Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions

Abstract

We present a one-dimensional (1D) fluid dynamic model that can predict blood flow and blood pressure during exercise using data collected at rest. To facilitate accurate prediction of blood flow, we developed an impedance boundary condition using morphologically derived structured trees. Our model was validated by computing blood flow through a model of large arteries extending from the thoracic aorta to the profunda arteries. The computed flow was compared against measured flow in the infrarenal (IR) aorta at rest and during exercise. Phase contrast-magnetic resonance imaging (PC-MRI) data was collected from 11 healthy volunteers at rest and during steady exercise. For each subject, an allometrically-scaled geometry of the large vessels was created. This geometry extends from the thoracic aorta to the femoral arteries and includes the celiac, superior mesenteric, renal, inferior mesenteric, internal iliac and profunda arteries. During rest, flow was simulated using measured supraceliac (SC) flow at the inlet and a uniform set of impedance boundary conditions at the 11 outlets. To simulate exercise, boundary conditions were modified. Inflow data collected during steady exercise was specified at the inlet and the outlet boundaries were adjusted as follows. The geometry of the structured trees used to compute impedance was scaled to simulate the effective change in the cross-sectional area of resistance vessels and capillaries due to exercise. The resulting computed flow through the IR aorta was compared to measured flow. This method produces good results with a mean difference between paired data to be 1.1 ± 7 cm³ s^− 1 at rest and 4.0 ± 15 cm³ s^− 1 at exercise. While future work will improve on these results, this method provides groundwork with which to predict the flow distributions in a network due to physiologic regulation.

Keywords:

• One-dimensional model
• Arterial blood flow
• Fractal
• Structured tree
• Impedance
• Exercise

Acknowledgements

This work was done as part of the thesis work of Dr Steele under the guidance of Dr Taylor at Stanford University, and was supported in part by the National Science Foundation under Grant No. 0205741, the Whitaker Foundation and the Ayers Foundation.

Notes

^§Tel:[phone]. Fax:[phone]. [email protected]

^|Tel:[phone]. Fax:[phone]. [email protected]

Additional information

Notes on contributors

Mette S. Olufsen

§ §Tel:[phone]. Fax:[phone]. [email protected]

Charles A. Taylor

| |Tel:[phone]. Fax:[phone]. [email protected]