Figure 1.
A generalized approach for model-based prediction and optimization of treatment outcome.
A model representing the underlying physiology is formulated and average patient parameters are estimated using data from literature and past clinical trials. GSA is used to reduce the parameter space and identify most sensitive parameters with sparse clinical data. Following nominal initial dose, few measurements are taken from an individual patient in order to adapt the model to the patient. Patient-specific model is used to predict the treatment outcome and subsequent doses are optimized based on NMPC prediction.
Figure 2.
Schematic representation of 6-MP metabolism.
Following oral intake to the gut, 6-MP is absorbed into the plasma from where it is eliminated through various routes. From plasma, 6-MP diffuses into the cells and enzymatically converted to 6-TGN and MeMP, which in turn are eliminated from the cells at a constant rate.
Table 1.
Glossary of state variables and parameters for 6-MP model.
Figure 3.
Simplified schematics of the leukopoiesis and erythropoiesis model.
Stem cells reside in the bone marrow, proliferate, mature and enter the circulation as fully functional leukocytes. Stem cells receive biochemical feedback for proliferation from the circulating blood. On treatment initiation, 6-MP enters the bone marrow and imparts cytotoxicity to the stem cells. Leukocytes and RBC MCV in the circulating blood are routinely measured and used as a dose-limiting parameter. A. Leukopoiesis, B. Erythropoiesis. Additional compartment for MCV was added to account for the dynamic changes following 6-MP treatment. Solid arrows represent cellular movement; dashed arrow represents property changes.
Table 2.
Glossary of state variables and parameters for leukopoiesis model.
Table 3.
Glossary of state variables and parameters for MCV model.
Figure 4.
Average patient 6-MP model fit to literature data.
A. Model fit to RBC 6-TGN concentration data. B. Model fit to RBC MeMP concentration data. Solid dots represent data points and curves represent 6-MP model (Eqn. 2) fit. Error bars represent standard error.
Figure 5.
Leukopoiesis model fit to average patient data.
Solid dots represent average patient data and curve represent leukocyte model (Eqn. 4) fit. The model mimics the clinical observation during 6-MP treatment; Depletion of leukocytes following 6-MP dosing has been countered by the body's feed-back mechanism. Error bars represent standard error.
Figure 6.
MCV model fit to average patient MCV data.
Solid dots represent the data from literature and the solid line shows the model (Eqn. 7) fit with 6-TGN concentration of 158 pmol/8×108 RBCs. The model fits the data well; it reaches the steady state and stays at ΔMCV of ∼8 fL, which is typically observed during 6-MP treatment at Riley Hospital for Children. Error bars represent standard error.
Table 4.
List of parameters identified for individualization through GSA (in bold letters) together with other fixed parameters.
Figure 7.
6-MP model fit to individual patient data obtained from literature.
Solid dots indicate the individual patient 6-TGN concentration and the solid line represents the model fit. Patient # 8 was omitted from analysis as it is observed that the dosing was discontinued or substantially lowered. The estimated patient-specific parameters are provided in Table 5.
Figure 8.
Leukopoiesis model fit to individual patient data obtained from literature.
Solid dots indicate the individual patient WBC count and solid lines represent the model fit. The estimated patient-specific parameters are provided in Table 5. The model mimics diverse behavior observed during 6-MP treatment.
Table 5.
Patient-specific parameters estimated for 6-MP, leukopoiesis and MCV models.
Figure 9.
MCV model fit to individual patient data obtained from Riley Hospital for Children.
Solid dots indicate ΔMCV of individual patient undergoing 6-MP treatment and solid lines represent the model fit. The estimated patient-specific parameters are provided in Table 5.
Figure 10.
Virtual patient simulation for leukocyte and MCV model.
Data for 6-MP model and leukocyte model are assumed to have originated from the same patient. The resultant estimated parameters for three representative patients are used to simulate the virtual patient response. It is apparent from the figure that different patients achieved different levels of response for the same dose, thereby achieving different treatment outcome. A. Leukocyte model, B. MCV model.
Table 6.
Comparison between model-predicted values (mean ± SD) and published clinical results for model response variables.
Figure 11.
Model-predicted standard deviation in the treatment response over treatment period.
A. Standard deviation for leukocytes response as a function of time, B. Standard deviation for ΔMCV. Variability explained by the models is in line with the pattern observed during 6-MP treatment.
Figure 12.
Optimal dosing based on 6-TGN concentration as therapeutic target.
A & B. Optimal 6-TGN concentration and optimal 6-MP regimen respectively, for a patient with low TPMT enzyme activity. C & D. Optimal profiles for a patient with high TPMT enzyme activity. Patient with low TPMT activity required significantly lower dose compared to the standard treatment and vice versa. Dashed line shows the therapeutic target level.
Figure 13.
Optimal dosing based on leukocyte count as target.
A. Evolution of leukocyte count in response to optimum 6-MP dosing. Dashed line represents critical leukocyte level and solid dots represent clinical data for an average patient. B. Optimum 6-MP dosing profile predicted by NMPC. The standard daily 6-MP dosing is 75 mg/day.
Figure 14.
Optimal dosing based on leukocyte count and MCV as target.
A. Evolution of leukocyte count in response to optimum 6-MP dosing. B. Evolution of ΔMCV response with optimum 6-MP dose. Dashed lines represent critical leukocyte and target MCV levels and solid dots represent clinical data for an average patient. C. Optimum 6-MP dosing profile predicted by NMPC. The standard daily 6-MP dosing is 75 mg/day.