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Critical Reviews™ in Biomedical Engineering
SJR: 0.26 SNIP: 0.375 CiteScore™: 1.4

ISSN Imprimir: 0278-940X
ISSN En Línea: 1943-619X

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Critical Reviews™ in Biomedical Engineering

DOI: 10.1615/CritRevBiomedEng.v24.i2-3.10
pages 73-139

Concepts, Properties, and Applications of Linear Systems to Describe Distribution, Identify Input, and Control Endogenous Substances and Drugs in Biological Systems

Davide Verotta
Department of Biopharmaceutical Sciences, and Pharmaceutical Chemistry, Box 0446, University of California San Francisco, San Francisco CA 94143-0446; Department of Epidemiology and Biostatistics, Box 0446, University of California San Francisco, San Fran


The response at time t (R(t)) of a (causal linear time invariant) system to an input A(t) is represented by:
where K(t) is called the unit impulse response function of the system, and the integration on the right side of the equation (above) is called the convolution (from the latin cum volvere: to intertwine) of A(t) and K(t). The system described by this equation is at zero (initial conditions) when t = 0. Although it does not even begin to describe the incredible variety of possible responses of biological systems to inputs, this representation has large applicability in biology. One of the most frequently used applications is known as deconvolution: to deintertwine R(t) given a known K(t) (or A(t)) and observations of R(t), to obtain A(t) (or K(t)). In this paper attention is focused on a greater variety of aspects associated with the use of linear systems to describe biological systems. In particular I define causal linear time-invariant systems and their properties and review the most important classes of methods to solve the deconvolution problem, address. The problem of model selection, the problem of obtaining statistics and in particular confidence bands for the estimated A(t) (and K(t)), and the problem of deconvolution in a population context is also addressed, and so is the application of linear system analysis to determine fraction of input absorbed (bioavailability). A general model to do so in a multiinput-site linear system is presented. Finally the application of linear system analysis to control a biological system, and in particular to target a desired response level, is described, and a general method to do so is presented. Applications to simulated, endocrinology, and pharmacokinetics data are reported.

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