Biomedical Engineering Reference
In-Depth Information
K
12
K
23
K
30
f
1
(t)
q
1
q
2
q
3
K
21
K
25
K
45
K
56
K
60
q
4
q
5
q
6
K
54
FIGURE 7.44
Illustration for Exercises 108 and 109.
109.
Solve for the quantity in each compartment shown in Figure 7.44 given
K
12
¼
1.6,
K
21
¼
0.5,
K
23
¼
2.0,
K
30
¼
0.5,
K
25
¼
2.5, K
45
¼
0.4,
K
54
¼
1.5,
K
60
¼
0.5, K
56
¼
0.4, and
f
1
(
t
)
¼
10d(
t
).
Suggested Reading and References
E. Ackerman, L.C. Gatewood, Mathematical Models in the Health Sciences, University of Minnesota Press,
Minneapolis, 1979.
E.S. Allman, J.A. Rhodes, Mathematical Models in Biology, An Introduction, Cambridge University Press,
Cambridge, UK, 2004.
S.A. Berger, W. Goldsmith, E.R. Lewis, Bioengineering, Oxford University Press, Oxford, UK, 1996.
G.E. Briggs, J.B.S. Haldane, A note on the kinetics of enzyme action, Biochem. J. 19 (1925) 338-339.
N.F. Britton, Essential Mathematical Biology, Springer, London, 2003.
J.H.U. Brown, J.E. Jacobs, L. Stark, Biomedical Engineering, F.A. Davis Company, Philadelphia, 1971.
E. Carson, C. Cobelli, Modeling Methodology for Physiology and Medicine, Academic Press, London, 2001.
J.R. Cameron, J.G. Skofroinick, R. Grant, Physics of the Body, Medical Physics Publishing, Madison, WI, 1999.
J.J. DiStefano, F. Mori, Am. J. Physiol. Regul. Integr. Comp. Physiol. 233 (1977) 134-144.
J.J. DiStefano, P.H. Mak, Am. J. Physiol. Regul. Integr. Comp. Physiol. 236 (1979) 137-141.
R. Fisher, Compartmental Analysis, in: J.D. Enderle, S.M. Blanchard, J.D. Bronzino (Eds.), Introduction to Biomedi-
cal Engineering, Academic Press, San Diego, California, 2000, pp. 1062.
M.E. Fisher, A Semiclosed-Loop Algorithm for the Control of Blood Glucose Levels in Diabetics, IEEE Trans.
Biomed. Eng. 38 (1) (1991).
K. Godfrey, Compartmental Models and Their Applications, Academic Press, San Diego, California, 1983.
A.C. Guyton, Textbook of Medical Physiology, eighth ed., W.B. Saunders Company, Philadelphia, 1991.
W.M. Haddad, V.S. Chellaboina, E. August, Stabilitiy and Dissipativity Theory for Discrete-Time Non-Negative
and Compartmental Dynamical Systems, International Journal of Control 76 (18) (2003) 1845-1861.
V. Henri, Lois G
´
n
´
rales de l'Action des Diastases, Hermann, Paris, 1903.
F.C. Hoppensteadt, C.S. Peskin, Mathematics in Medicine and the Life Sciences, Springer-Verlag, New York, 1990.
J.A. Jacquez, Modeling with Compartments, BioMedware, Ann Arbor, MI, 1999.
J.A. Jacquez, Compartmental Analysis in Biology and Medicine, third ed, BioMedware, Ann Arbor, MI, 1996.
J. Keener, J. Sneyd, Mathematical Physiology, Springer, New York, 1998.
L. Michaelis, M. Menten, Die Kinetik der Invertinwirkung, Biochem. Z. 49 (1913) 333-369.
J.D. Murray, Mathematical Biology, third ed., Springer, New York, 2001.
R.B. Northrop, Endogenous and Exogenous Regulation and Control of Physiological Systems, CRC Press, 1999.
A. Ritter, S. Reisman, B. Michniak, Biomedical Engineering Principles, CRC Press, Boca Raton, FL, 2005.
S. Schnell, C. Mendoza, Closed form solution for time-dependent enzyme kinetics, J. Theor. Biol. 187 (1997)
207-212.
