References

1

C.E. Miller and C.S. Henriquez. Finite element analysis of bioelectric phenomena. Crit. Rev. in Biomed. Eng., 18:181--205, 1990. This represents the first review paper on the use of the finite element method as applied to biomedical problems. As the authors note, bioengineers came to these methods only fairly recently, as compared to other engineers. It contains a good survey of applications.

2

J. Nenonen, H.M. Rajala, and T. Katilia. Biomagnetic Localization and 3D Modelling. Helsinki University of Technology, Espoo, Finland, 1992. Report TKK-F-A689.

Biomagnetic Localization and 3D Modelling. Helsinki University of Technology, Espoo, Finland, 1992. Report TKK-F-A689. This is a collection of papers devoted to inverse magneto-encephalography (MEG) and magneto-cardiography (MCG) problems. While perhaps difficult to obtain, it contains several interesting papers on the subject.

3

C.R. Johnson, R.S. MacLeod, and P.R. Ershler. A computer model for the study of electrical current flow in the human thorax. Computers in Biology and Medicine, 22(3):305--323, 1992. This is a paper by the author which details the construction of the three-dimensional model, part of which is described in the chapter.

4

C.R. Johnson, R.S. MacLeod, and M.A. Matheson. Computer simulations reveal complexity of electrical activity in the human thorax. Comp. in Physics, 6(3):230--237, May/June 1992. Another paper by the author. This one deals with some of the computational and visualization aspects of the work. It contains some nice color figures (including one on the cover of the journal).

5

O. Gandhi. Biological Effects and Medical Applications of Electromagnetic Energy. Prentice-Hall, Englewood Cliffs, 1990. This textbook surveys the subject of the effect of electromagnetic sources (powerlines, cellular phones, etc.) on the human body.

6

Y. Kim, J.B. Fahy, and B.J. Tupper. Optimal electrode designs for electrosurgery. IEEE Trans. Biomed. Eng., 33:845--853, 1986. This paper discusses an example of the modeling of bioelectric fields for applications in surgery.

7

R. Plonsey. Bioelectric Phenomena. McGraw-Hill, New York, 1969. This is the first text using physics, mathematics, and engineering principles to quantify bioelectric phenomena.

8

R.K. Hobbie. Intermediate Physics for Medicine and Biology. John Wiley and Sons, New York, 1988. This textbook is written for undergraduate science and engineering majors. It covers a wide variety of topics and contains a couple of chapters devoted to bioelectric phenomena.

9

J.D. Murray. Mathematical Biology. Springer-Verlag, New York, 1989. A textbook aimed at first year graduate mathematics students interested in applying mathematics to biological problems.

10

C.S. Henriquez and R. Plonsey. Simulation of propagation along a bundle of cardiac tissue. I. mathematical formulation. IEEE Trans Biomed Eng, 37:850--860, 1990. This paper and the companion paper below, describe the bidomain approach to the propagation of electrical signals through active cardiac tissue.

11

C.S. Henriquez and R. Plonsey. Simulation of propagation along a bundle of cardiac tissue. II. results of simulation. IEEE Trans Biomed Eng, 37:861--887, 1990.

12

J.P. Keener. Waves in excitable media. SIAM J. Appl. Math., 46:1039--1056, 1980. This paper describes mathematical models for wave propagation in various excitable media. Both chemical and physiological systems are addressed.

13

V.S. Zykov. Modelling Wave Processes in Excitable Media. Manchester University Press, Manchester, 1988. The first textbook devoted to the mathematical treatment of wave propagation in excitable media.

14

J. Hadamard. Sur les problemes aux derivees parielies et leur signification physique. Bull. Univ. of Princeton, pages 49--52, 1902. This is Hadamard's original paper describing the concepts of well- and ill-posedness. In French.

15

F. Greensite, G. Huiskamp, and A. van Oosterom. New quantitative and qualitative approaches to the inverse problem of electrocardiology: their theoretical relationship and experimental consistency. Medical Physics, 17(3):369--379, 1990. This paper describes methods for constraining the inverse problem of electrocardiology in terms of sources. Methods are developed which put bounds on the space of acceptable solutions.

16

A. Tikhonov and V. Arsenin. Solution of Ill-posed Problems. Winston, Washington, DC, 1977. This is the book in which Tikhonov describes his method of regularization for ill-posed problems.

17

A.N. Tikhonov and A.V. Goncharsky. Ill-Posed Problems in the Natural Sciences. MIR Publishers, Moscow, 1987. This is a collection of research papers from physics, geophysics, optics, medicine, etc., which describe ill-posed problems and the solution techniques the authors have developed.

18

V.B. Glasko. Inverse Problems of Mathematical Physics. American Institute of Physics, New York, 1984. This book has several introductory chapters on the mathematics of ill-posed problems followed by several chapters on specific applications.

19

P.C. Hansen. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 34(4):561--580, 1992. This is an excellent review paper which describes the various techniques developed to solve ill-posed problems. Special attention is paid to the selection of the a priori approximation of the regularization parameter.

20

P.C. Hansen. Regularization Tools: A Matlab package for analysis and solution of discrete ill-posed problems. Available via netlib in the library numeralgo/no4. This is an excellent set of tools for experimenting with and analyzing discrete ill-posed problems. The netlib library contains several Matlab routines as well as a postscript version of the accompanying technical report/manual.

21

Y. Yamashita. Theoretical studies on the inverse problem in electrocardiography and the uniqueness of the solution. IEEE Trans Biomed Eng, 29:719--725, 1982. The first paper to prove the uniqueness of the inverse problem in electrocardiography.

22

O. Bertrand. 3d finite element method in brain electrical activity studies. In J. Nenonen, H.M. Rajala, and T. Katila, editors, Biomagnetic Localization and 3D Modeling, pages 154--171. Helsinki University of Technology, Helsinki, 1991. This paper describes the inverse MEG problem using the finite element method.

23

I.M. Singer and J.A. Thorpe. Lecture Notes on Elementary Topology and Geometry. Springer-Verlag, New York, 1967. An excellent elementary textbook on topology and geometry.

24

A Bowyer. Computing Dirichlet tesselations. Computer J., 24:162--166, 1981. One of the first papers on the Delaunay triangulation in 3-space. If you read this paper, don't use Bowyer's algorithm for creating the triangulations as it in not computationally efficient.

25

S.R.H. Hoole. Computer-Aided Analysis and Design of Electromagnetic Devices. Elsevier, New York, 1989. While the title wouldn't make you think so, this is an excellent introductory text on the use of numerical techniques to solve boundary value problems in electrodynamics. The text also contains sections on mesh generation and solution methods. Furthermore, it provides pseudocode for most of the algorithms discussed throughout the text.

26

R.S. MacLeod, C.R. Johnson, and M.A. Matheson. Visualization tools for computational electrocardiography. In Visualization in Biomedical Computing, pages 433--444, 1992. This paper, and the paper which follows, concern the visualization aspect of the research described in the chapter.

27

R.S. MacLeod, C.R. Johnson, and M.A. Matheson. Visualization of cardiac bioelectricity --- a case study. In IEEE Visualization 92, pages 411--418, 1992. See previous comment.

28

T.C. Pilkington, B. Loftis, J.F. Thompson, S.L-Y. Woo, T.C. Palmer, and T.F. Budinger. High-Performance Computing in Biomedical Research. CRC Press, Boca Raton, 1993. This edited collection of papers gives an overview of the state of the art in high performance computing (as of 1993) as it pertains to biomedical research. While certainly not comprehensive, the text does showcase several interesting applications and methods.

29

J. Thompson and N.P. Weatherill. Structed and unstructed grid generation. In T.C. Pilkington, B. Loftis, J.F. Thompson, S.L-Y. Woo, T.C. Palmer, and T.F. Budinger, editors, High-Performance Computing in Biomedical Research, pages 63--112. CRC Press, Boca Raton, 1993. This paper contains some extensions of Thompson's classic textbook on numerical grid generation.

30

P.L. George. Automatic Mesh Generation. Wiley, New York, 1991. This is an excellent introduction to mesh generation. It contains a suvey of all the major mesh generation schemes.

31

J.F. Thompson, Z.U.A. Warsi, and C.W. Mastin. Numerical Grid Generation. North-Holland, New York, 1985. This is the classic on mesh generation. The mathematical level is higher than that of George's book, and most of the applications are directed towards computational fluid dynamics.

32

C.S. Henriquez, C.R. Johnson, K.A. Henneberg, L.J. Leon, and A.E. Pollard. Large scale biomedical modeling and simulation: from concept to results. In N. Thakor, editor, Frontiers in Biomedical Computing. IEEE Press, Philadelphia, 1994 (to appear). This paper describes the process of large scale modeling along with computational and visualization issues pertaining to bioelectric field problems.

33

J.E. Akin. Finite Element Analysis for Undergraduates. Academic Press, New York, 1986. This is an easy to read, self contained text on the finite element method aimed at undergraduate engineering students.

34

C. Johnson. Numerical solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, Cambridge, 1990. An excellent introductory book on the finite element method. The text assumes mathematical background of a first year graduate students in applied mathematics and computer science. An excellent introduction to the theory of adaptive methods.

35

J.D. Jackson. Classical Electrodynamics. John Wiley, New York, 1975. One of the classic books on electrodynamics and the standard graduate textbook for many first year graduate physics courses on the subject.

36

C.A. Brebbia and J. Dominguez. Boundary Elements: An Introductory Course. McGraw-Hill, Boston, 1989. This is an introductory book on the boundary element method by one of the foremost experts on the subject (C.A.B.).

37

M.A. Jawson and G.T. Symm. Integral Equation Methods in Potential Theory and Elastostatics. Academic Press, London, 1977. An introduction to the boundary integral method as applied to potential theory and elastostatics.

38

G. Beer and J.O. Watson. Introduction to Finite and Boundary Element Methods for Engineers. Wiley, New York, 1992. This is an excellent first book for those wishing to learn about the practical aspects of the numerical solution of boundary value problems. The book covers not only finite and boundary element methods, but also sections on mesh generation and the solution of large systems.

39

C.R. Johnson and R.S. MacLeod. Nonuniform spatial mesh adaption using a posteriori error estimates: applications to forward and inverse problems. Applied Numerical Mathematics, vol. 14, pp. 331-326, 1994. This is a paper by the author which describes the application of the h-method of mesh refinement for large scale two- and three-dimensional bioelectric field problems.

40

J.E. Flaherty. Adaptive Methods for Partial Differential Equations. SIAM, Philadelphia, 1989. This is a collection of papers on adaptive methods, many by the founders in the field. Most of the papers are applied to adaptive methods for finite element methods and deal with both theory and applications.

41

G.H. Golub, and C.F. Van Loan. Matrix Computations. Johns Hopkins, Baltimore, 1989. This is a classic reference for matrix computations and is highly recommended.

42

O.C. Zienkiewicz. The Finite Element Method in Engineering Science. McGraw-Hill, New York, 1971. This is a classic text on the finite element method. It is now in its fourth edition, 1991.

43

O.C. Zienkiewicz and J.Z Zhu. A simple error estimate and adaptive procedure for practical engineering analysis. Int. J. Num. Meth. Eng., 24, 337-357, 1987. This is a classic paper which describes the use of the energy norm to globally refine the mesh based upon a priori error estimates.

44

O.C. Zienkiewicz and J.Z Zhu. Adaptivity and mesh generation. Int. J. Num. Meth. Eng., 32, 783-810, 1991. This is another good paper on adaptive methods which describes some more advanced methods than their 1987 paper.

45

D.S. Burnett Finite Element Method. Addison Wesley, Reading, Mass., 1988. This is an excellent introduction to the finite element method. It covers all the basics and introduces more advanced concepts in an readily understandable context.

46

C.B. Barber, D.P. Dobkin, and H. Huhdanpaa The quickhull algorithm for convex hull. Geometry Cneter Technical Report GCG53. A public domain two- and three-dimensional Delaunay mesh generation code. Available via anonymous ftp from: geom.umn.edu:/pub/software/qhull.tar.Z. There is also a geometry viewer available from geom.umn.edu:/pub/software/geomview/geomview-sgi.tar.Z.