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 cm(3) s(- 1) at rest and 4.0 +/- 15 cm(3) 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.

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

“…Until such data are available, distributed and lumped models should be tuned numerically by constricting or dilating the distal vascular beds until the overall level of pressure and distribution of flow in the image-based model matches available measurements. Note that one advantage of distributed models is that physiologic variations are modeled easily for example, effects of lower extremity exercise on abdominal aortic blood flow can be modeled by changing the inflow waveform, dilating the vessels in the lower extremities, and constricting the beds that supply the abdominal organs (166). Finally, note that methods to couple 3-D and 1-D computational models of blood flow with the aim of minimizing wave reflections from the outlet of the 3-D domain (167) are inadequate unless the 1-D model is itself terminated with an impedance outlet condition.…”

Personalized blood flow computations: A hierarchical parameter estimation framework for tuning boundary conditions

“…rest, exercise, etc. [42]. The total resistance values given in Table 2 correspond to the rest state.…”

“…Calibration of the structured tree parameters is required since the tree is generated from a set of constant scaling parameters (see Table 1). A tiered structure could be used alternatively [42], but since the use of a non-generic tree (with no fractal structure) would be computationally too demanding and its structure impossible to obtain under patient-specific conditions, parameter calibration is the most suitable approach for matching patient-specific properties of the microvasculature. We hypothesize that, even if organ specific tree properties were used within a constrained constructive optimization procedure applied for growing optimal trees within patient-specific organ geometries [43], parameter calibration would still be required to exactly match desired hemodynamic quantities.…”

Simulation of the human intracranial arterial tree

“…The importance of outflow boundary conditions has been long recognized by the community and the large literature reflects the same (Olufsen 1999;Sherwin et al 2003b;Smith et al 2004;Formaggia et al 2006;Vignon-Clementel et al 2006;Spilker et al 2007). There are several methods to impose the pressure boundary conditions, and the four main approaches are: (i) constant pressure boundary condition, (ii) resistance boundary condition (Sherwin et al 2003b;Formaggia et al 2006;Vignon-Clementel et al 2006), (iii) windkessel model boundary condition (Gibbons & Shadwick 1991;Nichols et al 1998;Formaggia et al 2006), and (iv) impedance boundary condition ( Vignon-Clementel et al 2006;Spilker et al 2007;Steele et al 2007). The resistance, windkessel and impedance boundary conditions are derived from modelling the peripheral resistance and compliance, and require knowledge of the peripheral arterial network characteristics.…”