Determine microbial growth kinetics and doubling time
Calculation Results
Specific Growth Rate (µ)
0.00
hours⁻¹
Doubling Time (td)
0.00
hours
What is Maximum Specific Growth Rate (µmax)?
In microbiology and bioprocess engineering, the specific growth rate (µ) represents the increase in microbial biomass per unit of time per unit of biomass. When a culture is growing in its exponential phase with non-limiting nutrients and optimal conditions, this rate reaches its peak, known as the maximum specific growth rate (µmax).
The µmax Formula
The calculation is based on the natural logarithm of biomass change over time during the exponential phase:
Step 3: Divide by time interval (3 hours): 2.014 / 3 = 0.671 h⁻¹
Step 4: Doubling time: 0.693 / 0.671 = 1.03 hours
function calculateGrowthRate() {
var x1 = parseFloat(document.getElementById('initialBiomass').value);
var x2 = parseFloat(document.getElementById('finalBiomass').value);
var t1 = parseFloat(document.getElementById('startTime').value);
var t2 = parseFloat(document.getElementById('endTime').value);
// Validation
if (isNaN(x1) || isNaN(x2) || isNaN(t1) || isNaN(t2)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (x1 <= 0 || x2 <= 0) {
alert("Biomass/Cell concentration must be greater than zero.");
return;
}
if (t2 <= t1) {
alert("End time must be greater than start time.");
return;
}
if (x2 <= x1) {
alert("Final biomass must be greater than initial biomass for a positive growth rate.");
return;
}
// Calculation logic
var timeInterval = t2 – t1;
var lnX2 = Math.log(x2);
var lnX1 = Math.log(x1);
var mu = (lnX2 – lnX1) / timeInterval;
var doublingTime = Math.log(2) / mu;
// Display results
document.getElementById('growthRateVal').innerText = mu.toFixed(4);
document.getElementById('doublingTimeVal').innerText = doublingTime.toFixed(2);
document.getElementById('resultsArea').style.display = 'block';
// Smooth scroll to results
document.getElementById('resultsArea').scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}