 In this module, we again talk about the batch culture kinetics. In previous modules, we talked about linear regression equation. We would called as the equation which we can utilize for the estimation of mu which we called as specific growth rate constant. But that equation was only applicable when the cells are unicellular. But as we know that when we have the mass culturing of the organism and then we can also have the chance to grow the unicellular in which we include yeast and bacteria. But we can also utilize the multicellular mostly filamentous fungi and different other cell suspension cultures. But mu as concern is only applied when the cells are unicellular. Each an individual cells have the tendency to divide and have the equal chance to interact with equal substrate independently. But in case of multicellular organisms, some cells are growing at one time while other are at rest same time. So, at the one time different cells are at different phases of their growth. Some are at log phase while others are at stationary phase. That is why we cannot calculate the mu properly in that case. So, as we say that dx over dt is equal to mu x and while dh the change in height divided by the change in time can be called as mu h. The growth only happen in a area so we can call as the d change in area dA over dt so that is equal to mu A. So, here the h is the total length and the A is the number of growing tape or change in the area of the colony. So, by using these equations we can easily calculate the mu. But in submerged fermentation of mycelial organism when we talk about the filamentous fungi that may grow as dispersal of hyphal fragments or as pellets. The growth of pellet will be exponential until the density of the result in the diffusion limitations. So, under such limitation when the central biomass of the pellet will not receive a supply of nutrient nor will potentially toxic secretions are the product diffused out. So, thus the effect of growth of the pellet only growth proceed from the outer shell of the biomass which is actively grown growing zone. So, you can see that if any fungus grow in a pellet so only that the tendency of the mycelia grow at the tip on the periphery of that. So, because that have the most chance of the nutrient supply but as concern the dose health that is present in the center of the colony they having some effect of their secretions they have not the equal chance of growth. So, growth only happen on the tip of we can say that the periphery of the colony. So, in this case we cannot properly have the linear growth pattern we can have the correct specific growth rate constant. So, in this case we have to be an other equation derived by the part in this part give the solution of this here you can see that an equation that is the transform of that the previous equation in which you can see that ln x t is equal to ln x naught plus mu t but here you can see that m that is m naught is the mycelial mass at time naught and m t is basically the m mycelial mass at time t. So, if we take the under root cubic root of the mycelia and we plot against the time then we have a state line. So, in this case you can see that so, if we have time on x axis and m over 1 over 3 on y axis then we have a state line in this the slope of this that is the k. So, k is also equal to the mu which we called as specific growth rate constant in term of when we talk about fungal hypha at the mycelia and we know that the fungal hypha are mostly known as the mycelium. So, this equation can be used for the estimation of specific growth rate constant in term of fungal.