Understanding Vascular Resistance and Poiseuille Law Electrical Analogy
The cardiovascular system can be effectively modeled using fundamental electrical circuit principles. In this analogy, blood pressure acts as voltage ($\Delta P$), blood flow acts as current ($Q$), and vascular resistance corresponds to electrical resistance ($R$). Jean Léonard Marie Poiseuille formulated a landmark physical law describing laminar viscous fluid flow through cylindrical tubes, establishing that resistance is inversely proportional to the fourth power of the vessel radius.
Formula Used
The standard Poiseuille equation for vascular resistance ($R$) based on vessel dimensions is given by:
$$R = \frac{8 \eta L}{\pi r^4}$$
Where $\eta$ represents dynamic blood viscosity, $L$ represents the vessel length, and $r$ denotes the inner vessel radius. In parallel, the electrical circuit Ohm law adaptation calculates systemic resistance as:
$$R_{elec} = \frac{\Delta P}{Q}$$
How to Use This Calculator
- Input the dynamic viscosity of blood based on standard plasma properties or hematocrit adjustments.
- Specify the precise physical length and radius dimensions of the target vascular pathway.
- Enter operational hemodynamic variables including the pressure gradient and total volume flow rate.
- Review instant comparative outputs for both structural Poiseuille geometry and circuit electrical equivalents.