Pulsatile blood flow, shear force, energy dissipation and Murray's Law

BACKGROUND: Murray's Law states that, when a parent blood vessel branches into daughter vessels, the cube of the radius of the parent vessel is equal to the sum of the cubes of the radii of daughter blood vessels. Murray derived this law by defining a cost function that is the sum of the energy cost of the blood in a vessel and the energy cost of pumping blood through the vessel. The cost is minimized when vessel radii are consistent with Murray's Law. This law has also been derived from the hypothesis that the shear force of moving blood on the inner walls of vessels is constant throughout the vascular system. However, this derivation, like Murray's earlier derivation, is based on the assumption of constant blood flow. METHODS: To determine the implications of the constant shear force hypothesis and to extend Murray's energy cost minimization to the pulsatile arterial system, a model of pulsatile flow in an elastic tube is analyzed. A new and exact solution for flow velocity, blood flow rate and shear force is derived. RESULTS: For medium and small arteries with pulsatile flow, Murray's energy minimization leads to Murray's Law. Furthermore, the hypothesis that the maximum shear force during the cycle of pulsatile flow is constant throughout the arterial system implies that Murray's Law is approximately true. The approximation is good for all but the largest vessels (aorta and its major branches) of the arterial system. CONCLUSION: A cellular mechanism that senses shear force at the inner wall of a blood vessel and triggers remodeling that increases the circumference of the wall when a shear force threshold is exceeded would result in the observed scaling of vessel radii described by Murray's Law

Effect of Cytoskeletal Disruption on Mechanotransduction of Hydrostatic Pressure by C3H10T1/2 Murine Fibroblasts

Cyclic hydrostatic pressure of physiological magnitude (< 10 MPa) stimulates chondrogenic differentiation of mesenchymal stem cells, but mechanotransduction mechanisms are not well understood. It was hypothesized that an intact cytoskeleton would be required for uninhibited mechanotransduction of hydrostatic pressure. Therefore we examined the effects of drugs which selectively interfere with actin and tubulin polymerization on pressure-induced upregulation of aggrecan and col2a1 (type II collagen) mRNA expression. C3H10T1/2 cells were cultured as pellets in either 4µM cytochalasin D or 4µM nocodazole and subjected to 3 days of cyclic hydrostatic compression (1 Hz, 5 MPa, 2 h per day). Phalloidin staining and indirect immunostaining with anti α-tubulin antibody confirmed disruption of microfilament and microtubule assemblies, respectively. Real time RT-PCR revealed that both drugs substantially lowered the basal level of aggrecan and col2a1 mRNA, but that neither drug prevented a pressure-stimulated increase in gene expression relative to the altered basal state. Thus upregulation of macromolecular gene expression by cyclic hydrostatic pressure did not require a completely intact cytoskeleton

Nesprin-3 regulates endothelial cell morphology, perinuclear cytoskeletal architecture, and flow-induced polarization

Nesprin-3, a protein that links intermediate filaments to the nucleus, plays a role in vascular endothelial cell (EC) function. Nesprin-3 regulates EC morphology, perinuclear cytoskeletal organization, centrosome–nuclear connectivity, and flow-induced cell polarization and migration