dg = -mig – m2h dt (1) dh = m4g – dt - mzh (2) where g = g(t) represents the amount of glucose deviation from equilibrium, h(t) represents the amount of hormone (Insulin) deviation from equilibrium, and m1, m2, m3, m4 are constants which are determined from test data. (a) Prior to Ackerman et al work, Brolie (1960) also investigate establishing a criterion for determining diabetes from GTT using differential equations. Brolie used experimental data obtained from dogs which he extrapolated to non-diabetic humans and obtained the following empirical data: m1 = 2.92 m2 = 4.34 m4 = 0.208 m3 = 0.780 Using the equations (1) and (2) solve for g and h.

dg = -mig – m2h dt (1) dh = m4g – dt - mzh (2) where g = g(t) represents the amount of glucose deviation from equilibrium, h(t) represents the amount of hormone (Insulin) deviation from equilibrium, and m1, m2, m3, m4 are constants which are determined from test data. (a) Prior to Ackerman et al work, Brolie (1960) also investigate establishing a criterion for determining diabetes from GTT using differential equations. Brolie used experimental data obtained from dogs which he extrapolated to non-diabetic humans and obtained the following empirical data: m1 = 2.92 m2 = 4.34 m4 = 0.208 m3 = 0.780 Using the equations (1) and (2) solve for g and h.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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dg
-mig – m2h
dt
(1)
dh
= m4g –
dt
- mzh
(2)
where g = g(t) represents the amount of glucose deviation from equilibrium,
h(t) represents the amount of hormone (Insulin) deviation from equilibrium, and
m1, m2, m3, m4 are constants which are determined from test data.
(a) Prior to Ackerman et al work, Brolie (1960) also investigate establishing a criterion for
determining diabetes from GTT using differential equations. Brolie used experimental data
obtained from dogs which he extrapolated to non-diabetic humans and obtained the
following empirical data:
m1
= 2.92
m2 =
4.34
m4
= 0.208
m3 =
0.780
Using the equations (1) and (2) solve for g and h.

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