Birth function aggregation

There are over 40 lysosomal storage disorders (LSDs) characterized by the specific enzyme deficiency and accumulated substrate. Pathologies associated with LSDs are multisystemic and variable including CNS, skeletal, cardiovascular, renal, and ocular system involvement. The aggregate incidence is estimated to approach 1 in 7000 live births (Ellinwood et al., 2004). Inheritance for LSDs is primarily autosomal recessive with the exception of two X-linked diseases (Fabry and mucopolysaccharidosis (MPS) II). Treatment for LSDs relies on providing functional enzyme to the lysosomes of affected cells and has traditionally been confined to bone marrow transplantation, and enzyme replacement therapy (ERT). 

The first term in this partial differential equation describes the temporal change of the population tj the second term describes the atomistic growth of the particles (which assumes that G is independent of particle size r), and finally the last two terms account for the birth and death of particles of size r by an aggregation mechanism. The birth fimction describes the rate at which particles enter a particle size range r to r + Ar, and the death function describes the rate at which the particles leave this size range. In the case of continuous nucleation, an additional birth rate term is used for the production of atoms (or molecules) of product by chemical reaction. In this case, the size of the nuclei are the size of a single atom (or molecule) and the rate of their production is identical to the rate of chemical reaction, kfi, where C is the reactant concentration, giving... 

Dea lomeration can take place by two methods comminution and ultrasonification. Comminution is the subject of Chapter 4, so it will not be discussed in detail here. In the comminution of aggregates, the popvdation balance can be used to predict the size distribution as a function of time in a batch mill or as a function of mean residence time in a continuous mill. Aggregates have the same type of birth and death fvmctions for particle breakage as polycrystalline particles but the rate constants are much hi er and the size selectivities for aggregates are different than those for the comminution of crystalline materials. The... 

We shall now turn our attention to the birth and death functions associated with breakage and aggregation processes. 

Since the birth and death functions are now identified the complete population balance equation for an aggregating population is given by substituting for h in the right-hand side of (2.7.9) — h sls calculated from... 

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