Estimation of Reynolds number on microvasculature capillary bed using diffusion and perfusion MRI: the theoretical and experimental investigations

Abstract

Microvasculature biomechanical physiology may be characterized by the Reynolds number toward better diagnosis of vascular obstruction. The Reynolds number is formulated by the diffusion, perfusion and dynamical relaxation parameters such as the contrast-enhanced transverse relaxation rates (ΔR2, ΔR2*), apparent diffusion coefficient (ADC), cerebral blood volume (CBV), and mean transit time (MTT) along with a set of simple assumptions. The measurements were performed on different vasculature areas in 8 rats of male Wistar species by an MRI (7 T) device, and the diffusion/perfusion weighted was applied to the imaging. The spin–spin relaxation time was gauged via a standard two-dimensional Fourier transform multi-echo (4 echoes) multi-slice (7 slices). The practical maps obtained (ΔR2*, ΔR2, ADC, MTT, CBF and CBV) were assessed. The mean Reynolds number in the four various areas of the rats such as infarct-border, infarct-core, remote-border, and remote-core zones were found to be 128.93 ± 5.69, 130.72 ± 10.93, 91.48 ± 7.44, and 102.38 ± 3.63, respectively. Here, while this number is less than about 102, one may say that the flow is laminar, and by increasing this number, the flow will go toward turbulence. In general, this number for laminar flow is less than that of the turbulent one. The results based on our theory have demonstrated that the Reynolds number in the normal areas is less than that of the injured ones as well as is severely inversely dependent on the ADC, MTT, ΔR2*2/ΔR23 value, viscosity, and the power of fifth of the mean capillary radius. The estimation of the Reynolds number may be used for better diagnosis and treatment planning.