CN1055829C - Brain willis circulation dynamics analysing method and instrument - Google Patents

Abstract

The present invention belongs to a cerebral circulation blood dynamics analyzing method and an instrument. A method for rapidly analyzing and calculating the dynamical parameter of cerebral circulation is established according to the anatomical model of a cerebral circulating arterial vascular bed, an equivalent network model thereof and a corresponding control equation, by using a Doppler to detect the blood flow speed of main branch blood vessels in the skull and by using an imaging method to obtain the geometric parameter of cerebral vessels. According to the analytical method, the analytical instrument is designed and is composed of a detection system, a collection analysis and calculation system and a storage and output system. The present invention has the advantages of great enhancement of a detection analysis speed and has important significance for the basic research and the clinical application of cerebral circulation.

Description

Brain willis circulation dynamics analysing 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, vertebra-basilar artery and basis cranii WILLIS ring etc. constitute 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, diagnosing and treat 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 vertebra one 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 quick nondestructive check and analysis to whole cerebral circulation characteristic.

Because no matter cerebral circulation vascular bed is geometrical property or dynamics, all circulation has essential difference with body.Therefore, the kinetic model of extensive use once, analytical method etc. all can not be indiscriminately imitated in the research of cerebral circulation simply in the body circulating research.The present invention considers the particularity of brain Willis ring structure, in the kinetic parameter analytical method of having set up the suitable clinical practice of a cover on the theoretical model basis of experimental verification.

According to anatomical structure and data, the letter of cerebral circulation arteries can be become as Fig. 1.Shown anatomical model (Hillen, B et al, Analysis of flow andvascular resistance in a model of the circle of Willis, J.Biomech., 21,807-814,1988), wherein, each artery segment 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, we adopt one seven model of element simulation carotid artery subsystem, and in this subsystem, we have not only considered vascular resistance and compliance but also have considered the induction reactance (L of blood vessel _A1And L _A2).With a flow resistance R _AcDescribe the anterior communicating artery, the left and right sides carotid artery system is joined together.To vertebra one basilar artery system, respectively with the simulation of R-C two model of element, basilar artery are with a flow resistance R with every vertebral artery _bSimulation, its elasticity and induction reactance equivalence are in vertebral artery and posterior cerebral artery; The both sides posterior cerebral artery is adopted one 4 model of element simulation respectively; Between carotid artery system and vertebral-basilar artery system, adopt a R-L two model of elements simulations arteriae communicans posterior cerebri of connecting.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, be constant even be zero as some parameters (R, C, L etc.) that can get in the network model.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 Qv1 in the carotid artery of the left and right sides, Qv2 left and right sides vertebra power arteries and veins flow Qm1, Qm2 left and right sides middle cerebral artery flow Q _A1, Q _A2Flow Q in the anterior cerebral artery _PC1, Q _PC2Flow Q in the posterior cerebral artery _Lp1, Q _Lp2Flow is concluded Pi representative pressure as can be known, Q to above-mentioned parameter in the arteriae communicans posterior cerebri _iRepresent flow, R _iRepresent resistance of blood flow (also claiming flow resistance), C _iExpression vascular compliance (also claiming fluid capacitance), L represents 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

L _i＝1.341 _i/D _i ² (1)

R _i=1.631 _i/ D _i ⁴(2) wherein 1 _iAnd D _iBe the length and the diameter of corresponding vessel segment, unit is cm.

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, 0,0,0,0,0,0,0,0) ^T $b_1=\frac{P_1}{R_C},b_1=\frac{P_2}{R_{C2}},b_5=\frac{P_3}{R_{V1}}+\frac{P_4}{R_{V2}},----\left(5\right)$ The matrix D element is d ₁₁=C _C1, d ₂₂=C _C2, d ₃₃=C _A1, d ₄₄=C _A1, d ₅₅=C _v, 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 _B=Q _Lp1+ Q _Lp2,

${\mathrm{<figure-callout\; id="12"\; label="Q\; P"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">Q</figure-callout>}}_P=\frac{P_{P1}}{R_{\mathrm{<figure-callout\; id="12"\; label="P"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">P</figure-callout>}12}+R_{\mathrm{<figure-callout\; id="11"\; label="P"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">P</figure-callout>}11}}+\frac{R_{P11}}{R_{\mathrm{<figure-callout\; id="11"\; label="P"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">P</figure-callout>}11}+R_{P12}}{Q}_{\mathrm{PC}1},$ $Q_{P22}=\frac{P_{P2}}{R_{P22}+R_{P21}}+\frac{\mathrm{RP}21}{\mathrm{RP}21+\mathrm{RP}22}{Q}_{\mathrm{PC}2},$ 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 _iOtherwise, 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.Concrete grammar is seen another patent application (No95111513.8) of inventor.But this method is in clinical practice, and a patient's of analysis situation takes longer, generally wants more than 2 hours.The present invention utilizes the ultransonic state-of-the-art technology of current intracranial on above-mentioned model based, a kind of new analysis calculation method is provided, and the development corresponding instrument.The present invention adopts transcranial doppler to detect blood flow rate in the main branch vessel of intracranial, adopt the iconography method to obtain the cerebrovascular geometric parameter, and, reflect that brain Willis encircles the kinetic parameter of blood circulation state thereby can calculate rapidly and accurately to the simplification that equation is made a match and managed.

According to above-mentioned cerebrovascular dynamic model and state equation, can obtain the cerebral hemodynamic parameter value quickly and accurately particularly by following step.

1. use physiological pressure transducer or ultrasonic blood vessel diameter detecting instrument, detect patient's carotid artery and vertebrarterial pressure pulsation, and use brachial artery pressure numerical value, its waveform is demarcated, thereby obtain P1 (t), P2 (t), P3 (t), waveform and the numerical value of P4 (t) P1 (t).

2. use B ultrasound probe and doppler ultrasound velocity of blood flow probe, directly detect the interior blood-flow waveform of carotid artery and vertebral artery and numerical value: Qc1 (t), Qc2 (t), Qv1 (t), Qv2 (t).

3. use TCD,transcranial Doppler doppler transducer (TCD) and detect the intracranial middle cerebral artery, flow velocity waveforms and numerical value in anterior cerebral artery and the posterior cerebral artery.By patient DSA or/and the MRA blood vessel image is learned data, obtain the proportionate relationship of outer tremulous pulse (as common carotid artery, the vertebral artery etc.) diameter of entocranial artery diameter and cranium, the numerical value of the outer artery diameter of the cranium that application Type B ultrasonic probe or blood vessels caliber ultrasonic probe record, can obtain the caliber of intracranial vessel, further calculate endarterial blood-flow waveform and numerical value, i.e. Qa1 (t), Qa2 (t), Qm1 (t), Qm2 (t), Qlp1 (t) and Qlp2 (t) before, during and after the brain with formula group (8).

4. use DSA and MRA data, obtain the length and the diameter of relevant vessel segment, using formula (1), (2) calculate the resistance and the induction reactance of some single vessel of intracranial.Be the numerical value of Ra11, Ra12, Rpc1, Rpc2, Rac, Rb, La1, La2, Lpc1, Lpc2, Lp1, Lp2.

5. calculate carotid artery and vertebral artery resistance Rc1, Rc2, Rv1, Rv2. $\mathrm{Rci}=\frac{1}{k-2}\underset{j=3}{\overset{k}{\mathrm{\&Sigma;}}}\left|Z{c}_{\mathrm{ij}}\right|$ (9) $\mathrm{Rvi}=\frac{1}{k-2}\underset{j=3}{\overset{k}{\mathrm{\&Sigma;}}}\left|Z{v}_{\mathrm{ij}}\right|$ Wherein, i=1,2, k desirable 10,11 or 12, and Zc1, Zc2 and Zv1, Zv2 are respectively carotid artery and vertebrarterial input impedance mould.They can be analyzed by the Fouriev of carotid artery and vertebral artery pressure and flow waves and obtain, promptly $P_i\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{P}_{\mathrm{ij}}\cos (\left({\mathrm{\&omega;}}_{j}t\right)+{\mathrm{\&phi;}}_{\mathrm{pij}})$ i＝1，2...，4 (10) $Q_{\mathrm{ci}}\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{cij}}\cos (\left({\mathrm{\&omega;}}_{j}t\right)+{\mathrm{\&phi;}}_{\mathrm{qcij}})$ $Q_{\mathrm{vi}}\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{vij}}\cos (\left({\mathrm{\&omega;}}_{j}t\right)+{\mathrm{\&phi;}}_{\mathrm{qvij}})$ I=1,2 (11) p here _Ij, φ _Pij, Q _Cij, φ _QcijAnd Q _Vij, φ _QvijBe respectively mould and argument that pressure and flow Fourier change $\left|Z_{\mathrm{cij}}\right|=\frac{P_{\mathrm{ij}}}{Q_{\mathrm{cij}}}i=\mathrm{1,2};j=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,m----\left(12\right)$ $\left|Z_{\mathrm{vij}}\right|=\frac{P_{i+2,j}}{Q_{\mathrm{vij}}}i=\mathrm{1,2};j=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,m----\left(13\right)$

6. adopt permanent theoretical method, can obtain the resistance of each blood vessel terminal of intracranial by following formula: ${\mathrm{<figure-callout\; id="1"\; label="R\; m"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">R</figure-callout>}}_m=\frac{{\stackrel{-}{P}}_1-{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">c</figure-callout>}1}\&CenterDot;R_{c1}}{{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">m</figure-callout>}1}},{\mathrm{<figure-callout\; id="2"\; label="R\; m"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">R</figure-callout>}}_m=\frac{{\stackrel{-}{P}}_2-{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">c</figure-callout>}2}\&CenterDot;R_{c2}}{{\stackrel{-}{Q}}_{m2}}----\left(14\right)$ ${\mathrm{<figure-callout\; id="12"\; label="R\; P"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">R</figure-callout>}}_P=\frac{{\stackrel{-}{P}}_3-{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">v</figure-callout>}1}\&CenterDot;R_{v1}-({\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">v</figure-callout>}1}+{\stackrel{-}{Q}}_{v2}){\&CenterDot;R}_b-{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="1"\; label="LP"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">LP</figure-callout>}1}\&CenterDot;R_{P11}}{{\stackrel{-}{Q}}_{P12}}----\left(15\right)$ $R_{p22}=\frac{{\stackrel{-}{P}}_4-{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">v</figure-callout>}2}\&CenterDot;R_{v2}-({\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">v</figure-callout>}1}+{\stackrel{-}{Q}}_{v2})\&CenterDot;R_b-{\stackrel{-}{Q}}_{\mathrm{<figure-callout\; id="2"\; label="Lp"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">Lp</figure-callout>}2}\&CenterDot;R_{p21}}{{\stackrel{-}{Q}}_{p22}}----\left(16\right)$ $R_{a12}=\frac{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\&CenterDot;h_{22}-{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\&CenterDot;h_{12}}{{\mathrm{<figure-callout\; id="11"\; label="h"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">h</figure-callout>}}_{11}\&CenterDot;h_{22}-{\mathrm{<figure-callout\; id="12"\; label="h"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">h</figure-callout>}}_{12}\&CenterDot;h_{21}},R_{a22}=\frac{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\&CenterDot;h_{11}-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\&CenterDot;h_{21}}{{\mathrm{<figure-callout\; id="11"\; label="h"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">h</figure-callout>}}_{11}\&CenterDot;h_{22}-{\mathrm{<figure-callout\; id="12"\; label="h"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">h</figure-callout>}}_{12}\&CenterDot;h_{21}}----\left(17\right)$ Here P and Q represent P (t) and Q (t) meansigma methods at a cardiac cycle, and P _i=Q _CiR _Ci+ (Q _Ai2+ (1) ^I+1Qac) R _Ai1+ Q _Ai2R _Ai2(18) Q _Ac=(Q _A12R _A12-Q _A22R _A22)/R _Ac(19) Q _Pi2=Q _Lpi+ Q _Ci-Q _Mi-Q _Ai2+ (1) ^I+1Q _Ac(20) f _i=P _i-Q _CiR _Ci-Q _Ai2R _Ai1(21) h _Ii=(1+R _Ai1/ R _Ac) Q _Ai2(22) h ₁₂=-(R _A11/ R _Ac) Q _A22, h ₂₁=-(R _A21/ R _Ac) Q _A12(23) i=1,2

7. use equation group (8) and can further obtain the interior pressure P of each pipeline section _C1=P ₁-Q _C1R _C1., P _C2=P ₂-Q _C2R _C2(24) $P_v=\frac{1}{2}(P_3+P_4-Q_{v1}\&CenterDot;R_{v1}-Q_{v2}\&CenterDot;R_{v2})----\left(25\right)$ P _a1＝Q _a12·R _a12， P _a2＝Q _a22·R _a22 (26) ${\mathrm{<figure-callout\; id="1"\; label="P\; p"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">P</figure-callout>}}_p=P_v-R_b\&CenterDot;Q_b-{\mathrm{<figure-callout\; id="1"\; label="L\; p"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">L</figure-callout>}}_p\&CenterDot;\frac{\mathrm{<figure-callout\; id="1"\; label="d\; Q\; Lp"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">d</figure-callout>}{Q}_{\mathrm{Lp}}{1}_{}}{\mathrm{dt}}----\left(27\right)$ ${\mathrm{<figure-callout\; id="2"\; label="P\; p"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">P</figure-callout>}}_p=P_v-R_b\&CenterDot;Q_b-{\mathrm{<figure-callout\; id="2"\; label="L\; p"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">L</figure-callout>}}_p\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="d\; Q\; Lp"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">d</figure-callout>}{Q}_{\mathrm{Lp}}{2}_{}}{\mathrm{dt}}----\left(28\right)$

8. flow Q in other blood vessels of intracranial _A1, Q _A2, Q _Pc1And Q _Pc2For: $Q_{\mathrm{ai}}=e^{-\frac{\mathrm{<figure-callout\; id="1"\; label="Rai"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">Rai</figure-callout>}1}{\mathrm{Lai}}t}\&lsqb;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)}{\mathrm{Lai}}\&CenterDot;e^{\frac{\mathrm{Rai}1}{\mathrm{Lai}}\mathrm{\&tau;}}\mathrm{d\&tau;}+{S1}_i\&rsqb;----\left(29\right)$ Wherein ${S1}_i=\frac{T({\stackrel{-}{Q}}_{\mathrm{ai}2}-{(-1)}^i{\stackrel{-}{Q}}_{\mathrm{ac}})-{\&Integral;}_0^T{e}^{-\frac{\mathrm{Rai}}{\mathrm{Lai}}t}\&CenterDot;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)}{\mathrm{Lai}}\&CenterDot;e^{\frac{R_{\mathrm{ai}1}}{\mathrm{Lai}}\mathrm{\&tau;}}\mathrm{d\&tau;dt}}{{\&Integral;}_0^T{e}^{-\frac{\mathrm{Rai}1}{\mathrm{Lai}}t}\mathrm{dt}}$ i＝1，2 $Q_{\mathrm{pci}}=e^{-K_i\&CenterDot;t}\&lsqb;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-{\mathrm{<figure-callout\; id="2"\; label="R\; pi"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{pi}}\&CenterDot;P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)/({\mathrm{<figure-callout\; id="2"\; label="R\; pi"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{pi}}+R_{\mathrm{pi}1})}{L_{\mathrm{pci}}}\&CenterDot;e^{K_i\&CenterDot;\mathrm{\&tau;}}\mathrm{d\&tau;}+{S2}_i\&rsqb;---\left(30\right)$ Wherein $S{2}_i=\frac{T{\stackrel{-}{Q}}_{\mathrm{pci}}-{\&Integral;}_0^T{e}^{-K_i\&CenterDot;t}\&CenterDot;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-{\mathrm{<figure-callout\; id="2"\; label="R\; pi"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{pi}}\&CenterDot;P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)/({\mathrm{<figure-callout\; id="2"\; label="R\; pi"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{pi}}+R_{\mathrm{pi}1})}{L_{\mathrm{pci}}}\&CenterDot;e^{K_i\&CenterDot;\mathrm{\&tau;}}\mathrm{d\&tau;dt}}{{\&Integral;}_0^T{e}^{-K_i\&CenterDot;t}\mathrm{dt}}$ $K_i=\frac{R_{\mathrm{pci}}+R_{\mathrm{pil}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="R\; pi"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{pi}}/(R_{\mathrm{pil}}+R_{\mathrm{pi}2})}{L_{\mathrm{pci}}}$ i＝1，2

9. the intracranial compliance is: ${\mathrm{<figure-callout\; id="1"\; label="C\; c"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">C</figure-callout>}}_c=\frac{1}{P_{c1}\left(T_s\right)-P_{c1}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}({\mathrm{<figure-callout\; id="11"\; label="e"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">e</figure-callout>}}_{11}\&CenterDot;P_{c1}-Q_{\mathrm{pc}1}-Q_{a1}+\frac{P_1}{R_{c1}})\mathrm{dt}----\left(31\right)$ ${\mathrm{<figure-callout\; id="2"\; label="C\; c"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">C</figure-callout>}}_c=\frac{1}{P_{c2}\left(T_s\right)-P_{c2}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(e_{22}\&CenterDot;P_{c2}-Q_{\mathrm{pc}2}-Q_{a2}+\frac{P_2}{R_{c2}})\mathrm{dt}----\left(32\right)$ $C_v=C_{v1}+C_{v2}=\frac{1}{P_v\left(T_s\right)-P_v\left(T_0\right)}\&CenterDot;{\&Integral;}_{T_0}^{T_s}(-\frac{R_{v1}+R_{v2}}{R_{v1}\&CenterDot;R_{v2}}{P}_v+\frac{P_3}{R_{v1}}+\frac{P_4}{R_{v2}}-Q_b)\mathrm{dt}----\left(33\right)$ ${\mathrm{<figure-callout\; id="1"\; label="C\; p"\; filenames="C9611633900242.png"\; state="\{\{state\}\}">C</figure-callout>}}_p=\frac{1}{P_{p1}\left(T_s\right)-P_{p1}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(-\frac{P_{p1}}{{\mathrm{<figure-callout\; id="11"\; label="R\; p"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">R</figure-callout>}}_p+R_{p12}}-\frac{{\mathrm{<figure-callout\; id="12"\; label="R\; p"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">R</figure-callout>}}_p\&CenterDot;Q_{\mathrm{pc}1}}{{\mathrm{<figure-callout\; id="11"\; label="R\; p"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">R</figure-callout>}}_p+{\mathrm{<figure-callout\; id="12"\; label="R\; p"\; filenames="C9611633900241.png"\; state="\{\{state\}\}">R</figure-callout>}}_p}+Q_{\mathrm{Lp}1})\mathrm{dt}----\left(34\right)$ ${\mathrm{<figure-callout\; id="2"\; label="C\; p"\; filenames="C9611633900191.png"\; state="\{\{state\}\}">C</figure-callout>}}_p=\frac{1}{P_{p2}\left(T_s\right)-P_{p2}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(-\frac{P_{p2}}{R_{p21}+R_{p22}}-\frac{R_{p22}\&CenterDot;Q_{\mathrm{pc}2}}{R_{p21}+R_{p22}}+Q_{\mathrm{Lp}2})\mathrm{dt}----\left(35\right)$ $C_{a1}=\frac{1}{P_{a1}\left(T_s\right)-P_{a1}\left(T_0\right)}{\&Integral;}_{T_0}^{T_s}(e_{33}\&CenterDot;P_{a1}+e_{34}\&CenterDot;P_{a2}-Q_{a1})\mathrm{dt}----\left(36\right)$ $C_{a2}=\frac{1}{P_{a2}\left(T_s\right)-P_{a2}\left(T_0\right)}{\&Integral;}_{T_0}^{T_s}(e_{44}\&CenterDot;P_{a2}+e_{43}\&CenterDot;P_{a2}-Q_{a2})\mathrm{dt}----\left(37\right)$ Here, To and Ts are that heart contraction begins and the time that finishes.

According to above-mentioned analytical method, the present invention has also developed corresponding instrument, i.e. brain Willis ring circulation dynamics analytical tool.This instrument is divided into 3 parts: detection system, acquisition analysis system, storage output system.Wherein detection system has two parts, first is intracranial vessel blood flow rate test section, and it is a ultrasonic Doppler probe, and supersonic frequency is 2-3MHZ, adopt pulse to wear the cranium Doppler technology, can detect the blood flow rate in middle cerebral artery, prerolandic artery Rolando and artery and the basilar artery.This part also can adopt the TCD technology of present comparative maturity.Second portion is the outer vascular pressure flow detection part of cranium, comprises continuous ultrasound ripple doppler transducer, physiological pressure transducer or ultrasonic blood vessel diameter probe that a frequency is 5-8MHZ.Continuous ultrasound ripple probe is used to detect blood flow rate and the blood flow in cranium arteria carotis externa or the vertebral artery.Pressure transducer or ultraphonic pipe diameter probe are used to detect the blood vessel wall waveform of beating, and use brachial arterial pressure numerical value again it is demarcated, and then obtain pressure waveform numerical value.The collection computing system is reached by a master computer and A/D converter, communication microcomputer to be formed corresponding to the analytical calculation software of said method.By A/D converter aforementioned detected analog signal conversion is become digital signal, and adopt in the computer initial data as analytical calculation.If above-mentioned signal has converted digital signal (as data among the TCD) in collection, then can adopt the microcomputer communication mode, import data into master computer.Analytical calculation software is worked out according to the inventive method, and software block diagram is seen Fig. 5.It is according to above-mentioned blood flow and pressure information, and the cerebrovascular geometric parameter that obtains from imaging examination, and analysis meter is calculated the every hematodinamics index of brain Willis ring circulation.Data are stored with output and are made up of hard disk, floppy disk, tape, printer etc., the normal parameter value contrast of storing in patient's brain recirculation dynamic index that it can obtain the analytical calculation system and the main frame is judged, output analyzing and testing result, and prompting patient's hematodinamics state, for the clinical analysis cerebrovascular function provides quantitative target and reference proposition.

The apparatus structure block diagram as shown in Figure 6 and Figure 7.The present invention can provide two kinds of forms.A kind of distributing, promptly the test section utilizes existing equipment, and as TCD, CVA etc., promptly detecting the intracranial vessel blood flow rate is a unit, and detecting outer vascular flow speed of cranium and pressure is a unit, adopts communication modes to connect with main frame.Another kind is an integrated form, wherein all probes all is installed on the main frame, forms an integral body.

Clinical practice is for example: certain male patient, the applying pressure pick off records the left carotid artery pressure waveform, as shown in Figure 8, with ultrasonic technique detect flow waveform, as shown in Figure 9.The vertebral artery flow waveform, as shown in phantom in Figure 10.Use the inventive method, on Compaq486 DX-100 computer, moved about 30 seconds, promptly calculate cerebral hemodynamic parameter, list in the following table: the cerebral circulation power numerical value resistance (dyns/cm that Theoretical Calculation obtains ⁵) induction reactance (dyns ²/ cm ⁵) compliance (cm ⁵/ dyn) Rm ₁2.08 * 10 ⁴La1 1.04 * 10 ²Cc ₁7.53 * 10 ^-5Ra ₁₂4.11 * 10 ⁴Lpc1 3.16 * 10 ²Ca ₁8.26 * 10 ^-6Rp ₁₂2.22 * 10 ⁴Lp1 2.47 * 10 ²Cp ₁3.89 * 10 ^-6Rc ₁1.84 * 10 ³Cv1 5.23 * 10 ^-5Rv ₁2.37 * 10 ³These value inverse iterations are gone into the aforementioned calculation formula, calculate theoretical carotid artery and vertebral artery flow waveform and see solid line among Fig. 9 and Figure 10, contrast finds that Theoretical Calculation result is very approaching with the actual measurement value.This proves absolutely that the method that the present invention proposes is successful.It is feasible that clinical practice is used, and analytical calculation speed improves greatly.Fig. 1 is a cerebral circulation vascular bed anatomical model sketch map; Fig. 2 is the equivalent circuit network model corresponding to Fig. 1 anatomical model; Fig. 3 is a lumped parameter model of element sketch map; Fig. 4 is data flow block diagram among the present invention; Fig. 5 is analytical calculation software block diagram among the present invention; Fig. 6 is an instrument distributing block diagram of the present invention; Fig. 7 is the centralized block diagram of instrument of the present invention; Fig. 8 is detected carotid artery pressure waveform; Fig. 9 is carotid artery stream waveform, and wherein dotted line is a detection waveform, and solid line is the Theoretical Calculation waveform; Figure 10 is the vertebral artery flow waveform, and wherein dotted line is a detection waveform, and solid line is the Theoretical Calculation waveform;

Claims (2)

1 one kinds of brain willis circulation dynamics analysing methods according to the anatomical model of cerebrovascular bed, are set up equivalent circuit network model and control corresponding equation, it is characterized in that calculating the acquisition cerebral hemodynamic parameter by following step:

(1) uses physiological pressure transducer or ultrasonic blood vessel diameter detecting instrument, detect patient's carotid artery and vertebrarterial pressure pulsation, and use brachial artery pressure numerical value, its waveform is demarcated, thereby obtain P1 (t), P2 (t), P3 (t), waveform and the numerical value of P4 (t);

(2) use super ripple probe of Type B and doppler ultrasound velocity of blood flow probe, directly detect the interior blood-flow waveform of carotid artery and vertebral artery and numerical value: Qc1 (t), Qc2 (t), Qv1 (t), Qv2 (t);

(3) use TCD,transcranial Doppler doppler transducer (TCD) and detect the intracranial middle cerebral artery, flow velocity waveforms in anterior cerebral artery and the posterior cerebral artery and numerical value pass through patient DSA or/and the MRA blood vessel image is learned data, obtain the outer tremulous pulse of entocranial artery diameter and cranium (as common carotid artery, vertebral artery etc.) proportionate relationship of diameter, the numerical value of the outer artery diameter of the cranium that application Type B ultrasonic probe or blood vessels caliber ultrasonic probe record, can obtain the caliber of intracranial vessel, and before further calculating brain, in, blood-flow waveform and numerical value in the artery, i.e. Qa1 (t), Qa2 (t), Qm1 (t), Qm2 (t), Qlp1 (t) and Qlp2 (t);

(4) use DSA and MRA data, obtain the length and the diameter of relevant vessel segment, using formula

L _i＝1.341 _i/D _i ² (1)

R _i=1.631 _i/ D _i ⁴(2) resistance and the induction reactance that calculates some single vessel of intracranial is the numerical value of Ral1, Ral2, Rapc1, Rpc2, Rac, Rb, La1, La2, Lpc1, Lpc2, Lp1, Lp2;

(5) calculate carotid artery and vertebral artery resistance Rc1, Rc2, Rv1, Rv2: $\mathrm{Rci}=\frac{1}{k-2}\underset{j=3}{\overset{k}{\mathrm{\&Sigma;}}}\left|Z{c}_{\mathrm{ij}}\right|$ (9) $\mathrm{Rvi}=\frac{1}{k-2}\underset{j=3}{\overset{k}{\mathrm{\&Sigma;}}}\left|Z{v}_{\mathrm{ij}}\right|$ Wherein, i=1,2, k desirable 10,11 or 12, and Zc1, Zc2 and Zv1, Zv2 are respectively carotid artery and vertebrarterial input impedance mould, and they can be analyzed by the Fouriev of carotid artery and vertebral artery pressure and flow waves and obtain, promptly $P_i\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{P}_{\mathrm{ij}}\cos (\left({\mathrm{\&omega;}}_{j}t\right)+{\mathrm{\&phi;}}_{\mathrm{pij}})$

i＝1，2...，4 (10) $Q_{\mathrm{ci}}\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{cij}}\cos (\left({\mathrm{\&omega;}}_{j}t\right)+{\mathrm{\&phi;}}_{\mathrm{qcij}})$ $Q_{\mathrm{vi}}\left(t\right)=\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{vij}}\cos (\left({\mathrm{\&omega;}}_{j}t\right)+{\mathrm{\&phi;}}_{\mathrm{qvij}})$

I=1,2 (11) p here _Ij, φ _Pij, Q _Cij, φ _QcijAnd Q _Vij, φ _QvijBe respectively the mould argument that pressure and flow Fourier change $\left|Z_{\mathrm{cij}}\right|=\frac{P_{\mathrm{ij}}}{Q_{\mathrm{cij}}}i=\mathrm{1,2};j=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,m----\left(12\right)$ $\left|Z_{\mathrm{vij}}\right|=\frac{P_{i+2,j}}{Q_{\mathrm{vij}}}i=\mathrm{1,2};j=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,m----\left(13\right)$ (6) adopt permanent theoretical method, can obtain the resistance of each blood vessel terminal of intracranial by following formula: $R_{m1}=\frac{{\stackrel{-}{P}}_1-{\stackrel{-}{Q}}_{c1}\&CenterDot;R_{c1}}{{\stackrel{-}{Q}}_{m1}},R_{m2}=\frac{{\stackrel{-}{P}}_2-{\stackrel{-}{Q}}_{c2}\&CenterDot;R_{c2}}{{\stackrel{-}{Q}}_{m2}}----\left(14\right)$ $R_{p12}=\frac{{\stackrel{-}{P}}_3-{\stackrel{-}{Q}}_{v1}\&CenterDot;R_{v1}-({\stackrel{-}{Q}}_{v1}+{\stackrel{-}{Q}}_{v2})\&CenterDot;R_b-{\stackrel{-}{Q}}_{\mathrm{Lp}1}\&CenterDot;R_{p11}}{{\stackrel{-}{Q}}_{p12}}----\left(15\right)$ $R_{p22}=\frac{{\stackrel{-}{P}}_4-{\stackrel{-}{Q}}_{v2}\&CenterDot;R_{v2}-({\stackrel{-}{Q}}_{v1}+{\stackrel{-}{Q}}_{v2})\&CenterDot;R_b-{\stackrel{-}{Q}}_{\mathrm{Lp}2}\&CenterDot;R_{p21}}{{\stackrel{-}{Q}}_{p22}}----\left(16\right)$ $R_{a12}=\frac{f_1\&CenterDot;h_{22}-f_2\&CenterDot;h_{12}}{h_{11}\&CenterDot;h_{22}-h_{12}\&CenterDot;h_{21}},R_{a22}=\frac{f_2\&CenterDot;h_{11}-f_1\&CenterDot;h_{21}}{h_{11}\&CenterDot;h_{22}-h_{12}\&CenterDot;h_{21}}----\left(17\right)$ Here P and Q represent P (t) and Q (t) meansigma methods at a cardiac cycle, and P _i=Q _CiR _Ci+ (Q _Ai2+ (1) ^I+1Q _Ac) R _Ai1+ Q _Ai2R _Ai2(18) Q _Ac=(Q _A12R _A12-Q _A22R _A22)/R _Ac(19) Q _Pi2=Q _Lpi+ Q _Ci-Q _Mi-Q _Ai2+ (1) ^I+1Q _Ac(20) f _i=P _i-Q _CiR _Ci-Q _Ai2R _Ai1(21) h _Ii=(1+R _Ai1/ R _Ac) Q _Ai2(22) h ₁₂=-(R _A11/ R _Ac) Q _A22, h ₂₁=-(R _A21/ R _Ac) Q _A12(23) i=1,2 (7) use equation (8) can further obtain the interior pressure of pipeline section: P fully _C1=P ₁-Q _C1R _C1, P _C2=P ₂-Q _C2R _C2(24) $P_v=\frac{1}{2}(P_3+P_4-Q_{v1}\&CenterDot;R_{v1}-Q_{v2}\&CenterDot;R_{v2})----\left(25\right)$ P _a1＝Q _a12·R _a12， P _a2＝Q _a22·R _a22 (26) $P_{p1}=P_v-R_b\&CenterDot;Q_b-L_{p1}\&CenterDot;\frac{d{Q}_{\mathrm{Lp}1}}{\mathrm{dt}}----\left(27\right)$ $P_{p2}=P_v-R_b\&CenterDot;Q_b-L_{p1}\&CenterDot;\frac{d{Q}_{\mathrm{Lp}2}}{\mathrm{dt}}----\left(28\right)$ (8) flow Q in other blood vessels of intracranial _A1, Q _A2, Q _Pc1And Q _Pc2For: $\mathrm{Qai}=e^{-\frac{\mathrm{Rail}}{\mathrm{Lai}}t}\&lsqb;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)}{L_{\mathrm{ai}}}\&CenterDot;e^{\frac{\mathrm{Rail}}{\mathrm{Lai}}\mathrm{\&tau;}}\mathrm{d\&tau;}+S{1}_i\&rsqb;----\left(29\right)$ ${S1}_i=\frac{T({\stackrel{-}{Q}}_{\mathrm{ai}2}-{(-1)}^i{\stackrel{-}{Q}}_{\mathrm{ac}})-{\&Integral;}_0^T{e}^{-\frac{\mathrm{Rail}}{\mathrm{Lai}}t}\&CenterDot;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)}{L_{\mathrm{ai}}}\&CenterDot;e^{\frac{\mathrm{Rail}}{\mathrm{Lai}}\mathrm{\&tau;}}\mathrm{d\&tau;dt}}{{\&Integral;}_0^T{e}^{-\frac{\mathrm{Rail}}{\mathrm{Lai}}t}\mathrm{dt}}$ i＝1，2 $\mathrm{Qpci}=e^{-K_i\&CenterDot;t}\&lsqb;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-R_{\mathrm{pi}2}\&CenterDot;P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)/(R_{\mathrm{pi}2}+R_{\mathrm{pil}})}{L_{\mathrm{pci}}}\&CenterDot;e^{K_i\&CenterDot;\mathrm{\&tau;}}\mathrm{d\&tau;}+S{2}_i\&rsqb;----\left(30\right)$ ${S2}_i=\frac{T{\stackrel{-}{Q}}_{\mathrm{pci}}-{\&Integral;}_0^T{e}^{-K_i\&CenterDot;t}\&CenterDot;{\&Integral;}_0^t\frac{P_{\mathrm{ci}}\left(\mathrm{\&tau;}\right)-R_{\mathrm{pi}2}\&CenterDot;P_{\mathrm{ai}}\left(\mathrm{\&tau;}\right)/(R_{\mathrm{pi}2}+R_{\mathrm{pil}})}{L_{\mathrm{pci}}}\&CenterDot;e^{K_i\&CenterDot;\mathrm{\&tau;}}\mathrm{d\&tau;dt}}{{\&Integral;}_0^T{e}^{-K_i\&CenterDot;t}\mathrm{dt}}$ $\mathrm{Ki}=\frac{\mathrm{Rpci}+\mathrm{Rpi}1\&CenterDot;\mathrm{Rpi}2/(\mathrm{Rpi}1+\mathrm{Rpi}2)}{\mathrm{Lpci}}$ I=1,2 (9) intracranial compliances are: $C_{c1}=\frac{1}{P_{c1}\left(T_s\right)-P_{c1}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(e_{11}\&CenterDot;P_{c1}-Q_{\mathrm{pc}1}-Q_{a1}+\frac{P_1}{R_{c1}})\mathrm{dt}----\left(31\right)$ $C_{c2}=\frac{1}{P_{c2}\left(T_s\right)-P_{c2}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(e_{22}\&CenterDot;P_{c2}-Q_{\mathrm{pc}2}-Q_{a2}+\frac{P_2}{R_{c2}})\mathrm{dt}----\left(32\right)$ $C_v=C_{v1}+C_{v2}=\frac{1}{P_v\left(T_s\right)-P_v\left(T_0\right)}\&CenterDot;{\&Integral;}_{T_0}^{T_s}(-\frac{R_{v1}+R_{v2}}{R_{v1}\&CenterDot;R_{v2}}{P}_v+\frac{P_3}{R_{v1}}+\frac{P_4}{R_{v2}}-Q_b)\mathrm{dt}----\left(33\right)$ $C_{p1}=\frac{1}{P_{p1}\left(T_s\right)-P_{p1}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(-\frac{P_{p1}}{R_{p11}+R_{p12}}-\frac{R_{p12}\&CenterDot;Q_{\mathrm{pc}1}}{R_{p11}+R_{p12}}+Q_{\mathrm{Lp}1})\mathrm{dt}----\left(34\right)$ $C_{p2}=\frac{1}{P_{p2}\left(T_s\right)-P_{p2}\left(T_0\right)}({\&Integral;}_{T_0}^{T_s}(-\frac{P_{p2}}{R_{p21}+R_{p22}}-\frac{R_{p22}\&CenterDot;Q_{\mathrm{pc}2}}{R_{p21}+R_{p22}}+Q_{\mathrm{Lp}2})\mathrm{dt}----\left(35\right)$ $C_{a1}=\frac{1}{P_{a1}\left(T_s\right)-P_{a1}\left(T_0\right)}{\&Integral;}_{T_0}^{T_s}(e_{33}\&CenterDot;P_{a1}+e_{34}\&CenterDot;P_{a2}-Q_{a1})\mathrm{dt}----\left(36\right)$ $C_{a2}=\frac{1}{P_{a2}\left(T_s\right)-P_{a2}\left(T_0\right)}{\&Integral;}_{T_0}^{T_s}(e_{44}\&CenterDot;P_{a2}+e_{43}\&CenterDot;P_{a2}-Q_{a2})\mathrm{dt}----\left(37\right)$ Here, To and Ts are that heart contraction begins and the time that finishes, and have the implication of related parameter to be listed as follows: parameter meaning P ₁, P ₂, P ₃, P ₄Four 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 Qv1 in the carotid artery of the left and right sides, Qv2 left and right sides vertebra power arteries and veins flow Qm1, Qm2 left and right sides middle cerebral artery flow Q _A1, Q _A2Flow Q in the anterior cerebral artery _PC1, Q _PC2Flow Q in the posterior cerebral artery _Lp1, Q _Lp2Flow in the arteriae communicans posterior cerebri

2. a brain Willis encircles the circulation power analytical tool, by detection system, acquisition analysis system and storage output system are formed, wherein detection system comprises that a frequency that is used to detect intracranial vessel blood speed is the impulse ultrasound doppler transducer of 2-3MHZ, a frequency that is used to detect outer vascular flow speed of cranium and blood flow is the continuous ultrasound doppler transducer of 5-8MHZ, a physiological pressure transducer or a ultraphonic pipe diameter probe that is used to detect the blood vessel wall waveform, the storage output system is by being used to store the brain recirculation dynamic achievement data that cerebral circulation normal parameter numerical value and analytical calculation system obtain, and the hard disk of output comparing result, floppy disk, printer is formed, the collection analysis computing system comprises master computer, the analog signal conversion that the test section is obtained becomes the A/D converter of digital signal, it is characterized in that the analytical calculation system also comprise the digital signal that will measure import into the communication microcomputer of master computer and method according to claim 1 establishment be used for analytical calculation relatively the software of cerebral hemodynamic parameter form.

Images