Titlebook: Compartmental Modeling and Tracer Kinetics; David H. Anderson Book 1983 Springer-Verlag Berlin Heidelberg 1983 Biologisch-mathematisches M

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The Inverse of a Compartmental Matrix,. exists. A constant vector xe is an . of model (13.1) provided it has the property that once the state vector is equal to x it remains equal to that vector for all future time [153]. For the system (13.1), an equilibrium point xe satisfies the equation

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Structural Identification of the Model, can be uniquely determined from experimental observation or measurement of certain components of the solution vector x. The closely related problem of getting actual numerical estimates of the a.s will be considered later in Section 19.

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Yukio Sadahiro (Associate Professor)Our model for tracer kinetics in an n-compartment system is the set of first order linear differential equations.where x(t) is the n×l state vector for the amounts of tracer in the compartments, b(t) is the n×l driving vector of tracer inputs, and A is an n×n compartmental matrix of constant fractional transfer coefficients.

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https://doi.org/10.1007/978-3-031-01884-8The subject of this section is that of eigenvalues and eigenvectors of a compartmental matrix A. As we have seen, the solution of the model.can be decomposed into a sum of terms involving eigenvectors associated with various eigenvalues.

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Conclusion and Further Outlook,At this time let us consider the model.for the tracer kinetics in an n-compartment system in the case of a .. It is assumed that the system is open, that b is a nonnegative constant tracer input vector over time, and let us suppose that the system contains no traps so that A is invertible.

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