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Pharmacodynamic modeling of the effect of changes in the environment on cellular lifespan and cellular response

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Abstract

Lifespan-based pharmacodynamic (PD) models of cellular response assume that the lifespan of cells is predetermined at the time of cellular production, despite recognized changes in the cellular environment following production that may alter the survival of the cells. This work extends previously proposed cellular lifespan PD models to incorporate environmental effects on the cell lifespan by considering two basic classes of models from survival analysis: accelerated life and relative risk models. Cellular responses using both model classes were simulated using a steady-state cellular production rate with changes in the environmental effects resulting from three different basic profiles. The environmental effect models were also fitted to the red blood cell (RBC) and hemoglobin concentration data from six sheep following hematopoietic ablation by busulfan administration. The simulations indicated that the basic shapes of the cellular responses were different between the accelerated life and relative risk models. Due to the more direct physical interpretation, relatively simple steady-state relationship between the cellular response and environmental effects, and the ability to reduce the model to a “point” baseline lifespan distribution, the accelerated life model appears to be a more realistic and flexible model. The analysis of the sheep RBC and hemoglobin data indicated that the environmental effect began to decrease the survival of cells 1–2 weeks following initiation of ablation and that the average “severity” of the environmental effect increased 3.49 (29.5%) (mean (C.V.)) fold under the accelerated life model. Alternative models without an environmental effect did not describe the observed data as well. The proposed environmental effect cellular lifespan PD models allow for the incorporation of arbitrary changes in the conditions of the cellular environment and modeling of environmentally dependent cellular survival. These PD models have potential applications in hematological management of end-stage renal disease, transfusion medicine, and patients undergoing chemotherapy, among other diseases and therapies.

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Abbreviations

AIC:

Akaike’s Information Criterion

BV :

Blood volume

e(t, z):

Cumulative measure of the effect of the environment

e avg :

Average value of the environmental effect function

E {·|· }:

Conditional mathematical expectation of a random variable

f prod (t):

Production rate (i.e. input rate into the sampling compartment)

\({f_{prod}^{SS}}\) :

Steady-state production rate

g (t), h (t):

Environmental effect functions

\({\ell _b \left({\tau, z}\right)}\) :

Baseline p.d.f. of cellular lifespans

\({\ell _e \left({\tau, z}\right)}\) :

Observed p.d.f. of cellular lifespans with an environmental effect

λ b (t, z ):

Baseline hazard function

λ e (t, z):

Observed hazard function with an environmental effect

μ b :

Mean of the baseline cellular lifespan

μ SS :

Steady-state mean cellular lifespan

MCH :

Mean corpuscular hemoglobin

M :

Positive multiple of the baseline environmental effect function value

v, u :

Arbitrary integration variables

N (t):

Number of cells in the sampling compartment

P ( · ):

Probability

p.d.f.:

Probability density function

PD:

Pharmacodynamic

RBC:

Red blood cell

σ :

Standard deviation of the baseline cellular lifespan

SD:

Standard deviation

S b (t, z):

Baseline survival function

S e (t, z):

Observed survival function with an environmental effect

SS :

Steady-state (super- and sub-scripted with other terms)

τ, T :

Cellular lifespan, i.e. the time from input into the sampling space to the output from the sampling space (capital tau refers to a random cellular lifespan variable)

t :

Time

t 0 :

Time of initiation of busulfan administration

T decline :

Time period over which the production rate declines from \({f_{prod}^{SS}}\) to zero

z :

Time of production

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Authors and Affiliations

  1. College of Pharmacy, University of Iowa, 115 S. Grand Ave., Iowa City, IA, 52242, USA

    Kevin J. Freise & Peter Veng-Pedersen

  2. Department of Pediatrics, College of Medicine, The University of Iowa, Iowa City, IA, 52242, USA

    Robert L. Schmidt & John A. Widness

Authors
  1. Kevin J. Freise
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  2. Robert L. Schmidt
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  3. John A. Widness
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  4. Peter Veng-Pedersen
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Correspondence to Peter Veng-Pedersen.

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Freise, K.J., Schmidt, R.L., Widness, J.A. et al. Pharmacodynamic modeling of the effect of changes in the environment on cellular lifespan and cellular response. J Pharmacokinet Pharmacodyn 35, 527–552 (2008). https://doi.org/10.1007/s10928-008-9100-x

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