Modeling and Imaging Techniques with Potential for Application in Bioterrorism

In this paper we present a survey of several recent and emerging ideas and e orts on modeling and system interrogation in the presence of uncertainty that we feel have signi cant potential for applications related to bioterrorism. The rst focuses on physiologically based pharmacokinetic (PBPK) type models and the e ects of drugs, toxins and viruses on tissue, organs, individuals and populations wherein both intraand inter-individual variability are present when one attempts to determine kinetic rates, susceptibility, eÆcacy of toxins, antitoxins, etc., in aggregate populations. Methods combining deterministic and stochastic concepts are necessary to formulate and computationally solve the associated estimation problems. Similar issues arise in the HIV infectious models we also present below. A second e ort concerns the use of remote electromagnetic interrogation pulses linked to dielectric properties of materials to carry out macroscopic structural imaging of bulk packages (drugs, explosives, etc.) as well as test for presence and levels of toxic chemical compounds in tissue. These techniques also may be useful in functional imaging (e.g., of brain and CNS activity levels) to determine levels of threat in potential adversaries via changes in dielectric properties and conductivity. The PBPK and cellular level virus infectious models we discuss are special examples of a much wider class of population models that one might utilize to investigate potential agents for use in attacks, such as viruses, bacteria, fungi and other chemical, biochemical or radiological agents. These include general epidemiological models such as SIR infectious

[1]  Ieee Antennas,et al.  Electromagnetics: History, Theory, and Applications , 1993 .

[2]  R A Albanese,et al.  Physiologically based pharmacokinetic models for the transport of trichloroethylene in adipose tissue , 2002, Bulletin of mathematical biology.

[3]  Harvey Thomas Banks,et al.  Nondestructive evaluation of materials using pulsed microwave interrogating signals and acoustic wave induced reflections , 2002 .

[4]  C. C. Wang,et al.  Nonlinear optics. , 1966, Applied optics.

[5]  Laura Kay Potter,et al.  Physiologically Based Pharmacokinetic Models for the Systemic Transport of Trichloroethylene , 2001 .

[6]  Maya R. Gupta,et al.  Recent advances in terahertz imaging , 1999 .

[7]  Fumio Kojima,et al.  Boundary Shape Identification Problems in Two-Dimensional Domains Related to Thermal Testing of Materials. , 1989 .

[8]  J. L. Lions,et al.  Control of Systems Governed by Parabolic Partial Differential Equations , 1971 .

[9]  David M. Bortz,et al.  Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations , 2002 .

[10]  H. T. Banks IDENTIFICATION OF NONLINEAR DELAY SYSTEMS USING SPLINE METHODS , 1980 .

[11]  D M Bortz,et al.  Incorporation of variability into the modeling of viral delays in HIV infection dynamics. , 2003, Mathematical biosciences.

[12]  H. Banks,et al.  Spline approximations for functional differential equations , 1979 .

[13]  Catherine Sulem,et al.  The nonlinear Schrödinger equation , 2012 .

[14]  B. Lindsay Mixture models : theory, geometry, and applications , 1995 .

[15]  Harvey Thomas Banks,et al.  Boundary estimation problems arising in thermal tomography , 1989 .

[16]  Martin Vann De Berg,et al.  Toxicokinetics , 2000, Food additives and contaminants.

[17]  H T Banks,et al.  Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model. , 2004, Mathematical biosciences.

[18]  H. T. Banks,et al.  Electromagnetic material interrogation using conductive interfaces and acoustic wavefronts , 2000, Frontiers in applied mathematics.

[19]  B. Scaife,et al.  Principles of dielectrics , 1989 .

[20]  Michael S. Roberts,et al.  A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations , 1986, Journal of Pharmacokinetics and Biopharmaceutics.

[21]  H. Banks,et al.  Hereditary Control Problems: Numerical Methods Based on Averaging Approximations , 1978 .

[22]  Harvey Thomas Banks,et al.  Time domain electromagnetic scattering using perfectly matched layers , 2003 .

[23]  V. Komkov Optimal shape design for elliptic systems , 1986 .

[24]  Derek Abbott,et al.  Powder detection using THz imaging , 2002, CLEO 2002.

[25]  J. Timbrell,et al.  Casarett and Doull's Toxicology: The Basic Science of Poisons , 1981 .

[26]  C. Sulem,et al.  The nonlinear Schrödinger equation : self-focusing and wave collapse , 2004 .

[27]  Harvey Thomas Banks,et al.  Modeling and estimating uncertainty in parameter estimation , 2001 .

[28]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[29]  M. Emerman,et al.  The human immunodeficiency virus type 1 vpr gene prevents cell proliferation during chronic infection , 1995, Journal of virology.

[30]  Marie Davidian,et al.  Nonlinear Models for Repeated Measurement Data , 1995 .

[31]  Fred S. Roberts,et al.  Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Re , 2002 .

[32]  C. Balanis Advanced Engineering Electromagnetics , 1989 .

[33]  J. Lions Optimal Control of Systems Governed by Partial Differential Equations , 1971 .