Curve fitting and modeling in pharmacokinetics and some practical experiences with NONLIN and a new program FUNFIT

Pedersen, Peter Veng

doi:10.1007/bf01061732

Cited by 210 publications

(63 citation statements)

References 19 publications

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“…Thus, noting that dR(t)/dt = 0 for t < t p it is realized that Equation (9A) subject to Equation (13A) is valid for all values of t. Equations (9A) and (13A) completes the proof of the deconvolution algorithm Equation (20). Schematic diagram showing the different modeling approaches.…”

Section: Pd Transduction Functionmentioning

confidence: 69%

“…Quadratic programming to determine the population PD function was performed using the NCONF subroutine of the IMSL FORTRAN library [18] which is based on a FORTRAN code by Schittkowski [19]. The results obtained by running the FORTRAN programs were plotted using the graphic library PVPLOT of WINFUNFIT, a computer program for general nonlinear regression, which is a development from the earlier version, FUNFIT [20].…”

Section: Discussionmentioning

confidence: 99%

“…From Equations (14) to (16), we get: (17) The reticulocyte production rate, f(t), can be defined relative to the progenitor activation rate by the lag-time parameter a, (18) Substituting Equation (18) in Equation (17), gives the rate of change in the reticulocyte response in terms of the reticulocyte production rate, (19) Solving Equation (19) for f(t) (see Appendix), gives the reticulocyte production rate, f(t), due to the erythroid progenitor activation: (20) In Equation (20) t p is the start of the perturbation in the measured response (R(t)) resulting from the perturbation (from SS condition) in the activation rate taking place at time t 0 = t p -a. The INT(x) function is defined as the largest integer not exceeding the value of x.…”

Section: Cellular Convolution/deconvolutionmentioning

confidence: 99%

“…The INT(x) function is defined as the largest integer not exceeding the value of x. The above derivation of the key Equation (20) assumes that reticulocytes are not removed by the phlebotomy. Thus, the Equation can be used in this form to determine the reticulocyte production due to a perturbation (from steady state) resulting from an administration of exogenous EPO.…”

Section: Cellular Convolution/deconvolutionmentioning

confidence: 99%

“…The methodology requires the response data and its derivative (Equation (20)) to be estimated as accurately as possible, which is intrinsic to the deconvolution operation and not specific to this method. Besides, in contrast to exo-PK/PD experiments, the responses in endo-PK/PD experiments (e.g.…”

Section: Cellular Convolution/deconvolutionmentioning

confidence: 99%

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A ‘bottom‐up’ approach for endo‐PK/PD analysis

Neelakantan

Widness

Schmidt

et al. 2006

Biopharm & Drug Disp

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A 'bottom-up' PK/PD analysis approach employing system analysis principles of convolution/ deconvolution and special nonparametric estimation procedures is presented to resolve the complex 'endo-PK/PD' of the endogenous form of recombinant drugs using erythropoietin (EPO) as an example. A novel cellular deconvolution algorithm is presented that facilitates the identification of the functional relationship between the variables involved in EPO's complex PK/PD. Five sheep each underwent two phlebotomies spaced 4-6 weeks apart when their hemoglobin levels were reduced from 12 g/dl to 3-4 g/dl. EPO levels and reticulocyte counts were frequently sampled. The data were analysed using end-constrained cubic splines. The rate of reticulocyte production was determined using the novel deconvolution methodology. The erythroid progenitor cells activation rate by EPO was estimated from the reticulocyte production rate using a lag-time parameter which determines the delay in the reticulocyte appearance in the blood relative to the activation of erythroid progenitors. Hysteresis minimization combined with cellular deconvolution was employed to determine the population PK/PD transduction function relating the progenitor activation rate to EPO concentrations in a nonparametric manner without assuming a specific structure. The proposed approach provides a rational informative starting point for developing parametric PK/PD models to resolve the complex endo-PK/PD of recombinant drugs.

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Section: Pd Transduction Functionmentioning

confidence: 69%

Section: Discussionmentioning

confidence: 99%