On the principles of the vascular network branching.
We propose an explanation of Murray's law without applying the minimality principles. The model deals with a "delivering" artery system of an organ that is characterized, first, by the space-filling embedding into the organ tissue and, second, by the uniform distribution of the blood pressure drop over it. The latter assumption is justified using the available physiological data and the idea about conditions needed for perfect self-regulation. Based on the two statements we get Murray's law, and so, demonstrate that it can be also regarded as a direct consequence of the organism's capacity for controlling finely the blood flow redistribution over peripheral vascular networks.
Gafiychuk
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VV
Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Naukova srt. 3B., Lviv, Ukraine.
Lubashevsky
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IA
D000818:Animals; D001158:Arteries / Q000033:anatomy & histology / Q000502:physiology; D001775:Blood Circulation / Q000502:physiology*; D001794:Blood Pressure / Q000502:physiology; D001808:Blood Vessels / Q000033:anatomy & histology* / Q000502:physiology; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular