CN1055828C - Analysis method and instrument for dynamics of cerebral blood circulation - Google Patents

Abstract

The present invention relates to an analysis method and an instrument for the dynamics of cerebral blood circulation. According to the dissection model of an arterial vascular bed for cerebral circulation, an equivalent circuit network model is designed, and a corresponding control equation is established. By the equation, the blood flow and the pressure of various blood vessel sections can be determined by detecting the length and the diameter of the blood vessel sections and blood flow pressure on the mouth end of four persons. The characteristic parameter of the blood vessel sections can also be determined by detecting the blood flow of some cerebral vessels and the blood flow pressure on the mouth end of the four persons. According to the method, a detection analytical instrument composed of a detection system, a microcomputer and analysis software is designed. The present invention has very important significance for cerebral circulation physiological basic research and clinical cerebral circulation.

Description

Cerebro-blood circulation dynamics analytical method and instrument

The invention belongs to field of medical technology, is a kind of cerebro-blood circulation dynamics analytical method and instrument.

Cerebrovascular disease is serious threat human life's commonly encountered diseases and a frequently-occurring disease.Cerebrovascular disease at first causes disturbance of cerebral circulation, makes some regional area cerebral tissue ischemia, and then causes brain cell death.

The cerebral circulation Arterial system, mainly by carotid artery, vertebral-basilar artery and basis cranii WILLIS ring etc. constitutes blood supply net in the brain.Blood flows into this network from left and right sides internal carotid artery and left and right sides vertebral artery respectively.Analyze the interior blood motion rule of such multi-source network and the mechanical characteristic of each bifurcated artery blood vessel, crucial clinical and theory value is arranged preventing, diagnose and treating cerebrovascular disease.

Because brain blood bed is enclosed in the skull deeply, therefore accurate the measurement and the dynamics of analyzing cerebral circulation, still technical theoretically all very difficult.

The eighties is ground into the TCD of merit mid-term abroad, and the using ultrasound Doppler technology can detect some endarterial blood flow rate of intracranial, but still powerless with analysis to the analysis, the particularly detection of cerebrovascular dynamic characteristic of whole cerebral circulation.

External late nineteen seventies, domestic late nineteen eighties has been invented method and the instrument of measuring the carotid artery system vessel properties from common carotid artery in succession.But this quasi-instrument can only be done quantitative description and analysis to the carotid artery system blood vessel, but can't to whole cerebral circulation particularly vertebral-basilar artery system and WILLIS ring etc. detect and analyze.

Therefore, development is used to detect and analyze the method and the instrument of whole cerebral circulation characteristic, becomes present clinical urgency problem to be solved.

The objective of the invention is to design a kind of method and instrument that can carry out the not damaged check and analysis to whole cerebral circulation characteristic.

According to anatomical structure and data, the cerebral circulation arteries can be simplified to as Fig. 1. shown in anatomical model (Hillen, B et al, Analysis of flowand vascul ar resistance in a model of the circle ofWillis, J.Biomech., 21,807-814,1988), wherein, each tremulous pulse pipeline section of cerebral circulation dissects title and the symbol contrast is as follows:

Tremulous pulse title pipeline section symbol	Tremulous pulse title pipeline section symbol
		Internal carotid artery c 1，c 2Basilar artery b vertebral artery V 1，V 2Posterior communicating artery pc 1，pc 2Posterior cerebral artery I p 11，p 22	Anterior cerebral artery I a 11，a 21Anterior communicating artery ac middle cerebral artery m 1， m 2Posterior cerebral artery II p 12，p 22Anterior cerebral artery II a 12，a 22

R _A, R _M, R _PBefore representing brain respectively, in, the vascular bed Peripheral resistance in artery downstream, 1 and 2 are left and right sides internal carotid artery inlet, 3 and 4 are left and right sides vertebral artery inlet.

According to above-mentioned cerebrovascular anatomical model, the present invention has set up the cerebro-blood circulation dynamics lumped parameter model, and its equivalent circuit network model as shown in Figure 2.Wherein, adopt seven model of elements to simulate each bilateral common carotid artery system, with a flow resistance R _AcDescribe the anterior communicating artery, and the left and right sides carotid artery system is joined together.To the vertebral-basilar artery system, every vertebral artery is used a R respectively _v-C _vTwo model of elements simulation in parallel, basilar artery are with a flow resistance R _bSimulation, its elasticity and induction reactance equivalence are in vertebral artery and posterior cerebral artery; The both sides posterior cerebral artery is adopted one four model of element simulation respectively; Between carotid artery system and vertebral-basilar artery system, adopt a R _Pc-L _PcTwo model of elements of connecting simulation arteriae communicans posterior cerebri.The left and right sides cellular construction is symmetric in the model, is that its architectural feature of example is as follows with the left side.Carotid artery system seven model of elements comprise four flow resistances, two fluid capacitances and an induction reactance.At the carotid artery arrival end with a R _C1Simulation carotid artery resistance is at fluid capacitance C in parallel thereafter _C1Be used for simulating the carotid artery compliance, middle cerebral artery and terminal resistance R afterwards thereof are connected in parallel _m, at resistance R _mAfterwards, the anterior cerebral artery resistance R that is connected in series _A11With induction reactance L _A1, the fluid capacitance C of the simulation anterior cerebral artery compliance that is connected in parallel again thereafter _A1R with simulation anterior cerebral artery and terminal resistance thereof _A12At left side L _A1And R _A12Node and right side L _A2And R _A22Node between adopt a flow resistance R _AcLink to each other with the simulation anterior cerebral artery.To the vertebral-basilar artery system, at the vertebral artery arrival end with a flow resistance R _V1Simulation vertebral artery resistance, the fluid capacitance C of a simulation vertebral artery compliance in parallel thereafter _V1, the left and right sides vertebral artery is parallel-connected to simulated substrate tremulous pulse resistance R afterwards _bAn end on.Be connected in series in R after the parallel connection of both sides posterior cerebral artery system _bThe other end.Each side posterior cerebral artery system adopts one four model of element, and it comprises an influenza L _P1, a fluid capacitance C _P1With two flow resistance R _P11With R _P12In this four model of element, influenza L _P1One end is connected in series in R _bOn, the fluid capacitance C of an other end simulation posterior cerebral artery system compliance in parallel _P1Be used to simulate the resistance R of posterior cerebral artery _P11And terminal resistance R _P12Be connected in parallel on C after the series connection _P1Afterwards.The R of simulation posterior communicating artery _Pc1-L _Pc1Series unit one end is connected R _C1With R _M1The node place, the other end is connected R _P12And R _P11The node place.Adopt above-mentioned aggregative model can simulate the cerebral circulation physiological conditions more truly, and aspect Mathematical treatment, be unlikely to undue complexity.

To cerebral circulation model shown in Figure 1, in the middle of concrete the application, also can suitably simplify according to actual needs, as getting some the parameter (R in the network model _i, C _i, L _iDeng) for constant even be zero.The implication of each the parameter representative in the network model specifically is listed as follows: parameter meaning P ₁, P ₂, P ₃, P ₄, four inputs (carotid artery and vertebral artery) inlet pressure C _C1, C _C2Left and right sides common carotid artery compliance R _M1, R _M2Left and right sides middle cerebral artery bed resistance R _A12, R _A22Left and right sides anterior cerebral artery bed resistance C _A1, C _A2Left and right sides anterior cerebral artery compliance R _A11, R _A21Left and right sides anterior cerebral artery section resistance L _A1, L _A2Left and right sides anterior cerebral artery induction reactance R _AcArteriae communicans anterior cerebri resistance R _C1, R _C2Left and right sides carotid artery resistance R _V1, R _V2Left and right sides vertebral artery resistance R _bBasilar artery resistance C _V1, C _V2Left and right sides vertebral artery compliance R _PC1, R _PC2Left and right sides arteriae communicans posterior cerebri resistance L _PC1, L _PC2Left and right sides arteriae communicans posterior cerebri induction reactance C _P1, C _P2Left and right sides posterior cerebral artery compliance L _P1, L _P2Left and right sides posterior cerebral artery induction reactance R _P12, R _P22Left and right sides posterior cerebral artery bed resistance R _P11, R _P21Left and right sides posterior cerebral artery resistance Q _C1, Q _C2Flow Q in the carotid artery _A1, Q _A2Flow Q in the anterior cerebral artery _PC1, Q _PC2Flow Q in the arteriae communicans posterior cerebri _Lp1, Q _Lp2Flow is concluded Q as can be known to above-mentioned parameter in the posterior cerebral artery _iRepresent flow, R _iRepresent resistance of blood flow (also claiming flow resistance), C _iExpression vascular compliance (also claiming fluid capacitance), L _iExpression blood vessel induction reactance (also claiming influenza), subscript is represented the symbol of each corresponding vessel segment.

In the R-C-L analogue model that every blood vessel adopted

(1)L _i＝1.341 _i/D _i ²C _i＝0.7851 _i·D _i ²·β _i

(2) R _i=1.631 _i/ D _i ⁴Wherein 1 _iAnd D _iBe the length and the diameter of corresponding vessel segment, unit is cm, β _iBe the blood vessel elasticity constant, unit is mmHg ^-1

According to this equivalent network model, the present invention has set up the governing equation (also claiming state equation) of following brain circulation system: $D\frac{\mathrm{dX}}{\mathrm{dt}}=\mathrm{EX}+b---\left(3\right)$ Here D=[d _Ij], E=[e _Ij], be 13 rank matrixes, X=[x _i], b=[b _i], be 13 rank vectors,

Expression is to the derivative of time, wherein X=(P _C1, P _C2, P _A1, P _A2, P _v, P _P1, P _P2, Q _A1, Q _A2, Q _Pc1, Q _Pc2, Q _Lp1, Q _Lp2) ^T(4) b=(b ₁, b ₂, 0,0, b ₅, 0,0,0,0,0,0,0) ^T $b_1=\frac{P_1}{R_{C1}},b_1=\frac{P_2}{R_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C9511151300191.png"\; state="\{\{state\}\}">C</figure-callout>}2}},b_5=\frac{P_3}{R_{V1}}+\frac{P_4}{R_{V2}},--\left(5\right)$ The matrix D element is d ₁₁=C _C1, d ₂₂=C _C2, d ₃₃=C _A1, d ₄₄=C _A1, d ₅₅=C _v=C _V1+ C _V2, d ₆₆=C _P1, d ₇₇=C _P2, d ₈₈=L _A1, d ₉₉=L _A1, d ₁₀₁₀=L _PC1, d ₁₁₁₁=L _PC2, d ₁₂₁₂=L _P1, d ₁₃₁₃=L _P2, d _Ij=0 (i ≠ j) (6) matrix E element is

, e ₁₈=-1, e ₁₁₀=-1,

, e ₂₉=-1, e ₂₁₁=-1,

e ₃₈=1,

e ₄₉=1,

e ₅₁₂=-1, e ₅₁₃=-1,

e ₆₁₂=1,

e ₇₁₃=1, e ₈₈=-R _A11, e ₈₁=1, e ₈₃=-1, e ₉₉=-R _A21, e ₉₂=1, e ₉₄=-1,

e ₁₀₁=1,

e ₁₁₂=1,

e ₁₂₁₂=-R _b, e ₁₂₅=1, e ₁₂₆=-1, e ₁₂₁₃=-R _b, e ₁₂₁₃=-R _b, e ₁₃₅=1, e ₁₃₇=-1, e ₁₃₁₂=-R _b, all the other elements are 0.(7)

Use the result of equation (3), can calculate blood flow in other blood vessel by following formula: $Q_{C1}=\frac{P_1-P_{C1}}{R_{C1}},Q_{C1}=\frac{P_2-P_{C2}}{{\mathrm{<figure-callout\; id="2"\; label="R\; C"\; filenames="C9511151300191.png"\; state="\{\{state\}\}">R</figure-callout>}}_C},$ $Q_{V1}=\frac{P_3-P_V}{R_{V1}},{\mathrm{<figure-callout\; id="2"\; label="Q\; V"\; filenames="C9511151300191.png"\; state="\{\{state\}\}">Q</figure-callout>}}_V=\frac{P_4-P_{\mathrm{<figure-callout\; id="2"\; label="V\; R\; V"\; filenames="C9511151300191.png"\; state="\{\{state\}\}">V</figure-callout>}}}{R_V},$ $Q_{\mathrm{ac}}=\frac{P_{a1}-P_{a2}}{R_{\mathrm{ac}}},$ Q _B＝Q _Lp1+Q _Lp2， $Q_{m1}=\frac{P_{C1}}{R_{m1}},{\mathrm{<figure-callout\; id="2"\; label="Q\; m"\; filenames="C9511151300191.png"\; state="\{\{state\}\}">Q</figure-callout>}}_m=\frac{P_{C2}}{R_{m2}}$ $Q_{a12}=\frac{P_{a1}}{R_{a12}},Q_{a22}=\frac{P_{a2}}{R_{a22}},$ $Q_{P12}=\frac{P_{P1}}{R_{P12}+R_{P11}}+\frac{R_{P11}}{R_{P11}+R_{P12}}{Q}_{\mathrm{PC}1},$ $Q_{P22}=\frac{P_{P2}}{R_{P22}+R_{\mathrm{<figure-callout\; id="21"\; label="P"\; filenames="C9511151300181.png"\; state="\{\{state\}\}">P</figure-callout>}21}}+\frac{R_{P21}}{{\mathrm{<figure-callout\; id="21"\; label="R\; P"\; filenames="C9511151300181.png"\; state="\{\{state\}\}">R</figure-callout>}}_P+R_{P22}}{Q}_{\mathrm{PC}2},$ Q _P11＝Q _P12+Q _PC1，Q _P21＝Q _P22+Q _PC2， (8)

Governing equation (3) has provided the physical characteristic of network (as flow resistance R _i, fluid capacitance C _i, induction reactance L _i) wait with blood flowing characteristic (as pressure P _i, flow Q _i) between quantitative relationship.Can solve 13 unknown quantitys by equation (3).If known whole R _i, L _i, C _i, and know the pressure P of four arrival ends ₁-P ₄, can accurately solve every endovascular flow Q so _iAnd pressure P _{I, (i=1 ..., 13)}, be called direct problem.Otherwise, if known four end points pressure P ₁-P ₄And flow Q in some blood vessel that can measure _i(as carotid artery, vertebral artery, middle cerebral artery, the anterior communicating artery, or the like), just can use equation (3) and adopt approximating method to solve the physical characteristic of corresponding pipeline section (as resistance R _i, compliance C _iDeng), be called indirect problem.Specify as follows:

1. direct problem is found the solution:

(1) adopt iconography and morphological method (as MRA, DSA, color ultrasound etc.) can accurately detect the geometric parameter of blood vessel in the head at present: length 1 _i, diameter D _{I, i=1,2 ..., 13}Deng.

(2) using formula group (1)-(2) calculate the characterisitic parameter of these vessel segments: induction reactance L _i, flow resistance R _i, fluid capacitance C _iDeng, and estimate the terminal resistance.

(3) further detect the pressure P of four arrival ends ₁-P ₄

(4) to P _i(t) carry out the Fourier conversion respectively $P_i\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{P}_{\mathrm{ij}}\mathrm{Cos}({{\mathrm{\&omega;}}_j}^t+{\mathrm{\&phi;}}_{\mathrm{Pij}})i=\mathrm{1,2,3,4}--\left(9\right)$ Wherein, ω _j=ω ₀J, ω ₀=2 π/T, T are cardiac cycle.

(5) to each P _Ij, middle j _{(j=0,2..., m)}Can adopt Gauss's pivot elimination approach solving equation (3) respectively, promptly obtain solution vector X

(6) calculate every endovascular blood flow Q in the WILLIS ring again by formula group (8) _iAnd corresponding pressure P _i

Blood flow is provided by the very effective means that provide in intracranial vessel in order accurately to measure for this.The software for calculation block diagram as shown in Figure 4.

2. solution of inverse problems:

In most of the cases, people do not have condition (MRA, equipment prices such as DSA quite expensive) to detect the morphological characteristic of intracranial vessel, and the physics's feature that needs to understand intracranial vessel urgently (is R _i, C _i, L _iDeng numerical value), in such cases, we can adopt other technology such as ultrasonic doppler and TCD, detect some endovascular blood flow (as carotid artery Q _C1, Q _C2, vertebral artery Q _V1, Q _V2Middle cerebral artery Q _M1, Q _M2, posterior cerebral artery Q _P1, Q _P2Deng) and pressure P ₁-P ₄(carotid artery inlet and vertebral artery inlet).After the information that detects these blood motion, concern between blood motion that provides according to equation (3) and the blood vessel dynamics, can adopt the method for numerical fitting to calculate the physics characteristic (R of each vessel segment _i, C _i, L _iDeng), this just provides a kind of resistance R that adopts information such as detecting some interior blood flow of easy survey blood vessel of brain and pressure to calculate intracranial vessel _i, compliance C _iAnd induction reactance L _iMethod.Concrete steps are as follows:

(1) detects the blood flow Q of some vessel segment _i(t), i=1 ... K, K (＜14) is for detecting the blood vessel number of flow.Detect the blood stream pressure P of carotid artery and vertebral artery inlet ₁-P ₄

(2) these parameters are carried out the Fourier transform operation.

(3) consider the steady motion of a fluid and two kinds of situations of unsteady flow, utilize equation (3) to solve vascular resistance R respectively _i, compliance C _iWith induction reactance L _i, i=1,2 ..., 13.Computational methods and formula: to the pressure waveform P of detected four inlet end points _i(t) carry out the Fourier conversion $P_i\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{P}_{\mathrm{ij}}\mathrm{Cos}({{\mathrm{\&omega;}}_j}^t+{\mathrm{\&phi;}}_{\mathrm{pij}})i=\mathrm{1,2,3,3,4}----\left(9\right)$ Equally to flow waveform Q in the detected K root blood vessel _i(t) carry out the Fourier conversion $Q_i\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{ij}}\mathrm{Cos}({{\mathrm{\&omega;}}_j}^t+{\mathrm{\&phi;}}_{\mathrm{qij}})i=1\&hellip;\&hellip;k--\left(10\right)$ Wherein, ω _j=ω ₀J, ω ₀=2 π/T, T are cardiac cycle.

Under the hypothesis of linear system, can be to each P _Ij, Q _IjMiddle j (j=0 ..., m) difference solving equation (3).In two kinds of situation:

I. the steady motion of a fluid: P _i(t)=P _i, Q _i(t)=Q _i

Known: P _i(i=1 ..., 4), Q _i(i=1 ..., K), L _i=0, C _i=0;

Find the solution: R _i(i=1 ..., K) at this moment can obtain the resistance R of this K root blood vessel by establish an equation group (3) and formula group (8) of connection _i(i=1 ..., K) with the terminal resistance.

In unsteady flow, to the P in equation (9) and (10) _I0And Q _I0Also can adopt this method calculate vascular resistance R (=1 ..., K) and the terminal resistance.

II. unsteady flow (also claiming pulsating flow):

Because equation (3) is non-linear and separated numerously, directly solving equation (3) obtains R under the pulsating flow situation _i, C _i, L _iDeng parameter value, can only adopt the method approximate solution of numerical fitting.

Known: P _Ij(i=1 ..., 4; J=0,1 ..., m)

Q _ij(i＝1，...，K；J＝0，1，...，m)

Find the solution: R _i, C _i, L _i, (i=1 ..., 13)

At first use permanent method and obtain some resistance R _iDeng, provide the span of kinetic parameter then according to Human Physiology and anatomical features, as: R _i[R _I1, R _I2], C _i[C _I1, C _I2], L _j[L _I1, L _I2].And get R _i= (R _J1+ R _I2), C _i= (C _I1+ C _I2), L _i= (L _I1+ L _I2) as in the initial value substitution equation (3).Method in the employing direct problem can be tried to achieve one group of unique theory and be separated Q _Ij ^*, (i=1 ..., 13, j=0,1 ..., m) this group theory is separated Q _Ij ^*With actual measured value Q _IjRelatively, calculate error amount DD $\mathrm{DD}=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\frac{{(Q_{\mathrm{ij}}^{*}-Q_{\mathrm{ij}})}^2}{Q_{\mathrm{ij}}^2}k=13$ Use the nonlinear optimization method and change R _i, C _i, L _i, recomputate DD, up to finding out minimum DD.The pairing R of minimum DD _i, C _i, L _i, be the value of being asked.The software for calculation block diagram as shown in Figure 5.3. synthtic price index is found the solution:

In many cases, be subjected to condition restriction, can not detect the blood flow information of intracranial vessel bed, perhaps the information of Jian Ceing is limited, uses said method solving equation (3) and obtains the kinetic parameter of blood vessel (as R _i, C _i, L _i, etc.) possible error is bigger, perhaps amount of calculation is bigger.So just need simplify network model shown in Figure 2.For example: because the variation of induction reactance is little to the influence of blood flow characteristic, desirable so for most people induction reactance equals constant, need not find the solution by equation.Again for example: to carotid artery and vertebral artery, can adopt the ultrasonic measurement blood vessels caliber, can adopt above-mentioned two kinds of method synthesis to find the solution the dynamics parameter of intracranial vessel section so together.Again for example: except supposing that induction reactance is the constant, further some parameter of hypothesis is (as R to network shown in Figure 2 _P12, R _P22, R _A11, R _A21, even some C, be zero), so not only computational speed can be improved in some cases, but also the precision of institute's calculating parameter can be guaranteed.

According to above-mentioned cerebro-blood circulation dynamics analytical method, the present invention has also developed corresponding instrument.This instrument is by the test section, and microcomputer, cerebral circulation model analysis software are formed wherein test section partial pressure detection, flow detection and three subsystems of flow rate detection; These three subsystems all have the technology of comparative maturity at present, and flow rate detection mainly adopts continuous wave ultrasound Doppler measurement carotid artery flow velocity, measure flow velocity in entocranial artery and the vertebral artery with transcranial doppler (TCD).Flow detection mainly adopts impulse ultrasound to measure blood vessel diameter, and the speed that is recorded by the flow rate detection system multiply by the long-pending flow that obtains of tube section again.The main adopts pressure sensor of pressure detecting detects carotid artery pressure fluctuation waveform, adopt great arteriotony value to demarcate then, in most of the cases, the pressure waveform of vertebral artery arrival end can be similar to and adopt the carotid artery pressure waveform, it is the pulsating waveform that the employing ultrasonic technique detects blood vessels caliber that another kind of pressure waveform detects, and then demarcates with great arteriotony.The major function of test section is to detect the pulsating waveform and the numerical value of intravascular pressure and flow thereof.The information that detects mostly is analog quantity, can convert analog quantity to digital quantity by A/D (analog digital conversion) interface, thereby be accepted by microcomputer.The computer part major function of instrument is that 4. 3. 2. 1. control operation process show by special cerebro-blood circulation dynamics software analysis computational dynamics parameter through the A/D image data, stores, and prints result of calculation and sample waveform.Its structured flowchart as shown in Figure 6.

Above-mentioned cerebro-blood circulation dynamics software has comprised various computational methods in front and solution procedure.Meaning of the present invention is:

When known intracranial vessel morphological characteristic and cerebrovascular bed arrival end pressure and flow information, can calculate blood flow and pressure in each section of intracranial blood vessel, so just can understand the distribution state of intracranial blood flow, this is unsolved always in the world at present.

In detecting some blood vessel of intracranial, behind blood flow and the pressure information, can further calculate the dynamics of these vessel segments, as vascular resistance R _i, blood vessel elasticity compliance C _i, and blood vessel induction reactance L _iDeng.This provides a kind of accurately effective method for the mechanical characteristic that detects full cerebrovascular bed, and this did not solve in the world yet.

According to method and the instrument that this patent invention provides, can analyze the characteristic of every vessel segment of intracranial meticulously, this to cerebrovascular disease (as cerebral infarction, cerebral hemorrhage, vertebral-basilar artery insufficiency, cerebral vasospasm, etc.) diagnosis, prevention and treatment very important effect is arranged.Utilize the dynamics that the present invention can the rounded analysis cerebral circulation, comprise the compensatory situation of cerebral blood flow, characteristics such as cerebrovascular arteriosclerosis situation.These are all initiated in the world, and it is all to have a crucial meaning in that the physiological basic research of cerebral circulation or cerebral circulation are clinical.Fig. 1.Cerebral circulation arteries bed anatomical model sketch map Fig. 2.Fig. 3 of equivalent circuit network model corresponding to Fig. 1 anatomical model.Lumped parameter model of element sketch map Fig. 4.The computer software block diagram 5 that direct problem is found the solution.The computer software block diagram 6 of solution of inverse problems.Cerebro-blood circulation dynamics detector structured flowchart

Claims (4)

1. a cerebro-blood circulation dynamics analytical method according to the anatomical model of cerebral circulation vascular bed, has been set up cerebro-blood circulation dynamics equivalent circuit network model, it is characterized in that adopting seven model of elements to simulate each bilateral common carotid artery system, with a flow resistance R _AcDescribe the anterior communicating artery, and the left and right sides carotid artery system is joined together; To the vertebral-basilar artery system, every vertebral artery is used a R respectively _v-C _vTwo model of elements simulation in parallel, basilar artery are with a flow resistance R _bSimulation, its elasticity and induction reactance equivalence are in vertebral artery and posterior cerebral artery; The both sides posterior cerebral artery is adopted one four model of element simulation respectively; Between carotid artery system and vertebral-basilar artery system, adopt a R _Pc-L _PcTwo model of elements of connecting simulation arteriae communicans posterior cerebri; The left and right sides cellular construction is symmetric in the model, and its left carotid artery system seven model of elements comprise four flow resistances, two fluid capacitances and an induction reactance; At the carotid artery arrival end with a R _C1Simulation carotid artery resistance is at fluid capacitance C in parallel thereafter _C1Be used for simulating the carotid artery compliance, middle cerebral artery and terminal resistance R afterwards thereof are connected in parallel _m, at resistance R _mAfterwards, the anterior cerebral artery resistance R that is connected in series _A11With induction reactance L _A1, the fluid capacitance C of the simulation anterior cerebral artery compliance that is connected in parallel again thereafter _A1R with simulation anterior cerebral artery and terminal resistance thereof _A12, at left side L _A1And R _A12Node and right side L _A2And R _A22Node between adopt a flow resistance R _AcLink to each other with the simulation anterior cerebral artery; To vertebra one basilar artery system, at the vertebral artery arrival end with a flow resistance R _V1Simulation vertebral artery resistance, the fluid capacitance C of a simulation vertebral artery compliance in parallel thereafter _V1, the left and right sides vertebral artery is parallel-connected to simulated substrate tremulous pulse resistance R afterwards _bAn end on; Be connected in series in R after the parallel connection of both sides posterior cerebral artery system _bThe other end, each side posterior cerebral artery system adopts one four model of element, it comprises an influenza L _P1, a fluid capacitance C _P1With two flow resistance R _P11With R _P12In this four model of element, influenza L _P1One end is connected in series in R _bOn, the fluid capacitance C of an other end simulation posterior cerebral artery system compliance in parallel _P1, be used to simulate the resistance R of posterior cerebral artery _P11And terminal resistance R _P12Be connected in parallel on C after the series connection _P1Afterwards, the R of simulation posterior communicating artery _Pc1-L _Pc1Series unit one end is connected R _C1With R _M1The node place, the other end is connected R _P12And R _P11The node place.

2. cerebro-blood circulation dynamics analytical method according to claim 1 is characterized in that setting up following brain circulation system governing equation by above-mentioned equivalent network model $D\frac{\mathrm{dX}}{\mathrm{dt}}=\mathrm{EX}+b---\left(3\right)$ Here D=[d _Ij], E=[e _Ij], be 13 rank matrixes, X=[x _i], b=[b _i], be 13 rank vectors,

Expression is to the derivative of time, wherein X=(P _C1, P _C2, P _A1, P _A2, P _v, P _P1, P _P2, Q _A1, Q _A2, Qp _C1, Qp _C2, QL _P1, QL _P2) ^T(4) b=(b ₁, b ₂, 0,0, b ₅, 0,0,0,0,0,0,0,0) ^T $b_1=\frac{P_2}{R_{C1}},b_1=\frac{P_2}{R_{C2}},b_5=\frac{P_3}{R_{V1}}+\frac{P_4}{R_{V2}},---\left(5\right)$ The matrix D element is d ₁₁=C _C1, d ₂₂=C _C2, d ₃₃=C _A1, d ₄₄=C _A2, d ₅₅=C _v=C _V1+ C _V2, d ₆₆=C _P1, d ₇₇=C _P2, d ₈₈=L _A1, d ₉₉=L _A1, d ₁₀₁₀=L _PC1, d ₁₁₁₁=L _PC2, d ₁₂₁₂=L _P1, d ₁₃₁₃=L _P2, d _Ij=0 (i ≠ j) (6) matrix E element is

, e ₁₈=-1, e ₁₁₀=-1,

, e ₂₉=-1, e ₂₁₁=-1, e ₃₈=1,

, e ₄₉=1, , e ₅₁₂=-1, e ₅₁₃=-1,

e ₆₁₂=1, e ₇₁₃=1, e ₈₈=-R _A11, e ₈₁=1, e ₈₃=-1, e ₉₉=-R _A21, e ₉₂=1, e ₉₄=-1

e ₁₀₁=1,

e ₁₁₂=1,

e ₁₂₁₂=-R _b, e ₁₂₅=1, e ₁₂₆=-1, e ₁₂₁₃=-R _b, e ₁₂₁₃=-R _b, e ₁₃₅=1, e ₁₃₇=-1, e ₁₃₁₂=-R _b, all the other elements are 0; Wherein the meaning of each parameter is as follows: parameter meaning P ₁, P ₂, P ₃, P ₄, four input inlet pressure C _C1, C _C2Left and right sides common carotid artery compliance R _M1, R _M2Left and right sides middle cerebral artery bed resistance R _A12, R _A22Left and right sides anterior cerebral artery bed resistance C _A1, C _A2Left and right sides anterior cerebral artery compliance R _A11, R _A21Left and right sides anterior cerebral artery section resistance L _A1, L _A2Left and right sides anterior cerebral artery induction reactance R _AcArteriae communicans anterior cerebri resistance R _C1, R _C2Left and right sides carotid artery resistance R _V1, R _V2Left and right sides vertebral artery resistance R _bBasilar artery resistance C _V1, C _V2Left and right sides vertebral artery compliance R _PC1, R _PC2Left and right sides arteriae communicans posterior cerebri resistance L _PC1, L _PC2Left and right sides arteriae communicans posterior cerebri induction reactance C _P1, C _P2Left and right sides posterior cerebral artery compliance L _P1, L _P2Left and right sides posterior cerebral artery induction reactance R _P12, R _P22Left and right sides posterior cerebral artery bed resistance R _P11, R _P21Left and right sides posterior cerebral artery resistance Q _C1, Q _C2Flow Q in the carotid artery _A1, Q _A2Flow Q in the anterior cerebral artery _PC1, Q _PC2Flow Q in the arteriae communicans posterior cerebri _Lp1, Q _Lp2Flow in the posterior cerebral artery

3。Cerebro-blood circulation dynamics analytical method according to claim 2 is characterized in that concrete steps are as follows:

(1) the geometric parameter length l of detection head intracranial vessel _i, diameter D _{I, i=1 ... 13}, the cm of unit;

(2) calculate the characterisitic parameter of these vessel segments by following formula: induction reactance L _i, flow resistance R _iWith fluid capacitance C _i: L _i=1.341 _i/ D _i ²C _i=0.7851 _iD _i ²β _iR _i=1.631 _i/ D _i ⁴(3) pressure P of four arrival ends of detection ₁(t)-P ₄(t) and estimate terminal resistance (4) to P _i(t) carry out the Fourier conversion respectively: $P_i\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{P}_{\mathrm{ij}}\mathrm{Cos}({{\mathrm{\&omega;}}_j}^t+{\mathrm{\&phi;}}_{\mathrm{Pij}})$ Wherein, ω _j=ω ₀J, ω ₀=2 π/T, T are cardiac cycle;

(5) to each P _IjIn j (j=0,2 ..., m) find the solution state equation (3) respectively, solution vector X;

(6) calculate every section endovascular blood flow by formula (8) again.

4. cerebro-blood circulation dynamics analytical method according to claim 2 is characterized in that concrete steps are as follows:

(1) detects the blood flow Q of some vessel segment _i(t), i=1,2 ..., K, K≤13, K is detected blood vessel hop count, detects the blood stream pressure P of carotid artery and vertebral artery inlet ₁(t)-P ₄(t);

(2) to P _i(t) and Q _i(t) carry out Fourier conversion (3) respectively for permanent mobility status, equation (3) turns to Algebraic Equation set, can obtain unique solution, obtains the Resistance Value R of each section blood vessel _i, i=1,2 ..., K; (4) for the unsteadiness mobility status, ask equation (3) with fitting process, obtain the resistance R of each section blood vessel _iWith compliance C _iValue.

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