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Allometric scaling of wall shear stress from mice to humans: quantification using cine phase-contrast MRI and computational fluid dynamics

Departments of ¹Bioengineering, ²Mechanical Engineering, ³Surgery, and ⁴Radiology, Stanford University, Stanford, California

Submitted 16 March 2006 ; accepted in final form 7 May 2006

Allometric scaling laws relate structure or function between species of vastly different sizes. They have rarely been derived for hemodynamic parameters known to affect the cardiovascular system, e.g., wall shear stress (WSS). This work describes noninvasive methods to quantify and determine a scaling law for WSS. Geometry and blood flow velocities in the infrarenal aorta of mice and rats under isoflurane anesthesia were quantified using two-dimensional magnetic resonance angiography and phase-contrast magnetic resonance imaging at 4.7 tesla. Three-dimensional models constructed from anatomic data were discretized and used for computational fluid dynamic simulations using phase-contrast velocity imaging data as inlet boundary conditions. WSS was calculated along the infrarenal aorta and compared between species to formulate an allometric equation for WSS. Mean WSS along the infrarenal aorta was significantly greater in mice and rats compared with humans (87.6, 70.5, and 4.8 dyn/cm², P < 0.01), and a scaling exponent of –0.38 (R² = 0.92) was determined. Manipulation of the murine genome has made small animal models standard surrogates for better understanding the healthy and diseased human cardiovascular system. It has therefore become increasingly important to understand how results scale from mouse to human. This noninvasive methodology provides the opportunity to serially quantify changes in WSS during disease progression and/or therapeutic intervention.

allometric scaling; cardiovascular disease; magnetic resonance imaging

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