Solution and implementation of distributed lifespan models
- 239 Downloads
We consider a population where every individual has a unique lifespan. After expiring of its lifespan the individual has to leave the population. A realistic approach to describe these lifespans is by a continuous distribution. Such distributed lifespan models (DLSMs) were introduced earlier in the indirect response context and consist of the mathematical convolution operator to describe the rate of change. Therefore, DLSMs could not directly be implemented in standard PKPD software. In this work we present the solution representation of DLSMs with and without a precursor population and an implementation strategy for DLSMs in ADAPT , NONMEM and MATLAB . We fit hemoglobin measurements from literature and investigate computational properties.
KeywordsLifespan Distribution Convolution Population
The present project is supported by the National Research Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND).
- 5.D’Argenio DZ, Schumitzky A, Wang X (2009) ADAPT 5 user’s guide: pharmacokinetic/pharmacodynamic systems analysis software. Biomedical Simulations Resource, Los AngelesGoogle Scholar
- 6.Beal S, Sheiner LB, Boeckmann A, Bauer RJ (2009) NONMEM user’s guides. Icon Development Solutions, Ellicott CityGoogle Scholar
- 7.MATLAB Release (2012) The MathWorks, Inc., NatickGoogle Scholar
- 8.Nichols B, Shrestha RP, Horowitz J, Hollot CV, Germain MJ, Gaweda AE, Chait Y (2011) Simplification of an erythropoiesis model for design of anemia management protocols in end stage renal disease. In: 33rd Annual international conference of the IEEE EMBS Boston, Massachusetts, USAGoogle Scholar
- 9.Atkinson K (1989) An introduction to numerical analysis, 2nd edn. Wiley, New YorkGoogle Scholar
- 10.Thomas GB, Finney RL (1996) Calculus and analytic geometry, 9th edn. Addison-Wesley, ReadingGoogle Scholar
- 11.Marshall AW, Olkin I (2007) Life distributions. Springer, New YorkGoogle Scholar
- 14.Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in Fortran 77, the art of scientific computing, 2nd edn. Cambridge University Press, New YorkGoogle Scholar