[...]... model intractable with today’s computing power To see why, consider again the population pyramids in Fig 1.1 If one uses 10 bins in the histogram, then that requires keeping track of 10 variables Adding another state variable to the description, individual weight, for instance, and using again 10 bins in the weight histogram, the two-dimensional age-weight histogram will require 10-by-10 bins or 100 bins,... population balance model The simplifying modeling assumption, that a cell population can be split into separate subpopulations, each of which can then be modeled by an unstructured population balance, is often a convenient trick for modeling complex populations that would otherwise need structured models Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright ©... Balances in Biomedical Engineering Chapter 2 Unstructured PBMs Unstructured population balance models use a single variable, such as cell mass, to indicate the state of a cell in the culture Unstructured models are the least complex PBMs, and will be explored in this and the following chapters We will derive a general population balance model that uses cell mass or any other variable that is conserved in. .. When z z indicates a physical quantity that is conserved in division, such as total cell mass, the newborn cell cannot be born in a state with a larger value of z than the dividing cell The probability is therefore 1 that the newborn cell will be in a cell state in the interval [0, ˜ ], or z z ˜ 0 p(z, ˜)d z = 1 z (2.6) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)... the growth kinetics of the single cells These processes have therefore so far been ignored in the population balance models of cell cultures in the literature It is quite possible, of course, that interesting population balance problems can be identified for cell cultures in which sexual reproduction plays a large role or in which cell clumping is so significant that the growth kinetics of single cells... associate the kinetics of the entire cell population, represented here by (t), the specific growth rate in cell number, with the kinetics of the single cell Equation (2.10) is a key relationship in this connection and can often be simplified once f(z, t) is known Equations of this type, linking population kinetic parameters, such as , to single-cell kinetic parameters, will be called linkage equations... Age division intensity The age population balance has only one breakage function, the division intensity (a) This division intensity can in principle be obtained from mechanistic models of the cell cycle If the cell cycle is modeled as a completely deterministic process, then all divisions occur at the boundary of state space, and determining the division intensity is equivalent to determining this boundary... fail to accurately predict the true rate of product formation in this system Population balance models are therefore inherently more correct than distributed models However, distributed models are excellent models in many cases The error that is introduced by lumping Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies... that grow and break in a crystallizer Common to all population balances of this type is that they describe the dynamics of a population of particles in terms of the kinetics of the single particle, i.e., in terms of the growth rate of a single particle, the probability of breakage/division of this particle, and the probability that a newly formed particle is in a certain state In some particulate systems,... expands, the population of cells within a given interval of cell states will shift toward a wider interval of states Assuming no cell divisions or death, the number of cells in this population must remain constant and the integral of the distribution of states over this expanding interval must therefore be constant This is possible only if the value of the distribution of states decreases as the interval . website. Source: Population Balances in Biomedical Engineering axis signifying age, and two horizontal axes, running in opposite dirertions for males and females, indicating number of individuals in each. growth. In engineering, population balances are used to model not just populations of living cells, but also populations of inanimate particles, such as the size and number of crystals in a crystalizer. Terms of Use as given at the website. Source: Population Balances in Biomedical Engineering tank reactor, or even C*. In the biochemical engineering literature it is often called a chemostat,