Modeling Chemotherapy Induced Myelosuppression

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Modeling Chemotherapy Induced Myelosuppression

• J. Carl Panetta
• Department of Pharmaceutical Sciences, St. Jude
  Childrens Research Hospital and University of
  Tennessee, Memphis, TN

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Note delay in suppression of ANC
Lower bound of normal ANC
Actual TMZ treatment times
TMZ Proposed treatment times
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Note rebound effect
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Empirical Modeling Methods

• Describe the Pharmacodynamic (PD) effects of TMZ
  and MTIC based on empirical relations between
• PK effects AUC, time above threshold etc.
• PD effects Nadir, time between courses, or area
  between ANC curve (ABC).

• Useful in determining acceptable dose range

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Area Between the Curve (ABC)
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Karlsson Model(Karlsson, MO et al., Clin.
Pharmacol. Ther. 1998 63)

• AUC Model g11 and C50C.
• Threshold Model g1? and C50threshold
  concentration.

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Empirical Modeling Results

• Relationship between PK and PD effect is not
  strong.
• This could be due to all patients received a
  similar fixed dose. But, TMZ AUC 2.5 fold MTIC
  AUC 2 fold
• Even when there is a relation, the empirical
  model does not explain why.
• Empirical models are not predictive.

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Mechanistic Models

• Describe the effects of chemotherapeutic drugs
  such as TMZ, TPT etc. on neutrophil production
  via a dynamical system.
• There have been a variety of mathematical models
  to describe hematopoiesis over the last 25 years.
  (S. I. Rubinow and J. L. Lebowitz M. C. Mackey
  et al. Shochat, Stemmer, and Segel Panetta et
  al. Minami et al. Friberg et al. Zamboni et
  al.)
• By better understanding the mechanisms of
  haematopoiesis we can obtain a better
  understanding of possible causes of
  myelosuppression. (Varies by drug)

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Haematopoietic Regulation
Adapted from Mackey (1996)
Observe
Thrombopoietin
Mature Platelets
death
Maturation stage
CFU-M
Erythropoietin
Pluripotential Stem Cells
Mature RBC
Maturation stage
CFU-E
death
Granulopoietin (G-CSF)
Mature WBC
Maturation stage
CFU-C
death
Proliferating
Nonproliferating
Circulating
Bone Marrow
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Mackey and Glass Model (Science 1977)

• Homogeneous Population of mature circulating
  cells of density P
• Delay t between initiation of cellular production
  in the bone marrow and the release of mature
  cells into the blood.

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Growth Terms
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Delay6 days
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Delay20 days
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Minami et al. Clin. Pharmacol. Ther. (64) 1998

• Used to describe leukopenia due to Paclitaxel and
  etoposide
• Drug effect blocks stem cell production
• Stem cell pool unaffected by drug
• No feedback term included

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Negative Feedback

• An inverse relation has been observed between
  circulating neutrophil density and serum levels
  of granulocyte colony stimulating factor (G-CSF).
  (Kearns et al. J. Pediatr. 123)
• Administration of G-CSF leads to
• increased peripheral neutrophil counts
• increased amplitude of oscillations
• decreased period of oscillations
• decreased average maturation time
• Can lead to oscillations in the ANC.
• See multiple references by Mackey et al.

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Friberg et al.J. of Pharmacol. Exp. Ther. (295)
2000

• Used to describe the toxic effects of 5-FU in
  mice
• Negative feedback from circulating leukocytes
  affects stem cell production
• Drug effect kills sensitive cells (i.e. cells
  that are proliferating) in the B.M.
• Drug effect does not block stem cell production
• Stem cell pool unaffected by drug

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• Drug effects are cytotoxic to stem cells
• Negative feedback from circulating leukocytes
  affects stem cell production

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Drug Effects
TMZ blocks stem cells
TMZ cytotoxic to stem cells
Note To obtain a better description of the data
when TMZ only blocks stem cells, the drug would
have to be active 6? longer than is realistic
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Qualitative effects of feedback
No Feedback
Feedback
Single Dose
Two Doses
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• Predict Courses 2 and 3 from Course 1

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• Predict Course 2 from Course 1
• Predict Course 3-6 from Course 2

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Predict course 2 and 3 from course 1
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Model for TPT (Zamboni et al., CCR 2001)
We have added extra delay compartments to better
describe our data.
Filgrastim (G-CSF)
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Filgrastim (G-CSF)
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Platelets
Blue Course 1 Green Course 2
Time (days)
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Parameter Estimation
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Ordinary Least Squares
Minimize the following equation with respect to ?
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OLS fit
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Problem

• Method can be bias if concentrations vary widely.
• Why?

The large concentrations will have a large
influence while the small concentrations will
only have a small influence on the ordinary least
square equation.

• Fix give more weight to the smaller values.

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Weighted Least Squares
QUESTION How do we choose the weights?
Question Is there any theoretical basis for this
choice?
YES
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WLS Fit
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Maximum Likelihood Estimation
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Notes on MLE

• ? variance in ?i.
• Error must be a normal or lognormal dist. with a
  mean of zero.
• ? can be
• a function of ?
• a function of C
• fi is maximum when ?i0.
• The Best ? is the one that maximizes the
  likelihood function

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-2 log likelihood function
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Comments on MLE

• If ?i are constant (not functions of ?) and
  identical, this is equivalent to both OLS and
  WLS.
• If ?i are constant and functions of Ci this is
  equivalent to WLS.
• A typical form for ?i is

Normal Dist.
Note ? is a function of ?.
Lognormal Dist.
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ML Fit
Abs. Err. 0.1
Abs. Err. 0.01
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Comparison of Fit