Erzhen Gao

A theoretical model of cerebral hemodynamics: application to the study of arteriovenous malformations.

A comprehensive computer model of the cerebral circulation, based on both hydrodynamics and electrical network analysis, was used to investigate the influences of arteriovenous malformations (AVM) on regional cerebral hemodynamics. The basic model contained 114 normal compartments: 55 arteries, 37 veins, 20 microvessel groups (MVG), one compartment representing systemic and extracranial vascular resistance, and one representing the heart. Each microvessel group, which represented the arteriolar bed, consisted of 5000 microvessels. Cerebral blood flow autoregulation was simulated by a formula that determined the resistance and therefore the flow rate of the microvessel groups (arterioles) as a function of perfusion pressure. Elasticity was introduced to describe the compliance of each vessel. Flow rate was made a controlling factor for the positive regulation of the diameters of conductance vessels by calculation of shear stress on the vessel wall (vessel dilation). Models containing an AVM were constructed by adding an AVM compartment and its feeding arteries and draining veins. In addition to the basic model, AVM models were simulated with and without autoregulation and flow-induced conductance vessel dilation to evaluate the contributions of these factors on cerebral hemodynamics. Results for the model with vessel dilation were more similar to clinical observations than those without vessel dilation. Even in the presence of total vasoparalysis of the arteriolar bed equivalent, obliteration of a large (1000 mL/min) shunt flow AVM resulted in a near-field CBF increase from a baseline of 21 to a post-occlusion value of no more than 74 mL/100 g/min, casting doubt on a purely hemodynamic basis for severe hyperemia after treatment. The results of the simulations suggest that our model may be a useful tool to study hemodynamic problems of the cerebral circulation.

Mathematical considerations for modeling cerebral blood flow autoregulation to systemic arterial pressure

The shape of the autoregulation curve for cerebral blood flow (CBF) vs. pressure is depicted in a variety of ways to fit experimentally derived data. However, there is no general empirical description to reproduce CBF changes resulting from systemic arterial pressure variations that is consistent with the reported data. We analyzed previously reported experimental data used to construct autoregulation curves. To improve on existing portrayals of the fitting of the observed data, a compartmental model was developed for synthesis of the autoregulation curve. The resistive arterial and arteriolar network was simplified as an autoregulation device (ARD), which consists of four compartments in series controlling CBF. Each compartment consists of a group of identical vessels in parallel. The response of each vessel category to changes in perfusion pressure was simulated using reported experimental data. The CBF-pressure curve was calculated from the resistance of the ARD. The predicted autoregulation curve was consistent with reported experimental data. The lower and upper limits of autoregulation (LLA and ULA) were predicted as 69 and 153 mmHg, respectively. The average value of the slope of the CBF-pressure curve below LLA and beyond ULA was predicted as 1.3 and 3.3% change in CBF per mmHg, respectively. Our four-compartment ARD model, which simulated small arteries and arterioles, predicted an autoregulation function similar to experimental data with respect to the LLA, ULA, and average slopes of the autoregulation curve below LLA and above ULA.

Theoretical modelling of arteriovenous malformation rupture risk: a feasibility and validation study.

PURPOSE To explore the feasibility of using a theoretical computational model to simulate the risk of spontaneous arteriovenous malformation (AVM) haemorrhage. METHODS Data from 12 patients were collected from a prospective databank which documented the angioarchitecture and morphological characteristics of the AVM and the feeding mean arterial pressure (FMAP) measured during initial superselective angiography prior to any treatment. Using the data, a computational model of the cerebral circulation and the AVM was constructed for each patient (patient-specific model). Two model risk (Risk(model)) calculations (haemodynamic- and structural-weighted estimates) were performed by using the patient-specific models. In our previously developed method of haemodynamic-weighted estimate, Risk(model) was calculated with the simulated intranidal pressures related to its maximal and minimal values. In the method of structural-weighted estimate developed and described in this paper, the vessel mechanical properties and probability calculation were considered in more detail than in the haemodynamic-weighted estimate. Risk(model) was then compared to experimentally determined risk which was calculated using a statistical method for determining the relative risk of having initially presented with AVM haemorrhage, termed Risk(exp). RESULTS The Risk(model) calculated by both haemodynamic- and structural-weighted estimates correlated with experimental risks with chi2 = 6.0 and 0.64, respectively. The risks of the structural-weighted estimate were more correlated to experimental risks. CONCLUSIONS Using two different approaches to the calculation of AVM haemorrhage risk, we found a general agreement with independent statistical estimates of haemorrhagic risk based on patient data. Computational approaches are feasible; future work can focus on specific pathomechanistic questions. Detailed patient-specific computational models can also be developed as an adjunct to individual patient risk assessment for risk-stratification purposes.