A personalized whole-brain small artery angiogenesis method based on multiple constraints

Abstract

A personalized whole-brain small artery angiogenesis method based on multiple constraints, belonging to the field of mathematical modeling algorithm development, includes the following steps: constructing a personalized three-dimensional model based on real head and carotid CTA images to determine the starting position of blood vessel growth; recording the geometric parameters (such as outlet area, outlet blood vessel length, etc.) of each blood vessel model based on the personalized model; using the Brainstorm standard head model three-dimensional point cloud file, uniformly sampling it as the ending position of blood vessel growth; based on multiple constraints, using the simulated annealing algorithm to optimize the geometric parameters of small blood vessels and calculate the spatial positions of bifurcations of blood vessels at all levels after meeting the constraints. The personalized whole-brain small artery angiogenesis real model of the present invention improves the accuracy for numerical simulation and hemodynamic calculation.

Description

Technical Field

[0001] The present invention belongs to the field of mathematical modeling algorithm development, and is a method for automatically generating fast and personalized whole-brain small artery blood vessels. Background Art

[0002] Due to the limitations of current medical imaging technologies, small arteries in the front and their peripheral blood vessels, such as those in the cerebral arteries, cannot be distinguished by computed tomography or magnetic resonance imaging, and are usually not easily distinguishable in CT angiography, i.e., CTA. Therefore, we designed relevant algorithms according to the natural laws of blood vessel growth to generate a small artery model of the cerebral blood vessels. This method proposes a vascular generation optimization algorithm based on multiple constraints, including scaling rate, HK diameter model, and HK angle rule, to establish a small artery model of the cerebral blood vessels in front, with a diameter greater than 100 μm and less than 1 mm, and generate personalized whole-brain small artery blood vessels. Summary of the Invention

[0003] The present invention provides a method for generating personalized whole-brain small artery blood vessels based on multiple constraints, which can approximately reflect the personalized cerebral blood flow changes, improve the accuracy of non-invasive cerebral blood flow calculation, and is applicable to cerebral blood flow dynamics calculation using a cerebral blood vessel 3D / 1D / 0D geometric multi-scale coupling model.

[0004] To achieve the above object, the present invention is realized through the following technical solutions:

[0005] A method for generating personalized whole-brain small artery blood vessels based on multiple constraints, characterized in that the small artery blood vessels of the brain are generated by the following method, including the following steps:

[0006] Step A1: Based on real head and neck CTA images, construct a personalized three-dimensional model of large cerebral arteries through threshold segmentation using mimics software;

[0007] Step A2: Record the geometric parameters of the blood vessel model based on the three-dimensional model, including the outlet area, diameter, and outlet blood vessel length, and record each large cerebral artery branch and its blood supply area;

[0008] Step A3: Perform uniform sampling of the point cloud based on the three-dimensional point cloud file of the Brainstorm standard head model;

[0009] Step A4: Based on the vascular bifurcation scaling rate and the principle of minimum energy, adopt the simulated annealing algorithm to optimize the optimal diameter and length after vascular bifurcation by setting the initial temperature, cooling coefficient, number of iterations, and the optimized objective function;

[0010] Step A5: Based on the diameters and lengths of the branches at Step A4, the HK bifurcation angle rule is adopted to constrain the blood vessel bifurcation angles and spatial positions, thereby generating the spatial position coordinates of each blood vessel bifurcation and finally forming a one-dimensional blood vessel model of the small arteries in the intracranial space;

[0011] As a further technical solution of the present invention, for the feature described in Step A1, the mimics software is used to import the CTA images of the real head and neck arteries. Through threshold segmentation, the real three-dimensional cerebral arteries are reconstructed, and the coordinates at each outlet are obtained as the starting position coordinates for blood vessel growth.

[0012] As a further technical solution of the present invention, for the feature described in Step A2, the cross-sectional area and length of the real cerebral artery at the outlet of the brain are measured by Geomagic software, and the diameter is calculated. Among them, the blood supply areas of the branches of the anterior cerebral artery include: medial orbital gyrus, lateral orbital gyrus, olfactory area, frontal pole, cingulate gyrus, paracentral lobule, superior frontal gyrus, middle frontal gyrus, precentral gyrus, postcentral gyrus, precuneus, superior parietal lobule, and inferior parietal lobule. The blood supply areas of the branches of the middle cerebral artery include the orbital surface of the frontal lobe, lateral frontal, inferior frontal gyrus, precentral gyrus, postcentral gyrus, inferior parietal lobule, superior parietal lobule, supramarginal gyrus, superior temporal gyrus, middle temporal gyrus, inferior temporal gyrus, lateral occipital lobe, and temporal pole. The blood supply areas of the branches of the posterior cerebral artery include: inferior temporal gyrus, fusiform gyrus, lingual gyrus, occipital lobe, cuneus, precuneus, lateral occipital lobe, and superior parietal lobule.

[0013] As a further technical solution of the present invention, for the feature described in Step A3, by exporting the three-dimensional point cloud file of the standard head model of the open-source program Brainstorm, the three-dimensional point cloud coordinates corresponding to 68 brain regions of the cerebral cortex are exported respectively. By uniformly sampling the point cloud, it is used as the end position coordinates for the growth of small artery blood vessels. Among them, the 68 brain regions are based on the Desikan–Killiany atlas, including the superior temporal sulcus, caudal anterior cingulate, middle frontal gyrus, cuneus, entorhinal area, frontal pole, fusiform gyrus, inferior parietal lobe, inferior temporal gyrus, insula, isthmus of the cingulate gyrus, lateral occipital lobe, lateral orbital frontal lobe, lingual gyrus, medial orbital frontal lobe, middle temporal gyrus, paracentral lobule, hippocampal gyrus, inferior frontal gyrus, orbital part, triangular part, cingulate gyrus, postcentral gyrus, posterior cingulate gyrus, precentral gyrus, precentral lobule, parietal lobe, lateral anterior cingulate, lateral frontal, superior frontal gyrus, superior parietal lobule, superior temporal gyrus, supramarginal gyrus, temporal pole, and transverse temporal gyrus.

[0014] As a further technical solution of the present invention, for the feature described in Step A4, the blood vessel bifurcation diameter model and the blood vessel diameter-volume, flow-length, and diameter-length scaling ratios are used as one of the constraints for blood vessel growth.

[0015] According to the principle of minimum energy loss derived from the Hagen-Poiseuille law, the minimum energy for generating blood vessels is used as one of the constraints.

[0016] Finally, the simulated annealing algorithm is used to optimize the optimal diameter and length after blood vessel bifurcation.

[0017] As a further technical solution of the present invention, for the features described in step A5, based on the diameters and lengths of the blood vessel bifurcations at all levels obtained in step A4, and based on steps A2 and A3, the starting and ending positions of blood vessel growth are determined, and then the spatial constraints of the bifurcation angles are performed according to the following HK angle rules to obtain the spatial position coordinates of the bifurcations at all levels.

[0018] The personalized whole-brain small artery angiogenesis real model of the method of the present invention improves a certain accuracy for numerical simulation and hemodynamic calculation. Brief Description of the Drawings

[0019] Figure 1 : Flow chart of the method of the present invention

[0020] Figure 2 : Schematic diagram of HK angle and stem crown parameters in the three-dimensional reconstruction map of cerebral arteries

[0021] Figure 3 : Flow chart of the optimization algorithm

[0022] Figure 4 : Preliminary result diagram Detailed Embodiments

[0023] The following further illustrates the present invention in conjunction with embodiments, but the present invention is not limited to the following embodiments.

[0024] Embodiment 1

[0025] A method for personalized whole-brain small artery angiogenesis based on multiple constraints generates cerebral small arteries through the following method, including the following steps:

[0026] Step A1: Based on real head and neck CTA images, a personalized three-dimensional model of cerebral large arteries is constructed by threshold segmentation using mimics software;

[0027] Step A2: Based on the three-dimensional model, record the geometric parameters of the blood vessel model, including the outlet area, diameter, and outlet blood vessel length, and record each cerebral artery branch and its blood supply area;

[0028] Step A3: Based on the three-dimensional point cloud file of the Brainstorm standard head model, perform uniform sampling of the point cloud;

[0029] Step A4: Based on the blood vessel bifurcation scaling rate and the minimum energy principle, use the simulated annealing algorithm to optimize the optimal diameter and length after blood vessel bifurcation by setting the initial temperature, cooling coefficient, number of iterations, and the optimized objective function;

[0030] Step A5: Based on the diameters and lengths of the bifurcations in Step A4, the HK bifurcation angle rule is used to constrain the blood vessel bifurcation angle and spatial position, thereby generating the spatial position coordinates of each blood vessel bifurcation, and finally forming a one-dimensional blood vessel model of the small arteries in the intracranial space;

[0031] As a further technical solution of the present invention, for the feature described in Step A1, the mimics software is used to import the CTA images of the real head and neck arteries. Through threshold segmentation, the real three-dimensional cerebral arteries are reconstructed, and the coordinates at each outlet are obtained as the starting position coordinates for the growth of the small artery blood vessels.

[0032] As a further technical solution of the present invention, for the feature described in Step A2, through the Geomagic software, the cross-sectional area and length of the real cerebral artery at the outlet are measured, and the diameter is calculated. Among them, the blood supply areas of the branches of the anterior cerebral artery include: medial orbital gyrus, lateral orbital gyrus, olfactory area, frontal pole, cingulate gyrus, paracentral lobule, superior frontal gyrus, middle frontal gyrus, precentral gyrus, postcentral gyrus, precuneus, superior parietal lobule, and inferior parietal lobule. The blood supply areas of the branches of the middle cerebral artery include the orbital surface of the frontal lobe, lateral frontal, inferior frontal gyrus, precentral gyrus, postcentral gyrus, inferior parietal lobule, superior parietal lobule, supramarginal gyrus, superior temporal gyrus, middle temporal gyrus, inferior temporal gyrus, lateral occipital lobe, and temporal pole. The blood supply areas of the branches of the posterior cerebral artery include: inferior temporal gyrus, fusiform gyrus, lingual gyrus, occipital lobe, cuneus, precuneus, lateral occipital lobe, and superior parietal lobule.

[0033] As a further technical solution of the present invention, for the feature described in Step A3, by exporting the three-dimensional point cloud file of the Brainstorm standard head model, the point cloud coordinates corresponding to 68 brain regions of the cerebral cortex are exported respectively. By uniformly sampling the point cloud, it is used as the end position coordinates for the growth of the small artery blood vessels. Among them, the 68 brain regions are based on the Desikan–Killiany atlas, including the superior temporal sulcus, caudal anterior cingulate, middle frontal gyrus, cuneus, entorhinal area, frontal pole, fusiform gyrus, inferior parietal lobe, inferior temporal gyrus, insula, isthmus of the cingulate gyrus, lateral occipital lobe, lateral orbital frontal lobe, lingual gyrus, medial orbital frontal lobe, middle temporal gyrus, paracentral lobule, hippocampal gyrus, inferior frontal gyrus, orbital part, triangular part, cingulate gyrus, postcentral gyrus, posterior cingulate gyrus, precentral gyrus, precentral lobule, parietal lobe, lateral anterior cingulate, lateral frontal, superior frontal gyrus, superior parietal lobule, superior temporal gyrus, supramarginal gyrus, temporal pole, and transverse temporal gyrus.

[0034] As a further technical solution of the present invention, for the feature described in Step A4, based on the following blood vessel bifurcation diameter model and the diameter-volume, flow-length, diameter-length scaling ratio, and the principle of minimum energy, the simulated annealing algorithm is used to optimize the optimal diameter and length after blood vessel bifurcation. The specific implementation process includes the following steps:

[0035] Step B1: The HK diameter model formula based on the minimum energy assumption of the entire tree structure is expressed as follows, where D m, D l and D s respectively represent the mother blood vessel, the larger daughter blood vessel, and the smaller daughter blood vessel.

[0036]

[0037] The diameter - length, volume - diameter, and flow - length scaling rate formulas are as follows, where the proximal blood vessel segment is defined as the main trunk, and the tree distal to the main trunk is defined as the crown. Among them, D s , L s and D s respectively represent the diameter, length, and flow of the blood vessel branch trunk, (D s ) max and (Q s ) max represent the diameter and flow of the most proximal blood vessel main trunk, (L c ) max and (V c ) max represent the sum of the lengths of the entire crown and the sum of the cumulative volumes.

[0038]

[0039]

[0040]

[0041] According to the Hagen - Poiseuille's law, the resistance of the steady laminar flow in the trunk of the entire tree where ΔPs is the pressure gradient along the trunk, and Qs is the flow through the trunk volume, can be written as:

[0042]

[0043] Principle of minimum energy loss: The growth of the blood vessel tree should follow the principle of minimizing the energy consumed by blood flow as much as possible. Using Poiseuille's law in fluid mechanics, for a section of blood vessel with radius r and length l, the flow rate is

[0044]

[0045] where ΔP is the pressure difference at both ends of the blood vessel, and μ is the viscosity coefficient of the blood. During blood flow, the energy consumed by the body to overcome the resistance is E1 = q * ΔP. Substituting the above formula (6) gives

[0046]

[0047] Step B2: Calculate the Euclidean distance from the starting point to the ending point of the arteriole blood vessel growth based on the results obtained in Steps A2 and A3.

[0048] Step B3: Based on the diameter and length of the starting arteriolar vessel, the diameter and length of each level of arteriolar vessels are preliminarily given, and their upper and lower limits are set. The root mean square error of the diameter-length, volume-diameter, and flow-length scaling ratios are calculated respectively, and the energy loss is calculated based on Poiseuille's law as the objective function of this optimization.

[0049] Step B4: Output the optimized arteriolar vessel diameter and length.

[0050] As a further technical solution of the present invention, the features described in step A5 are based on the diameters and lengths of the various levels of bifurcations of the blood vessels obtained in step A4, the starting and ending positions of the blood vessel growth are determined based on steps A2 and A3, and then the bifurcation angle is spatially constrained according to the following HK angle rule to obtain the spatial position coordinates of the bifurcations at various levels.

[0051] Step C1: The HK angle rule is as follows, where α, β, and γ are the angles between the mother vessel and the larger daughter vessel, the mother vessel and the smaller daughter vessel, and the two daughter vessels, respectively.

[0052]

[0053]

[0054]

[0055] Step C2: According to the HK angle rule calculation formula, the optimized arteriolar diameter is substituted to calculate the bifurcation angles α, β and γ.

[0056] Step C3: Based on the starting coordinate A and the diameter and length optimized in step A5, a coordinate network is established with A as the center and the length corresponding to the bifurcation blood vessel as the radius for the next bifurcation point B, and a coordinate network is established with bifurcation point B as the center and the length corresponding to the bifurcation blood vessel as the radius for the left bifurcation C and the right bifurcation D, thereby finding all possible coordinates for the growth of small arteries.

[0057] Step C4: Loop through the bifurcation coordinate networks B, C and D, calculate the angles at the bifurcation points according to the angle calculation formula between vectors, and compare them with α, β and γ.

[0058] Step C5: traverse and calculate the difference between the angles between the vectors and α, β and γ respectively, and output the coordinates of B, C and D when the difference is the smallest. Point B of this level is used as point A of the next level of growth, and points C and D of this level are used as points B of the next level of bifurcation. The coordinates of the remaining levels are calculated according to the above steps to obtain the coordinates of each bifurcation and terminal position in turn.

[0059] Step C6: When the distance between the generated coordinates of the arteriole vessel terminal and the coordinates of the end position in Step A3 is minimized, stop growing, end the optimization, and obtain the spatial position coordinates of arteriole vessels at all levels.

[0060] The arterioles grown by this method satisfy the natural laws of blood vessel growth, and certain accuracy is improved for numerical simulation and hemodynamic calculation.

Claims

1. A method for generating personalized small cerebral artery blood vessels based on multiple constraint conditions, characterized in that The following method is used to generate small cerebral artery blood vessels, including the following steps: Step A1: Based on real head and carotid CTA images, a personalized three-dimensional model of large cerebral arteries is constructed by threshold segmentation using Mimics software; Step A2: Based on the three-dimensional model, record the geometric parameters of the blood vessel model, including: outlet area, diameter, outlet blood vessel length, and record each major cerebral artery branch and its blood supply area; Step A3: Based on the three-dimensional point cloud file of the Brainstorm standard head model, perform uniform sampling of the point cloud; Step A4: Based on the blood vessel bifurcation scaling ratio and the principle of minimum energy, use the simulated annealing algorithm to optimize the optimal diameter and length after blood vessel bifurcation by setting the initial temperature, cooling coefficient, number of iterations, and the optimized objective function; The specific implementation process includes the following steps: Step B1: The HK diameter model formula based on the assumption of the minimum energy of the entire tree structure is expressed as follows, where D m , D l , and D s represent the parent blood vessel, the relatively larger daughter blood vessel, and the relatively smaller daughter blood vessel, respectively; The diameter-length, volume-diameter, and flow-length scaling rate formulas are as follows, where the proximal vascular segment is defined as the main trunk, and the tree distal to the main trunk is defined as the crown; where D s , L s , and Q s represent the diameter, length, and flow of the vascular branch, respectively, (D s ) max and (Q s ) max represent the diameter and flow of the most proximal vascular main trunk, (L c ) max and (V c ) max represent the sum of the lengths of the entire crown and the sum of the cumulative volumes; According to the Hagen-Poiseuille law, the resistance to steady laminar flow in the trunk of the whole tree where ΔPs is the pressure gradient along the trunk and Qs is the flow rate through the trunk volume, is written as: Principle of minimum energy loss: Using Poiseuille's law of fluid mechanics, for a section of blood vessel with radius r and length l, the flow rate is where ΔP is the pressure difference at both ends of the blood vessel and μ is the blood viscosity coefficient; during blood flow, the energy consumed by the body to overcome resistance is E1 = q * ΔP. Substituting the above formula (6) gives Step B2: Based on the Euclidean distance from the starting point to the ending point of the small artery blood vessel growth calculated in Steps A2 and A3, and dividing this Euclidean distance by the starting length of the blood vessel, obtain the maximum number of levels of blood vessel growth; Step B3: Based on the diameter and length of the starting small artery blood vessel, initially assign the diameter and length of each level of small artery blood vessel and set their upper and lower limit ranges; calculate the root mean square errors of the diameter-length, volume-diameter, and flow-length scaling ratios respectively, and calculate the energy loss based on Poiseuille's law as the objective function of this optimization; Step B4: Output the optimized diameter and length of the small artery blood vessel; Step A5: Based on the diameter and length of each bifurcation in Step A4, use the HK bifurcation angle rule to constrain the blood vessel bifurcation angle and spatial position, thereby generating the spatial position coordinates of each blood vessel bifurcation, and finally forming a one-dimensional small artery blood vessel model in the intracranial space.

2. The method for generating a personalized whole-brain small artery vessel based on multiple constraint conditions according to claim 1, wherein, For the feature described in Step A1, using Mimics software, import the CTA images of real head and carotid arteries, and through threshold segmentation, reconstruct the real three-dimensional cerebral arteries and obtain the coordinates at each outlet as the starting position coordinates of blood vessel growth.

3. A method for generating personalized whole-brain small artery blood vessels based on multiple constraint conditions according to claim 1, characterized in that, For the feature described in Step A2, through Geomagic software, measure the geometric parameters of the real cerebral artery at the outlet, including cross-sectional area and length, and record each major cerebral artery branch and its blood supply area; among them, the blood supply areas of each branch of the anterior cerebral artery include: medial orbital gyrus, lateral orbital gyrus, olfactory area, frontal pole, cingulate gyrus, paracentral lobule, superior frontal gyrus, middle frontal gyrus, precentral gyrus, postcentral gyrus, precuneus, superior parietal lobule, and inferior parietal lobule; the blood supply areas of each branch of the middle cerebral artery include the orbital surface of the frontal lobe, lateral frontal, inferior frontal gyrus, precentral gyrus, postcentral gyrus, inferior parietal lobule, superior parietal lobule, supramarginal gyrus, superior temporal gyrus, middle temporal gyrus, inferior temporal gyrus, lateral occipital lobe, and temporal pole; the blood supply areas of each branch of the posterior cerebral artery include: inferior temporal gyrus, fusiform gyrus, lingual gyrus, occipital lobe, cuneus, precuneus, lateral occipital lobe, and superior parietal lobule.

4. A method for generating personalized whole-brain small artery blood vessels based on multiple constraint conditions according to claim 1, characterized in that: The features described in step A3 are as follows: by exporting the 3D point cloud file of the open-source program Brainstorm standard head model, the point cloud coordinates corresponding to 68 brain regions of the cerebral cortex are exported respectively. By uniformly sampling the point cloud, it is used as the end position coordinates for the growth of cerebral arterioles. Among them, the 68 brain regions are based on the Desikan–Killiany atlas, including the superior temporal sulcus, caudal anterior cingulate, middle frontal gyrus, cuneus, entorhinal area, frontal pole, fusiform gyrus, inferior parietal lobule, inferior temporal gyrus, insula, isthmus of cingulate gyrus, lateral occipital lobe, lateral orbital frontal cortex, lingual gyrus, medial orbital frontal cortex, middle temporal gyrus, paracentral lobule, hippocampal gyrus, inferior frontal gyrus, orbital part, triangular part, cingulate gyrus, postcentral gyrus, posterior cingulate gyrus, precentral gyrus, precuneus, parietal lobe, lateral anterior cingulate, lateral frontal, superior frontal gyrus, superior parietal lobule, superior temporal gyrus, supramarginal gyrus, temporal pole, transverse temporal gyrus.

5. A method for generating personalized whole-brain small artery blood vessels based on multiple constraint conditions according to claim 1, characterized in that: The features described in step A4 are as follows: based on the following blood vessel bifurcation diameter model and the scaling ratios of blood vessel diameter-volume, flow-length, diameter-length, and the principle of minimum energy, the simulated annealing algorithm is used to optimize the optimal diameter and length after blood vessel bifurcation. The features described in step A5 are as follows: based on the diameters and lengths of all levels of blood vessel bifurcations obtained in step A4, and based on the starting and ending positions of blood vessel growth determined in steps A2 and A3, then the spatial constraints of the bifurcation angle are performed according to the following HK angle rule to obtain the spatial position coordinates of all levels of bifurcations. Step C1: The HK angle rule is as follows, where α, β, and γ are the angles between the parent blood vessel and the larger daughter blood vessel, the parent blood vessel and the smaller daughter blood vessel, and the two daughter blood vessels respectively. Step C2: According to the HK angle rule calculation formula, substitute the optimized arteriole blood vessel diameter to calculate the bifurcation angles α, β, and γ. Step C3: Based on the starting coordinate A and the diameters and lengths optimized in step A5, establish a coordinate network with A as the center and the length corresponding to the bifurcated blood vessel as the radius to make the coordinates of the next bifurcation point B, and with the bifurcation point B as the center and the length corresponding to the bifurcated blood vessel as the radius respectively make the coordinate networks of the left bifurcation C and the right bifurcation D, thereby finding all possible coordinates for the growth of cerebral arterioles. Step C4: Traverse the bifurcation coordinate networks B, C, and D in a loop, and according to the vector angle calculation formula, calculate the angles between each pair respectively, and compare them with α, β, and γ. Step C5: Traverse and calculate the differences between the angles of the vectors and α, β, and γ respectively. When the difference is the smallest, output the coordinates of B, C, and D; take the B point of this level as the A point for the next level of growth, and the C point and D point of this level are respectively used as the B points for the next level of bifurcation; the coordinates of the remaining levels are calculated according to the above steps in turn to obtain the coordinates of each bifurcation and the terminal position. Step C6: When the distance between the terminal coordinates of the generated cerebral arterioles and the end position coordinates in step A3 is the smallest, stop the growth, the optimization ends, and the spatial position coordinates of all levels of cerebral arterioles are obtained.

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