AN ANATOMICALLY REALISTIC CORONARY MODEL N.P. Smith, P.J. Hunter, A.J. Pullan and M.P. Nash
Department of Engineering Science, University of Auckland, Auckland, NZ
INTRODUCTION: An anatomically realistic mathematical model of the coronary network has been developed to quantitativeiy investigate the effect the cardiac cycle has on coronary flow. The model is based on the anatomically accurate finite element model of the heart developed by the Auckland University Cardiac Research Group and the topological coronary data from Kassab (1993). METHODS: Data points measured from vessels on the surface of canine hearts were used to construct an epicardial finite element mesh. The next 4 generations of myocardial vessels were generated by adding spatial information to the existing topological data (Kassab 1993) defining connectivity, generation, vessel radius and length. Starting at the highest generation the directions of myocardial vessel elements were calculated sequentially using an avoidance algorithm. Central to this avoidance algorithm was the calculation of a scalar function whose value in space was determined from the weighted distances to all previously generated vessels. The direction of a vessel segment was then determined by maximising this function and thus tbe distance from all other vessels. This problem was solved for each vessel segment by iteratively finding the stationary points to the Lagrangian function of the problem. On this mesh a collocation grid has been generated and a one dimensional form of the Navier Stokes equations governing coronary flow has been solved over the cardiac cycle using the Lax Wendroff finite difference technique. As the flow equations are solved, a large deformation mechanics problem modelling vetricular contraction is simultaneously solved on the host mesh. The compressive force on the coronary vessels during this cycle has been calculated by coupling tbe flow equations at each grid point to myocardial pressure within the host mesh. RESULTS AND DISCUSSION: A finite element mesh, modelling the largest 6 generations of the coronary network has been constructed (shown below) using the outlined method. This network has radius, lengths and connectivity which conforms to the anatomical data. The spatial properties of branch angles are consistent with the principle of minimum shear stress at bifurcations and effective spatial distribution of the whole organ network has been achieved. The effect of myocardial contraction on coronary flows is being quantitatively investigated using the coupled model presented in this abstract.
The six generation finite element coronary mesh CONCLUSIONS: The model of the coronary network provides an anatomically realistic geometric and computational foundation for investigating the effects of contraction of the heart on blood flow through the coronary network. REFERENCES: Kassab, G.S., Rider, C.A., Tang, N.J., Fung, YC.,Morphometry of pig coronary arterial trees, Am. J Physid. Vol. 265, pp H350H3651993 CORRRSPONDENCE: Nicolas Smith, Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand. ph 3737599 ex7490, email@example.com
A NOVEL METHOD FOR DERIVING CENTRAL AORTIC PRESSURE WAVE FROMPERIPHERAL PRESSURE AND
VELOCITY MEASUREMENTS N. Stergiopulos, B. E. Westerhof, N. Westerhof3
Biomedical Engineering Laboratory, Swiss Federal Institute of Technology, Lausanne, ?NO Biomedical Instrumentation, Academic
Medical Center, Amsterdam, Laboratory for Physiology, ICAR-VU, Free University of Amsterdam
INTRODUCTION: Knowledge of the central aortic pressure wave is of importance in several aspects. The central aortic pressure waveform, however, cannot be obtained noninvasively. Therefore, a number of research groups have recently tried to obtain aortic pressure from (noninvasive) measurement of peripheral pressures, like the carotid artery, brachial artery and radial artery pressure. Others have determined the relation between finger pressure and brachial pressure. The methods are based on the determination of an average pressure transfer function between the peripheral and aortic locations. Differences between individual patients and the averaged pressure transfer function may exist and thus the use of a generalized average transfer function may result in errors in the prediction of aortic pressure.
The goal of the present study was to develop a method, based on the separation of peripheral waves into their forward and backward components, to derive the central aortic pressure from noninvasively determined peripheral pressure and flow velocity. In contrast to previous transfer function methods, this new method can be applied on a per patient basis. METHODS: We propose a new method to derive aortic pressure from peripheral pressure and velocity. Peripheral pressure is separated in its forward and backward components, these components are shifted with a delay time which is the ratio of wave speed and distance, and added again to reconstruct aortic pressure. We tested the method on a distributed model of the human systemic arterial tree. RESULTS AND DISCUSSION: From carotid and brachial artery pressure and velocity, aortic systolic and diastolic pressure could be predicted within 0.3 and 0. 1 mmHg and 0.4 and 1 mmHg respectively. The pressure transfer function depends on the reflection coefficient at the site of peripheral measurement and the delay time. A 50% decrease in arterial compliance had a considerable effect on reconstructed pressure when the control transfer function was used. A 70% decrease in arm resistance did not affect the reconstructed pressure. The transfer function thus depends little on vasoactive state.
The delay time turns out to be an important parameter and changes in arterial compliance, due to atherosclerosis, age or, indirectly through mean pressure, may affect the transfer function. The method should be easily applicable to patients since pressure (e.g. tonometty) and velocity (e.g. ultrasound) can be obtained noninvasively. The time delay may be obtained from simultaneous measurement of ECG or heart sounds.
We conclude that central aortic pressure and the transfer function can be derived from peripheral pressure and velocity. CORRESPONDENCE: Nikos Stergiopulos, Biomedical Engineering Laboratory, PSE-Ecublens, 1015 Lausanne, Switzerland
140 11 Conference of the ESB, July 8-11 98, Toulouse, France