The Tohoku Journal of Experimental Medicine
Online ISSN : 1349-3329
Print ISSN : 0040-8727
ISSN-L : 0040-8727
Estimation of Intravascular Blood Pressure Gradient by Mathematical Analysis of Arterial Casts
Norio SuwaTakashi NiwaHitoshi FukasawaYasuhiko Sasaki
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1963 Volume 79 Issue 2 Pages 168-198


1) Arterial blood flow was expressed as a power function of arterial radius. In the relation defined by Q=qrn, Q was blood flow, q an organ specific constant, and n had a value about 2.7 regardless of organ difference.
2) On account of the above relation, Hagen-Poiseuille's formula was transformed to Δp=K•q•l'/r4-n Th in which K was an organ unspeeific constant determined by viscosity coefficient of blood and selected units, l' was the effective length and r was the radius of an arterial branch. In the transformed formula, pressure difference between both ends of an unbranching stretch of arteries Δp was given by the product of organ unspeeific and organ specific constants and a quantity determined by anatomical properties of arteries. By means of successive determinations of l'/r4-n by way of any arbitrarily selected route, the total blood pressure drop could be determined by ΣΔp=K•q•Σ l'/r4-n.
3) The relation of the effective branch length l' and the radius r of an arterial system was expressed by l'=hri, in which h and i were organ specific constants. A higher value of i indicated a higher proportion of large arterial branches in the total arterial length.
4) Assuming successive dichotomy of arterial branches, an arterial model was constructed with. radius as a continuous variable. Blood pressure drop between any two given radii could be estimated by the calculation on the model by:
ΔP=K•q•h/1-δg [rg]r1r2 for g ≠ 0 and ΔP=K•q•h/-log δ [log r]r1r2 for g=0.
5) Some organ differences in the pattern of blood pressure gradient and intravascular blood pressure values were confirmed and were discussed in reference to different anatomical properties of arterial systems. Renal. artery was characterized by pronounced acceleration of blood pressure drop in the arteriolar region and by only insignificant pressure drop in its large branches. On the contrary, considerable blood pressure drop took place in large arterial branches of mesenteric, femoral and cerebral arteries in contrast to comparatively mild pressure drop in the arteriolar region. The estimated blood pressure level in the arteriolar region was correlated to the effective length of arterial systems. It was found to be higher in the arterial group with short effective arterial length. It was suggested that arterial systems with high susceptibility to hypertensive arteriolar injuries belonged to arteries with high hood pressure level in the region of r=100μ to r=200μ.
6) Artificial arterial dilatation due to resin infusion. could be defined by a power function of arterial radius. The function could be used as the correction equation of the radius of arterial casts, and the radius of living arteries was estimated on. the basis of blood pressure estimation with corrected arterial models.

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