Computing calcium dynamics in man
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Current practice in the construction and use of models in medicine is considered. CAMET2 is a compartment model calcium metabolism. Its description of the flow of material in the gut is inconsistent, and is corrected in CAMET3. In CAMET2, the rate of emptying of the stomach is proportional to the square root of its volume. In CAMET3, the distension of the duodenum inhibits the emptying of the stomach. There is experimental evidence for this mechanism. An observed 10-20 minute delay in the appearance in blood of radioactive calcium taken by mouth, is still unaccounted for. Present methods for fitting sums decaying exponential functions to radioactive tracer measurements are reviewed. Even when the measurement errors are as low as 2%, and the nearest exponents are the ratio 2:1, the number of exponential components cannot be reliably determined. The parameters may be in error by 60%. The method of Lemaitre and Malenge (Lemaitre A., Malenge J-P. (1971), “An efficient method for multiexponential fitting with a computer”, Cptrs. and Biomed. Res. 4: 555), is the most flexible and efficient where least squares is the criterion of goodness of fit. Data commonly are a measure of a function which is a convolution of a desired function and a known or measured function. The Fourier transforms of both the function to which the data belong, and of the known or measured function must both be zero at the same points in the complex plane. The data are both truncated and also contain experimental error. When the error dominates the problem, the constraints on the positions of the zeros are used to improve the estimate of one or more of the functions above. When, on the other hand, the truncation dominates, the constraints are used to estimate values outside the interval of the data; in this way the effect the truncation is removed. In a new version of the simulation program to solve CAMET3, the integration step length is adjusted automatically to ensure that not only is the integration efficiently performed, but also that the steps fit the inputs and outputs. A five-fold reduction in computer time results in the present case. For the simulation of small models or parts of large models, a new interactive program SIMUL8, has been developed. The model equations are expressed simply in a FORTRAN subroutine and flexible control of graphical output on an oscilloscope display is provided.