The linear cable theory as a model of gill blood flow

The vascular organization of the teleost gill suggests that blood flow distribution from the filamental artery to the respiratory lamellae is governed by relationships analogous to the cable conduction properties of a nerve axon. The space constant (λ) by definition is the distance along the gill filament at which the in-series resistance of the afferent filament artery equals the in-parallel resistance of the afferent lamellar arteriolar, lamellar, efferent lamellar arteriolar (ALA-L-ELA) segments. Constriction of the afferent filamental artery or uniform dilation of the ALA-L-ELA will decrease λ. As λ decreases, flow through the proximal (basal) lamellae greatly increases at the expense of distal lamellar perfusion. When λ increases in a system of finite length the flow profile must account for reflected pressures within the main vessel. The λ calculated from corrosion casts of gill vasculature is $\text{1}\text{4}$ to $\text{1}\text{2}$ the filament length. This favors blood flow through the proximal lamellae and when cardiac output increases, the proportion of cardiac output perfusing the proximal areas increases at the expense of distal lamellar blood flow. To offset these changes it is proposed that increased distal lamellar perfusion is achieved by simultaneous vasodilatation of distal and constriction of proximal ALA-L-ELA segments and dilation of the afferent filamental artery.