Blood Flow Rate Calculator
Understanding Blood Flow Rate
Blood flow rate, often measured in milliliters per minute (mL/min) or cubic centimeters per second (cm³/s), is a critical physiological parameter representing the volume of blood that passes through a particular point in the circulatory system over a unit of time. It's a fundamental aspect of cardiovascular health, influencing oxygen and nutrient delivery to tissues and waste removal.
The calculation of blood flow rate can be complex, but a simplified model, often derived from Poiseuille's Law, provides a useful approximation under certain conditions, particularly for laminar flow in a cylindrical vessel. Poiseuille's Law describes the pressure drop across a viscous fluid in a cylindrical pipe. The formula for volumetric flow rate (Q) is:
Q = (π * r⁴ * ΔP) / (8 * η * L)
Where:
- Q is the volumetric flow rate.
- π (pi) is a mathematical constant approximately equal to 3.14159.
- r is the radius of the vessel.
- ΔP is the pressure gradient (the difference in pressure between the two ends of the vessel).
- η (eta) is the dynamic viscosity of the blood.
- L is the length of the vessel.
In this calculator, we've simplified the formula by assuming a typical dynamic viscosity for blood. For a more precise calculation, the specific viscosity of the blood, which can vary based on hematocrit and other factors, would need to be considered.
Key Inputs:
- Vessel Radius (cm): The internal radius of the blood vessel. A smaller radius significantly reduces blood flow due to the radius being raised to the fourth power (r⁴).
- Pressure Gradient (dynes/cm²): The difference in pressure between the arterial and venous ends of the vessel. A higher pressure gradient drives more blood flow.
- Vessel Length (cm): The length of the blood vessel segment. Longer vessels offer more resistance, thus reducing flow rate.
This calculator helps illustrate how changes in vessel dimensions and pressure can impact the rate at which blood circulates, which is crucial for understanding conditions like hypertension, atherosclerosis, and shock.
function calculateBloodFlow() {
var vesselRadius = parseFloat(document.getElementById("vesselRadius").value);
var pressureGradient = parseFloat(document.getElementById("pressureGradient").value);
var vesselLength = parseFloat(document.getElementById("vesselLength").value);
// Assume a typical dynamic viscosity for blood (in poise, which is g/(cm*s))
// For simplicity, we'll use a value around 0.035 to 0.04 poise for blood.
// Let's use 0.035 poise as an example value.
var bloodViscosity = 0.035; // poise (g/(cm*s))
var resultElement = document.getElementById("result");
resultElement.innerHTML = ""; // Clear previous results
if (isNaN(vesselRadius) || isNaN(pressureGradient) || isNaN(vesselLength)) {
resultElement.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (vesselRadius <= 0 || pressureGradient < 0 || vesselLength <= 0) {
resultElement.innerHTML = "Radius and length must be positive, and pressure gradient cannot be negative.";
return;
}
// Poiseuille's Law: Q = (π * r^4 * ΔP) / (8 * η * L)
// The units of Q will be cm^3/s if:
// r is in cm
// ΔP is in dynes/cm^2 (which is equivalent to Pascals * 10)
// η is in poise (g/(cm*s))
// L is in cm
// Poise = dyne * s / cm^2. So, 1 Poise = 0.1 Pa*s.
// If ΔP is in dynes/cm^2 and η is in poise, Q will be in cm^3/s.
var pi = Math.PI;
var flowRate_cm3_per_sec = (pi * Math.pow(vesselRadius, 4) * pressureGradient) / (8 * bloodViscosity * vesselLength);
// Convert to mL/min for a more common physiological unit
// 1 cm^3 = 1 mL
// 1 min = 60 seconds
var flowRate_mL_per_min = flowRate_cm3_per_sec * 60;
resultElement.innerHTML =
"Calculated Blood Flow Rate (Q):" +
"
" + flowRate_cm3_per_sec.toFixed(4) + " cm³/s" +
"
" + flowRate_mL_per_min.toFixed(2) + " mL/min";
}
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