Boundary conditions, compartmentalized

In implementing the above approach, there are no limitations on the geometry of the compartmentalized system or on the nature of the boundary conditions imposed. The price paid for this generality is that the problem must be resolved for every choice of system geometry, and for each temporal boundary condition. One is then left with the task of extracting from the numerical data, in the spirit of an experimentalist, trends and correlations, rather than having at one s disposal an analytic solution from which the... 

Figure 4.19. A plot of the average walklength ( ) versus system size (normalized edge length ) for N X N X N simple cubic lattices. The curve through the filled circles gives the results for a d = 3 walk to a central trap. The curve through the open squares displays the results obtained using the tracking boundary condition (see text), with the trap anchored at a centrosymmetric site on the boundary of the compartmentalized (lattice) system.

Figure 4.30. A comparison of the average walklength n) versus the total number of lattice sites for a one-layer (circles), two-layer (squares), and three-layer (triangles) hexagonal lattice assembly subject to confining boundary conditions (see text), with the reaction center positioned at centrosymmetric site of the lowest (basal) layer of the compartmentalized system.

The problem is reduced to a set of linear differential equations and can be solved for given boundary conditions. The RCL characteristics of a given problem may be derived fixim the known physical properties of blood and blood vessels (Dinnar, 1981 Van der Twell, 1957). This compartmental approach allowed for computer simulations of complex arterial circuits with clinical applications (McMahon et al., 1971 Clark et al., 1980 Bamea et al., 1990 Olansen et al., 2000 Westerhof and Stergiopulos, 2000 Ripplinger et al., 2001). 

Compartmentalization is a concept that can be used widely in multienzymatic processes whereby different parts of the reactor operate imder different conditions (e.g., two-liquid phase biocatalysis) or catalysts are separated (e.g., by immobilization). The two compartments may be separated by a phase boundary (most likely solid-liquid or liquid-liquid). The compartments will selectively contain enzymes and reaction components such that not all enzymes and components are present in all parts of the reactor at the same concentration at a given time. This has benefits not only for the reaction itself (e.g., reducing product inhibition) but also downstream processing (e.g., separation of enzymes). 

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