clinician to make diagnosis and/or treatment based on the flow information calculated from the scan data. In other embodiments, the action is performed after the procedure as part of a diagnosis (eg, as part of a checkup), or before the procedure for planning purposes. The method can be repeated to provide comparative information over time, or to provide flow information for different vessels.

This action is performed automatically by the processor. The user has the patient scanned, or obtains scan data for the patient from a previous scan. A user may activate the program and enter patient-specific information, such as radius of outflow of the scanned vessel, threshold vessel tip size, measurements of pressure and/or measurements of flow. As long as activated, the method is executed without any user input, such as without user testing of different properties of the structured tree. Alternatively, the user assists in a semi-automatic procedure, such as the user indicating possible attribute values. Other user inputs may be provided, such as for changing modeling parameter values, correcting outputs, and/or confirming accuracy.

In act 20, scan data representing a vessel of the patient and one or more outlets of the vessel are acquired. Data is acquired by scanning the patient. Any type of medical imaging data can be used. For example, acquire computed tomography (CT), C-arm x-ray, standard x-ray, CT-like, magnetic resonance (MR), or ultrasound data for representation of vessels and outlets. Any scan order or method can be used.

In an alternative embodiment, data is retrieved by loading from memory. Data from previously performed scans of the patient are stored in memory, such as a picture archiving and communication system (PACS) database. Select data from this database. The data may be obtained by transfer, such as over a network or on a portable memory device.

Data represent volumes. Data is organized or formatted as frames, a data set, multiple data sets, or other collections to represent volumes. The data represents the location of the distribution in three dimensions. The volume includes one or more vessels 40 . Single-branch or multi-branch vasculature is represented. Vasculature 40 may include any number of outlets (eg, one or more) and extend within any extent of the patient's cardiac system or vasculature.

In one embodiment, the data as acquired is segmented. Thresholding, edge detection, contrast detection, shape fitting, flow detection, combinations thereof, or other procedures are used to identify locations associated with vessels relative to other anatomy. The type of scan or detection may result in data being acquired from vessels rather than other anatomy, such as by contrast detection and/or flow detection. A vessel may be represented as the tissue of the vessel wall, the boundary of the vascular tissue with blood, and/or the exterior of the column of blood. Alternatively, the acquired data is processed to segment the vessel 40 .

In act 22, a structured tree model 42 is generated. In the example of FIG. 2 , the processor generates the structured tree model by modeling the peripheral vessel as a tree structure in act 24 and automatically adapting the tree structure in act 26 based on information from the particular patient. Additional, different or fewer actions may be provided. This action is performed separately or together, such as adjustments as part of the modeling.

A structured tree model 42 is generated by the processor creating the structured tree and computing properties of the structured tree. Alternatively, a number of different structured trees associated with different root radii are precomputed and stored. Given the radius of the patient's vessels, a structured tree is generated by loading the appropriate predetermined model. Because instead of adjusting the model to a specific patient by just the radius of the outlet, the predetermined structured tree model can be altered by this adjustment. Alternatively, the act of computing the structured tree model from scratch is also adjusted based on other patient-specific information. In yet another embodiment, predetermined structured tree models are provided for various combinations of possible patient-specific information to identify and load an appropriate pre-computed structured tree model for a given outlet for a given patient.

The structured tree model 42 represents the attachment outlet of the peripheral vessel tree structure. Model blood flow and/or geometry beyond the outlet. The general shape and material properties of the structured tree affect blood flow and corresponding boundary conditions at the root of the structured tree model 42 . Since patient scan data for this tip tree structure is not available or used, assumptions are used to model or simulate the tip tree structure and corresponding flow.

Generate a separate structured tree model for each outlet. Since each outlet is independent or unconnected except through the vessel for which scan data is available, a separate structured tree model is created.

Any structured tree model can be used. Known information can be used to generate models. For example, larger radius outlets are more likely to connect to larger terminal tree structures, so the size of the outlet's radius can be used to model the length and number of forks. The root of the structured tree model has the same radius as the outlet for the connection modeled with the outlet, but may have a different radius. Forks other than three-way or more branches can be assumed. The length of each branch before the next fork can be based on the radius attributed to that branch. For bifurcations, each terminal branch can be assumed to have a smaller radius. The radius reduction may be scaled between branches, such as one branch being larger than the other. Each branch is scaled down by an unequal factor, creating an asymmetric binary tree where each branch decreases in radius starting from the closest branch. Alternatively, both branch radii are the same, but reduced by a factor. The factor of radius reduction may be experimentally determined or assumed.

The model represents the entire terminal tree structure or only a part. For example, apply a radius threshold (eg, 0.05µm). The model terminates for any branch with a radius smaller than a threshold. This creates the terminal end with the given radius in the structured tree. Beyond these terminal ends, there is no modeling and the boundary conditions at the terminal ends are assumed or solved as part of the tuning. In other embodiments, the entire terminal tree is modeled for vessels, terminating at arteries.

In one embodiment of act 24, "Numerical simulation and experimental validation of blood flow in arteries with structured-treeoutflow conditions," Annals of Biomedical Engineering, vol. 28, pp. 1281-1299, 2000 or One of the structured tree models and the corresponding boundary conditions disclosed in "Boundary Conditions for Hemodynamics: The Structured Tree Revisited," Journal of Computational Physics, Vol. 231, pp.6086–6096, 2012 by Cousins et al.

The structured tree is an asymmetric binary tree where each vessel is axisymmetric and has a constant radius. Use a power law at the bifurcation in order to describe the radii of the two sub-vessels:

(1)

Among them, the subscripts p , d ₁ and d ₂ refer to the parent vessel and the two child vessels, respectively. The power law assumes that the energy required for blood flow and maintenance of the vasculature is minimal (eg, for laminar flow ξ = 3.0). Other values may be used, such as values based on the parent radius. For example, ξ = 3.0 was used for large coronary vessels, while smaller values were used for other vessels. The type of flow to the patient can be determined and values are assigned to the tree or portions of the tree based on the type (eg, ξ varies in intervals between 2.33 for turbulent flow and 3.0 for laminar flow). The value may depend on the part of the cardiac system being modeled, such as 2.73 for coronary bifurcations.

For the structured tree boundary condition, the bifurcation is considered asymmetric, and thus the radius of the child vessel is determined based on the radius of the parent vessel by using two parameters:

(2)

where α and β are two scaling parameters between 0 and 1. Other ratios can be used. The scale parameter is either predetermined or calculated. For the calculation, two additional parameters, the area ratio and the asymmetry ratio, are respectively introduced as defined below:

(3).

The parameters ξ, η and γ are interdependent by the following relationship:

(4).

The two scale parameters can be calculated as:

(5).

Starting from a given root radius (eg, exit radius), the structured tree forks until the radius of the vessel becomes smaller than the minimum radius. The length of each vessel branch is expressed in terms of the radius of each vessel. For example, the length to radius _{ratio lrr} is 50, but other values may be used.

Once the branching structure (ie, geometry) of the structured tree model is determined, the flow, material, and/or other properties of the tree are modeled. Any modeling that uses the non-geometric nature of the structured tree model can be used. In one embodiment, Young's model is used. Young's model includes various material properties. Because arterioles are composed of the same type of tissue as large arteries, the relationship for large arteries based on the best fit to experimental data can also be used in the structured tree down to the smallest vessel represented in the structured tree the wall properties. An example representation is given below:

(6)

where x is the distance along the branch, _r0 is the radius of the branch, ki- ₃ is a material property, and E is Young's modulus and h is the thickness of the vessel wall. Table 1 shows example parameter values defining the structure and properties of the structured tree.

These values are examples or initial values. For a given patient, the values may differ due to adjustment to the patient. One or more of the values may be used as constants that vary without adjustment, such as ξ, γ, η, α, β, l _rr and/or k ₂ .

The governing equations for blood flow in the structured tree are derived from the axisymmetric Navier-Stokes equations, but other modeling of flow could be used. Since viscous effects are much more important than inertial effects in arterioles, the non-linear inertial term was ignored. If the flow and pressure are periodic, an analytical solution can be determined in the frequency domain:

(7)

(8)

where Q is the flow rate, P is the pressure, ρ is the density, c is the wave propagation velocity, and F _J depends on the Bessel function and is calculated using Womersley numbers. C _A is the area compliance and can be determined as:

(9)

where A is the cross-sectional area.

Use the following formula to recursively calculate the root impedance of a structured tree:

(10)

in , is the impedance at the entrance of the vessel segment or branch, and is the impedance at the outlet of the vessel segment or branch. Then, the root impedance is applied as the outlet boundary condition, expressed as:

(11).

By applying the inverse Fourier transform, is converted to And using the convolution theorem rewrite equation (11) as:

(12)

where T is the period.

In act 26, the material properties, flow characteristics and/or structure of the structured tree model are adjusted to the specific patient. The adjustment changes or assigns values of one or more parameters of the structured tree model, resulting in different boundary conditions. Adjust each of these structured tree models.

Rather than randomly assigning values to determine appropriate boundary conditions, the structured tree is adjusted by matching one or more properties of the structured tree model to one or more properties of the patient. For example, a structured tree model can be used to calculate resistance and/or compliance at the root or outlet. The resistance and/or compliance used for reference in matching may be calculated from measurements of the patient's pressure or flow. The total resistance and/or total compliance of the structured tree is then matched to the patient's resistance and/or compliance at the exit. The matching adjusts the structured tree boundary conditions.

Various properties of the structured tree are changed to provide matching. The properties or combination of properties of the structured tree model are determined by solving for a match of compliance and/or resistance boundary conditions.

Any adjustment may be used, such as an adjustment suitable for hemodynamic simulation. In one embodiment, the determination of the structured tree parameters is formulated as the solution of a system of non-linear equations with roots, where the calculated properties of the structured tree match the reference values. To determine the value of the residual of the objective function: f(x i ₎ for a set of parameter values _xi , the zero frequency impedance in equation (10) is calculated for the structured tree and the total compliance is determined. The set of parameter values xi is one or more of the attributes or characteristics that are changed or resolved for adjustment _.

The nonlinear system f ( xi ₎ = 0 is solved using the polyline trust region method, which is a quasi-Newton method, but other optimizations can be used. The performance of this method for updating parameters is independent of the difference in real parameters and objective function values. However, because the absolute values of total resistance and total compliance typically differ by more than six orders of magnitude, both parameters and target residuals have been scaled using typical values as described below.

The nonlinear system of equations can be formulated as:

(13)

where R _term is the terminal resistance imposed at each exit of the structured tree (e.g., the terminal resistance at the smallest branch at the end of the model due to a threshold), R _comp is the calculated resistance of the structured tree, and R _ref is derived from The patient's reference resistance, C _comp is the calculated compliance, and C _ref is the reference compliance from the patient. In this example, R _term and k ₃ are two properties or properties of the structured tree that are altered or resolved to provide a match (eg, zero difference). Additional, different or fewer features may be used in the solution.

Reference values (eg, C _ref and R _ref ) are obtained from the patient. Measures an aspect of a patient's cardiac system. For example, measuring pressure with a cuff or ultrasound or the difference between systolic and diastolic blood pressure. As another example, ultrasound is used to measure volume flow, flow rate, or other aspects of flow. Thus for any two patients, different or identical values for this aspect result.

Measured pressure, measured flow, or both are used to calculate the patient's reference compliance and/or resistance. Any now known or later developed estimate of compliance or resistance from measured pressure and/or flow may be used. For example, a pulse-to-pressure approach can be used to estimate compliance, while resistance can be estimated from the ratio of pressure to flow rate. Pressure and flow rate can be measured invasively or non-invasively, or estimated from physiological models or scaling laws.

To iteratively solve the nonlinear equations for the structured tree model, the total resistance and the total compliance of the structured tree are calculated. To determine material properties (eg, k ₃ ) and terminal resistance (eg, R _term ) of the structured tree model, combinations of values that result in a match are calculated. This adjustment fits the structured tree to a given patient for subsequent computation of boundary conditions at the outlet (eg, the root or sum of the structured tree model).

The total resistance and the corresponding adjustment of the total resistance are a function of the terminal resistance at the end of the structured tree. To adjust the total resistance, the resistance at the terminal vessel of the structured tree is assigned. All terminal resistances are considered equal, which is a reasonable assumption since all terminal vessels have nearly the same radius. In other embodiments, terminal resistance may vary by terminal position. The total resistance of the structured tree is equal to the impedance determined for the zero frequency in equation (10).

Any method for adapting the total resistance represented by the structure tree may be used. In one approach, the minimum radius at which the structured tree is terminated is modified. The calculated total resistance is used to match the reference value during iterative solution. Modifying the tip radius may only provide adjustments in a discrete space, not a continuous space, making a perfect match to a particular value less likely. Furthermore, if the total resistance is very high, the minimum radius becomes very small, leading to a considerable increase in the computational cost required to determine the impedance at the root of the structured tree. For the imposition of resistance at each end.

In another approach, resistance is imposed at each terminal vessel of the structured tree. The specific total resistance is divided by multiple exits and the results are imposed at the terminal locations of the structured tree. This method can lead to the desired result only if the resistance of vessels inside the structured tree is negligible compared to the terminal resistance. This assumption applies only to large arteries, not to arterioles that branch off into a structured tree down to the level of arterioles.

As another approach, matching can be used to calculate resistance. Matching solutions will be applied to one terminal resistance of each terminal, or solutions will be applied to different terminal resistances of the corresponding terminals. Provides an iterative solution to the desired match to solve the terminal resistance of the structured tree.

Use any method to determine compliance of the structured tree. The reference total compliance is matched to that of the structured tree by adjusting one or more material properties such as _k1 and _k3 of equation (6).

In one method for calculating the compliance of a structured tree, the total compliance C _an is calculated analytically by summing the volumetric compliances of all vessels in the structured tree. The volumetric compliance C _anb for a given branch is determined using the area compliance as follows:

(14)

where lrr is the _ratio of the length to the radius introduced.

Table 1 and r is the radius of the corresponding vessel. As given in equation (9), _CA is the elasticity of the wall of the vessel.

In another approach, the pulse pressure method is used to numerically calculate the total compliance of the structured tree. Figure 3 shows the estimation of the total compliance of the structured tree boundary conditions based on this impulse pressure method. First, an asymmetric Gaussian function is used to calculate the analytical flow rate profile q ( t ). The mean flow velocity of the time-varying profile was calculated from the mean blood velocity value of 20 cm/s and the root radius of the structured tree. An empirically determined flow rate profile for a given radius may be used. Alternatively, measured flow rates are used. Next, determine the impedance z(t) of the structured tree boundary condition (see equation (10)). Then, the calculation is run by imposing the previously calculated flow rate profile at the entry of the structured tree. As a result, a pressure profile is obtained, which is used to calculate the resistance of the structured tree ( ) and pulse pressure PP _ST . Finally, the pulse pressure method is used to calculate the equivalent compliance C _PPM of the structured tree. The pulse pressure method estimates compliance downstream of a location in the arterial tree based on time-varying flow rate, mean and pulse pressure at the location in the arterial tree. It is based on a two-element elastic cavity model, while the resistance of the model is calculated directly from the input data and only the compliance is unknown.

The final compliance value is substantially independent of the chosen mean blood flow velocity (e.g., the difference is on the order of 10 ⁻⁸ cm ⁴ ∙s ² /g), and the numerically calculated resistance is substantially equal to Equation (10 ) in zero-frequency impedance (for example, the difference is on the order of 10 ⁻⁵ g/(cm ⁴ ∙s)).

For use in matching solutions, the method shown in Figure 3 is applied several times until the tuning procedure for the structured tree boundary conditions converges. This aspect and the fact that the pulse pressure method is an iterative process leads to the application of an efficient search method inside the pulse pressure method for reducing the overall execution time. An example search method is the polyline trust region method. This broken-line trust-region method is not only applied to tune the structured tree parameters, but also to determine the compliance C _PPM , which leads to the reference pulse pressure PP _ST .

The sum of volume compliance is computationally faster than the pulse pressure method. Pulse pressure methods may provide more precise or efficient results. Other methods of calculating the total compliance of the structured tree can be used.

Using calculations of compliance and drag for reference and structured trees, a nonlinear system of equations can be solved using matching. The difference between the compliance measured from the patient and the compliance of the structured tree model and the difference between the resistance measured from the patient and the resistance of the structured tree model are minimized. Any optimization can be used, such as a trust region approach.

Figure 4 is a flowchart of one method for adjustment. The adaptation uses matching to resolve properties or properties of the structured tree. Additional, different or fewer actions may be provided. The acts are performed in the order shown or in a different order, such as act 42 is performed before act 40 .

In the example of Figure 4, the trust region approach is used for optimization. Finding the roots of a nonlinear system of equations can be formulated for optimization applications. To apply the trust region approach, a figure of merit function is formulated that is used to determine how the actual reduction in the residual function behaves in relation to the predicted reduction. Any merit function can be used, such as:

(15)

Among them, operator Refers to the Euclidean norm. The model function on the other hand is based on the Taylor series expansion of g (x) around the current point x _i :

(16)

where J _i is the Jacobian of f ( x ) at _xi , and s is the step taken to minimize the merit function. xi is the set of attributes or characteristics adapted as part of the tuning _, such as k ₃ and R _term .

In act 40, the minimum radius of the ends of the structured tree is initialized before iterating the solution. This initialization ensures that the resistance of the structured tree model is positive to match the reference resistance. An example algorithm is provided below to initialize the minimum radius at which the structured tree is terminated.

Algorithm 1. Initialize the minimum 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 may be used.

A starting value of 50 μm was used, which almost corresponds to the beginning of the arteriole level, but other starting values could be used. If the calculated total resistance R _comp obtained with zero terminal resistance is smaller than the reference value, the algorithm terminates, otherwise the algorithm gradually increases the minimum radius until the calculated total resistance becomes smaller than the reference value. Algorithm 1 ensures that a positive terminal resistance is required to obtain the reference resistance.

In act 42, the material properties of the structured tree are initialized prior to iterating the solution. The initialization ensures that the compliance of the structured tree is positive to match the reference compliance. An example algorithm for initializing the material properties of a structured tree is provided below.

Algorithm 2. Initialize the wall properties

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 material properties represented by the parameter k ₁ of Young's model are initialized. The values shown in Table ₁ are the first values for k1. k3 is set to ₀ . Use these settings or values to calculate the total compliance of the structured tree. A method similar to that in Algorithm ₁ is used, where the value of k1 is gradually reduced until the calculated compliance becomes smaller than the reference compliance.

Using a value of k ₁ and a minimum radius, perform a trust region optimization for tuning. The solution for tuning in one embodiment uses a Jacobian matrix and a polyline trust region, but other solutions for optimization, merit functions, and/or step size calculations may be used. In act 44, an initial Jacobian (J) is calculated. In action 46 , typical step size values are determined so that the Jacobian matrix for both the update of the parameters and the parameter values (eg k ₃ and R _term ) can be scaled. Use the gradient information from the Jacobian estimate to choose some typical value f ^typ for the target residual and determine a typical step size for each parameter :

(17)

where n _eq is the number of equations, 2 in this case (see equation 13). Initially, the Jacobian J is calculated using the central difference formula around the values of R _term =10 ⁴ g/cm ⁴ ∙s and k ₃ =5∙10 ⁴ or other initial values. Typical values for the objective function were chosen to be 1/50 of the reference value, but other typical value calculations or empirical knowledge could be used.

In act 48, a fixed-point method is used to find a finite-difference Jacobian determined using a typical step size that is consistent with the selected typical value of the target residual. The components of the Jacobian approximation are computed as follows:

(18)

where using equation (17) to calculate , and e _i and e _j denote the unit vectors in the i-th and j-th directions. This is provided only by the corresponding and The iterative process terminates in action 50 if the Euclidean norm of the difference of two consecutive Jacobians normalized by values is less than 10 ⁻⁶ or another value. The typical step size value determined by this iterative process is used in the following action along with the typical target residual to normalize the quantities used for the polyline trust region algorithm.

In act 52, the polyline trusted region method is initialized using the values of Table 2 or other values.

In act 54 the target residual f ( xi ₎ is calculated within the trust region algorithm and in act 56 a convergence test is performed. If each of the residual functions is less than 1/100 or the corresponding typical residual value ( ), the algorithm terminates in action 58. Otherwise in act 60 a new Jacobian J _i ( xi ₎ is computed and in act 62 the polyline algorithm is used to determine the next step value s _i . _{Steps si} are computed in action 62 by finding an approximate solution to the subproblem:

obey

where Δ is the trust zone radius.

The polyline algorithm represents a combination between Cauchy steps (determined along the steepest descending path) and Newton steps, given a specific trust region. Therefore, the Cauchy point is computed as:

(19)

in

(20)

Use the following formula to calculate Newton steps:

(twenty one).

Newton stepping is introduced to improve the speed of convergence especially in the terminal phase of the search process. The power of the trust region method is how easily the transition from the steepest descent with its nice global properties to Newton's method can be managed.

In one embodiment, the polyline method is implemented as:

Algorithm 3. Polyline method

Compute

if

else

Compute

where τ is the largest value in [0,1] such that

end(if)

Other algorithms can be used to implement the polyline method.

In act 64, the ratio of actual to predicted reduction is calculated for each iteration of the trust region. This ratio estimates how well the quadratic model approximates the merit function and is expressed as:

(twenty two).

If the ratio ρ _i is less than ρ _low , then use ω _down to update the trust region radius. If the ratio is greater than ρ _high , then ω _up is used to update the trust region. If the ratio is greater than ρ ₀ , the step si is accepted _.

In one embodiment, the update of the trust zone radius is implemented as:

Algorithm 4. Trust Region Method

Use the polyline method to calculate s _i

Use (22) to calculate _ρi

if ρ _i < ρ _low

Δ = ω _down Δ

else

if ρ _i > ρ _high and = Δ

Δ = ω _up Δ

end(if)

end(if)

if ρ _i > ρ ₀

x _{i + 1} = x _i + s _i

end(if).

Other algorithms can be used to implement the update of the trust region radius. The method incorporates the test of act 66 into the recomputation of the step value or update of _xi+1 in act 68 and returns to the computation of the target residual in act 54 .

Referring to FIG. 2, one or more boundary conditions are determined for each of the outlets according to the corresponding adjusted structured tree. Boundary conditions are calculated from a structured tree model as adjusted to a specific patient. Any of the properties of the structured tree model may be used. For example, the impedance calculated for the structured tree is used to determine the flow or pressure profile over the cardiac cycle according to equations (7) and (8) (see equations (11) and (12)). The values of _k1 and _k3 determined by solving the tree structure were used to find the area compliance used in determining these boundary conditions. Another example boundary condition may be a pressure profile partially responsive to the terminal resistance R _{term solved} by creating a structured tree. Other information can be determined as boundary conditions using properties of the adjusted tree structure, such as any of the Young's model or Navier-Stokes equation properties. Pressure profiles and/or time-varying flow rates may be calculated as boundary conditions based on one or more material properties and terminal resistances solved for by tuning to a specific patient.

The properties used to find the boundary conditions respond to compliance and resistance. The patient-specific compliance and/or resistance is used as a reference during creation of the structured tree to adjust the structured tree to the patient. Any boundary conditions can be computed from the adjusted tree for a given outlet.

In act 30 one or more blood flows are calculated for a vessel 40 . Boundary conditions are used in calculating this quantity. Resistance, compliance, wave propagation, wave reflection, combinations thereof, or other properties of the total peripheral vascular tree for a given outlet can be used to determine volumetric flow, pressure, or other quantification of flow in the vessel. Flow in vessels is based in part on properties of the peripheral vascular tree, which are specified by boundary conditions. Any hemodynamic property of the patient's vasculature can be determined as a function of boundary conditions.

In act 32, blood flow is displayed. An image is presented with blood flow on a screen or display device. Images are of that amount. Other information may also be presented, such as the rendering of the vessel from the scan data, geometric information about the vessel, properties of the structured tree, boundary conditions, or other information useful for diagnosing the patient. For example, vessels are shown from a three-dimensional depiction of scan data from a given view. Blood flow, such as flow rate and/or pressure over time, is displayed as a graph, histogram, or numerical value (eg, mean or variance per cycle) adjacent to or overlaid on the delineation.

Known arterial trees can be used to test the methods of Figures 2-4 for tuning the total resistance and total compliance of the structured tree boundary conditions. Specifically, the total resistance and total compliance values of the outlet boundary conditions in the known arterial tree are used as reference values, and the structured tree boundary is adjusted separately for each outlet vessel of any of the various vessels condition. In Table 3 the results of the adjustment process are shown. For some arteries, the smallest radius at which the structured tree terminated was greater than 0.005 cm. In those cases, even if there is no terminal resistance, the total initial resistance is greater than the reference value.

The total resistance values given in Table 3 correspond to resting conditions. If the training state is to be simulated, the total resistance can be smaller and a larger minimum radius can be used. Typically, the terminal resistance imposed at the terminal site of the structured tree is three to five orders of magnitude higher than the total resistance of the structured tree.

Regarding the adjustment of the overall compliance, the results show that the analytically calculated compliance differs significantly from the compliance based on the pulse pressure method. The pulse pressure method may be more accurate. Regarding k ₁ , Algorithm 2 changes this value, showing that a smaller value of k ₁ than the initial value shown in Table 1 is generally required to obtain a reference compliance with a positive value for k ₃ .

Although compliance is numerically computed at each tuning iteration, the execution time for tuning each structured tree can be less than 10 seconds on a personal computer. The proposed adjustment is computationally efficient. Only 3-10 iterations may be required for convergence. The polyline trust region method is not only applied to the adjustment of the properties of the structured tree, but also to the search process performed for the impulsive pressure method.

The reference resistance and compliance values are physiological which allow the successful application of the adjustment procedure. Equation (13) may not have a solution if either of the two reference parameters has unrealistic values. For example, if the reference compliance value is too high, _a negative value for ki may be required, which in turn leads to an unstable structured tree impedance.

Structured tree boundary conditions are automatically adjusted for hemodynamic calculations. Adjust the parameters of the structured tree boundary conditions to obtain specific reference values for total resistance and total compliance. Two parameters (the minimum radius at which the structured tree terminates and the constant k ₁ ) are initially adapted in order to determine the starting point, which leads to positive values for the actual adjustment parameters. Two parameters are adapted to tune two properties of the structured tree: terminal resistance (equal at all terminal sites), and a constant ( k ₃ ) that determines the wall properties. Other initial and/or adaptive properties may be used.

Adjustments are performed using the polyline trust region method, which is an efficient method requiring only 3-10 iterations. Other numbers of iterations may occur. One advantage of the proposed method is that no initial search algorithm is required, and the initial starting point obtained by Algorithms 1 and 2 is good enough for the initial solution of the trust region method.

The method can be easily integrated in higher order tuning algorithms for hemodynamic calculations, where elastic cavity boundary conditions are used to match some specific patient hemodynamic properties. Instead of directly using elastic cavity parameter values given by a higher order tuning algorithm at each iteration, structured tree boundary conditions are used, and the tuned structured tree is used to specify reference resistance and compliance values. Alternatively, directly tune the parameters of the structured tree boundary conditions without using resistance and compliance as intermediate quantities.

Figure 5 shows a system for automatically adjusting boundary conditions of a peripheral vascular tree. The system includes a medical imaging system 11 , a processor 12 , a memory 14 and a display 16 . Processor 12 and memory 14 are shown separate from medical imaging system 11 , and thus associated with a computer or workstation remote from medical imaging system 11 . In other embodiments, processor 12 and/or memory 14 are part of medical imaging system 11 . In an alternative embodiment, the system is a workstation, computer or server for adjusting boundary conditions and calculating blood flow from data acquired in real time by a separate system or using previously acquired patient-specific data stored in memory. For example, a medical imaging system 11 is provided for acquiring data representing volumes, and a separate database, server, workstation and/or computer is provided for making adjustments and calculations. Additional, different, or fewer components may be used.

Computing components, devices or machines of a system such as medical imaging system 11 and/or processor 12 are configured by hardware, software and/or designed to perform computations or other actions. The computing components operate independently or in conjunction with each other to perform any given action such as those of FIGS. 2-4 . Actions are performed by one of the computing components, another of the computing components, or a combination of computing components. Other components may be used or controlled by the computing component to scan or perform other functions.

Medical imaging system 11 is any now known or later developed modality for scanning a patient. The medical imaging system 11 scans the patient for vascular regions. For example, a C-arm x-ray system (eg, DynaCT from Siemens), a CT-like system, or a CT system is used. Other modalities include MR, x-ray, angiography, fluoroscopy, PET, SPECT, or ultrasound. The medical imaging system 11 is configured to acquire medical imaging data representative of one or more vessels. Data is acquired by scanning the patient using transmissions made by the scanner and/or by receiving signals from the patient. The type or mode of scanning may result in only vessel data being received. Alternatively, volume region data is received and the vascular information is segmented based on other anatomical information.

Memory 14 is a buffer, cache, RAM, removable media, hard drive, magnetic, optical, database, or other now known or later developed memory. The memory 14 is a single device or a group of two or more devices. Memory 14 is within system 11, part of the computer with processor 12, or external to or remote from other components.

Memory 14 stores the structured tree, properties of the structured tree, intermediate solution data, measured properties of the patient, scan data, or other vascular or flow information. Memory 14 stores data resulting from the processes described herein, such as storing constants, initial values, adjusted values, or other attributes.

Memory 14 additionally or alternatively is a non-transitory computer-readable storage medium having processing instructions. Memory 14 stores data representing instructions executable by programmed processor 12 to automatically adjust boundary conditions for the peripheral vascular tree. Instructions for implementing the processes, methods and/or techniques discussed herein are provided on a computer-readable storage medium or memory, such as cache, buffers, RAM, removable media , hard drive, or other computer-readable storage medium. Computer readable storage media include various types of volatile and nonvolatile storage media. The functions, acts or tasks illustrated in the figures or described herein are executed in response to one or more sets of instructions stored in or on computer readable storage media. Functions, acts or tasks are independent of a particular type of instruction set, storage medium, processor or processing strategy and may be performed by software, hardware, integrated circuits, firmware, microcode, etc., operating alone or in combination. Likewise, processing strategies may include multiprocessing, multitasking, parallel processing, and the like. In one embodiment, the instructions are stored on a removable media device for reading by a local or remote system. In other embodiments, the instructions are stored in a remote location for transfer over a computer network or over telephone lines. In yet another embodiment, the instructions are stored within a given computer, CPU, GPU or system.

The processor 12 is a general-purpose processor, a digital signal processor, a three-dimensional data processor, a graphics processing unit, an application-specific integrated circuit, a field programmable gate array, a digital circuit, an analog circuit, a combination thereof, or other existing devices for processing medical data. known or later developed devices. Processor 12 is a single device, multiple devices or a network. For more than one device, parallel or sequential division of processing may be used. Different devices making up processor 12 may perform different functions, such as adjustments by one device and calculations of boundary conditions and/or flow rates by another device. In one embodiment, processor 12 is a control processor or other processor of medical imaging system 11 . Processor 12 operates in accordance with stored instructions to perform the various actions described herein.

Processor 12 is configured to determine a property of the structured tree construction based on a match of one or more other properties of the structured tree construction to the patient-specific value. For example, the terminal resistance and material properties of the structured tree construct are determined from the match of the overall compliance and total resistance of the structured tree construct to the compliance and resistance at the outlet of the vessel of a given patient. The structured tree construct created by the processor 12 represents the vascular tree of the vessel extremities for which scan data is acquired and calculations are performed.

Processor 12 is configured to determine one or more boundary conditions of the vessel from the structured tree construction. The flow characteristics at the outlet of the vessel are the boundary conditions. Structured tree properties are used to compute boundary conditions. The properties themselves may be boundary conditions.

Processor 12 is configured to determine flow characteristics of the vessel using boundary conditions. The boundary conditions for the peripheral vessel are used in part to determine some aspect of the flow in the vessel.

Processor 12 is configured to generate an image. The image includes calculated quantities of flow in the vessel. The images may include representations of vessels and/or structured tree models.

Display 16 is a CRT, LCD, plasma, projector, printer, or other output device for displaying images. Display 16 shows one or more quantities calculated using boundary conditions. The quantity can be displayed on a graph, in a graph and/or on a graph.

Although the invention has been described above by reference to various embodiments, it should be understood that many changes and modifications can be made without departing from the scope of the invention. It is therefore intended that the foregoing detailed description be regarded as illustrative rather than restrictive, and that the following claims be understood to include all equivalents which are intended to define the spirit and scope of the invention.

Claims (20)

1. A method for automatically adjusting (26) boundary conditions of a distal vessel tree, the method comprising:

acquiring (20) scan data representing a vessel of a patient and one or more exits of the vessel at an edge of a scan region for scan data;

modeling (24) a distal vascular tree structure for each of one or more outlets of the vessel, the distal vascular structure modeling vasculature extending from the one or more outlets of the vessel;

adjusting (26) the modeling (24) as a function of matching one or more characteristics of the patient, the one or more characteristics including resistance and compliance of a root of the distal vascular tree model;

determining (28) one or more boundary conditions for the respective one or more outlets from the adjusting (26) based on a relationship between flow and pressure at the outlets of the vessel;

calculating (30) a blood flow as a function of the boundary condition for the vessel of the patient; and

the blood flow is displayed (32) to a clinician in real time.

2. The method of claim 1 wherein modeling (24) comprises modeling (24) as a structured tree model, and wherein adjusting (26) comprises adjusting (26) the structured tree model.

3. The method of claim 1 wherein modeling (24) includes modeling (24) with scaled radii for the bifurcations, the length of the branches between the bifurcations being a function of the respective radii, and the root radius being based on the radius of the exit from the scan data.

4. The method of claim 1, wherein adjusting (26) comprises: adjusting (26) as a function of matching the resistance and the compliance measured from the patient to the resistance and the compliance of the modeling (24).

5. The method of claim 4, wherein the resistance and the compliance measured from the patient include measuring pressure or flow from the patient, and calculating (30) the resistance and the compliance from the pressure or flow.

6. The method of claim 4, wherein adjusting (26) comprises solving a non-linear system of equations with the matching, the matching comprising minimizing a difference between the compliance measured from the patient and the compliance of the modeling (24) and a difference between the resistance measured from the patient and the resistance of the modeling (24).

7. The method of claim 6, wherein solving comprises performing trust zone optimization.

8. The method of claim 4 wherein the resistance of the modeling (24) is set as a function of terminal resistance at an end of a structured tree, and wherein the adjusting (26) comprises initializing a minimum radius for the end such that the resistance of the structured tree is positive to match the resistance from the patient.

9. The method of claim 4, wherein the compliance of the modeling (24) is determined according to a pulse pressure method.

10. The method of claim 4 wherein modeling (24) comprises modeling (24) properties with a Young's model comprising first material properties, and wherein adjusting (26) comprises performing said matching as a function of said first material properties.

11. The method of claim 10 wherein adjusting (26) comprises initializing a second material property of the young's model such that the compliance of the modeling (24) is positive to match the compliance from the patient.

12. The method of claim 1, wherein adjusting (26) comprises: the adjustment (26) is made as a function of the tip resistance and the material properties.

13. The method of claim 1, wherein adjusting (26) comprises: the adjustment is made as a function of the jacobian matrix and the polyline trust zone.

14. The method of claim 1, wherein determining (28) the one or more boundary conditions comprises determining (28) a time-varying flow rate and pressure profile for a first one of the outlets from the modeling (24) as adjusted.

15. The method of claim 1 wherein calculating (30) the blood flow comprises calculating (30) as a function of the boundary conditions, the boundary conditions comprising resistance, compliance, and wave and reflection effects, and wherein displaying (32) comprises displaying (32) an image with the blood flow.

16. A non-transitory computer readable storage medium (14) having stored therein data representing instructions executable by a programmed processor (12) to automatically adjust (26) boundary conditions for a distal vessel tree, the storage medium comprising instructions for:

generating (22) a structured tree model of the vasculature extending from the outlet of the vessel, the structured tree model being generated with the compliance and resistance values set to values obtained from the patient;

calculating (28) boundary conditions for the outlet from the structured tree model, the boundary conditions being calculated from characteristics of the structured tree model responsive to the compliance and resistance values;

determining (30) hemodynamic properties of a vessel of the patient as a function of the boundary condition; and displaying the hemodynamic properties of the vessel to a clinician.

17. The non-transitory computer readable storage medium (14) of claim 16, wherein generating (22) the structured tree model comprises generating (22) the structured tree model having a root radius set to a vessel radius of the patient, and solving a characteristic of the structured tree model with a match of the compliance and resistance values to the values obtained from the patient as reference values, the reference values obtained from the patient being a function of pressure measured from the patient, flow measured, or both pressure and flow measured.

18. The non-transitory computer readable storage medium (14) of claim 16 wherein generating (22) comprises iteratively solving nonlinear equations for a structured tree model, the solving providing material properties and terminal resistance of the structured tree model, and wherein calculating (28) boundary conditions comprises calculating (28) a pressure profile, a time-varying flow rate, or both as a function of the material properties and the terminal resistance.

19. A system for automatically adjusting (26) boundary conditions of a distal vessel tree, the system comprising:

a scanner (11) configured to scan a vessel of a patient;

a processor (12) configured to determine a boundary condition of the vessel from a structured tree construction of an exit of the vessel, to determine a first characteristic of the structured tree construction as a terminal resistance and material property of the structured tree construction from a matching of one or more second characteristics of the structured tree construction comprising a total compliance and a total resistance with the patient-specific values of the compliance and resistance comprised at the exit of the vessel, and to determine a flow characteristic of the vessel with the boundary condition; and

a display configured to display a flow characteristic of the vessel.

20. The system of claim 19, wherein the structured tree constructs a vessel tree representing the vessel tip.