PBPK models provide a convenient structure for depicting systemic distribution of chemotherapeutics following administration, provided that sufficient data are available to support the more involved model structure. Using plasma, tumor, and tissue Doc concentration versus time data obtained from SKOV-3 bearing SCID mice dosed i.v. at 10 mg
kg, a mouse PBPK model was constructed with separate compartments for plasma, tumor, liver, kidney, lung, heart, spleen, brain, muscle, fat, and red blood cells. Due to the presence of tissue concentration PK with significantly different concentration versus time profiles from plasma (tissues had bi-phasic elimination while plasma was tri-phasic), it was necessary to include two tissue subcompartments, corresponding to tissue transport
0 4 8 12 16 20 24 102
104
Time (hours)
[Doc] (nM)
Plasma
0 4 8 12 16 20 24 102
104
Time (hours)
[Doc] (nM)
Liver
0 4 8 12 16 20 24 102
104
Time (hours)
[Doc] (nM)
Kidney
Figure 4.7: Plasma (top left), liver (top right), and kidney (bottom left) Doc predictions from the model developed in Figure 4.1 (dash-dot) and those predicted by a PBPK model from the literature [5] (solid) compared with actual plasma Doc concentration versus time data from tumor-bearing SCID mice (circles, µ, with ±σ error bars, n = 3 mice per point) dosed at 10 mg
kg.
0 4 8 12 16 20 25 102
104
Time (hours)
[Doc] (nM)
Plasma
0 4 8 12 16 20 25 102
104
Time (hours)
[Doc] (nM)
Liver
0 4 8 12 16 20 25 102
104
Time (hours)
[Doc] (nM)
Kidney
Figure 4.8: Plasma (top left), liver (top right), and kidney (bottom left) Doc predictions from the model developed in Figure 4.1 (dash-dot) and those predicted by a PBPK model from the literature [5] (solid) compared with actual plasma Doc concentration versus time data from BALB/c mice (circles) dosed at 20 mg
kg.
and tissue retention of Doc, respectively. To minimize the number of parameters requiring estimation, the same parameter values for Doc retention were used for all tissues. While this provides a reasonable approximation, two separate sets of parameter values are likely necessary based upon inspection of tissue half-lives in Table 4.2.
Tissue half-lives reveal that the longest drug retention is predicted within the tumor, which agrees with previous Doc tumor studies, though the half-life seen from the current study was significantly longer than that described in others [160]. This increased retention may be tumor-type specific, however, samples at later time points are required to characterize the Doc elimination from the tumor appropriately. While the half-lives of Doc in plasma, tumor, and normal tissues were longer in the current study than those previously reported in the literature [160], the values agreed with half-lives reported from Bradshaw-Pierce et al. [5]. This latter study, which was performed more recently and without radiolabeled Doc, may more accurately represent actual Doc tissue concentrations versus time. Muscle had the second longest Doc half-life at 10.6 hours. While the Doc Cmax of muscle was 2-15 fold lower than Doc Cmax in other tissues, the Doc concentration at 24 hours in muscle was similar to that in the majority of other tissues with the exception of tumor. Given the overall percentage of body weight represented by muscle as compared to other tissues, muscle may be the primary contributor to terminal Doc retention following dosing.
Comparisons between the mouse PBPK model developed in this chapter and a previous one [5] agreed well for mouse Doc dosing levels of 10 and 20 mg
kg, despite using different model structures. More compartments were included within the PBPK model developed within this chapter, while the previous PBPK model included intestinal compartment concentrations and additional routes of elimination, including urinary and fecal excretion, that account for approximately 10% of drug removal. Furthermore, the previous model [5] has nonlinear elimination rates and binding relationships within tissues, while the model developed in this chapter has only linear components. However, our PBPK model also utilized a structure seen as less desirable in the literature due to the large number of model parameters and uncertainty associated with the vascular fraction term within the model. Therefore, the ideal model may depend on the needs of the user, whether a lower-order system with nonlinearities, or a higher-order linear system is preferred. It is likely, though, that a linear model is sufficient
for describing Doc PK dynamics in humans, as no nonlinearities over a range of dosing levels have been observed [161] and the human scale-up model of the previously published PBPK model did not exhibit any nonlinear behavior regarding patient Doc plasma concentration predictions. Also, even for patients with altered CYP3A enzyme levels, these alterations would affect the enzymatic rate of elimination, and not the saturation. Therefore, a linear elimination rate should be sufficient for describing Doc elimination. Futhermore, for Doc administration of 5, 10, and 20 mg
kg, all common tissues (kidney and liver) had similar half-life values, though plasma half-half-life was 2-fold greater for the 20 mg
kg dosing level. Combined with the extensive preclinical and clinical work performed using Doc, these results suggest that a linear model may be sufficient for describing systemic Doc distribution.
The incorporation of a tumor compartment within the current Doc PBPK model structure also represents an extension of the earlier mouse PBPK model [5] and may aid human scale-up predictions of total tumor Doc exposure. Furthermore, the 3-fold greater tumor half-life compared to the next longest tissue may explain why similar efficacy is attainable on weekly versus q3w Doc schedules. Model simulations have demonstrated that week-to-week tumor accumulation of Doc is predicted to occur (results not shown), and these findings will be further explored in Chapter 5.
Additional Doc distribution studies from our group have revealed that extended Doc tumor retention also applies to Pc-3 human tumor xenografts [150]. Measured tumor tissue Doc concentrations from these xenografts were lower than those obtained from SKOV-3 human tumor xenografts, necessitating a reevaluation of the model parameters for tumor distribution. Either a reduction in the tumor vascular fraction (ft) from 10% (for SKOV-3) to 3.1%, or a one-third reduction in the ktve parameter, were necessary to describe the measured Pc-3 tumor Doc concentrations (Figure 4.9). Finding two parameter alterations capable of describing the new data was not unexpected based upon the parameter sensitivity and coupling previously discussed in this Chapter. However, given that Pc-3 xenografts are typically less vascularized than SKOV-3 xenografts [150], alterations to ftmay be suitable for predicting tumor concentration variation between different tumor lines. Also, Doc samples in Pc-3 tumor xenografts were obtained out to 72 hours, as opposed to the 24-hour sampling utilized in the modeling study. While the estimated interstitial-to-vascular transition rate
for tumor could not be properly estimated due to limited dynamic information in docetaxel tumor concentration over the 24-hour sampling window, this additional data demonstrates that the elimination rate predicted by the model may indeed be accurate.
Table 4.3: PBPK model predictive performance comparison at dosing levels of 10 mg kg and 20 mg
kg.
10 mg
kg 20 mg
kg
Model Tissue MAPE MPE RMSPE MAPE MPE RMSPE
Plasma 26.4 -0.2 8.1 39.0 39.0 15.4
Florian et al. Liver 12.3 5.7 12.5 64.2 7.5 32.9
Kidney 32.3 20.0 13.6 29.7 27.4 14.5
Plasma 61.3 -37.4 48.7 38.4 38.4 14.1
Bradshaw-Pierce et al. [5] Liver 82.4 -82.4 189.5 59.1 -59.1 69.0
Kidney 62.7 8.9 45.2 46.5 36.3 34.6
0 50 100 150 200 250 300 350
101 102 103
Time (min)
[Doc] nM
0 1000 2000 3000 4000
101 102 103
Time (min)
[Doc] nM
Figure 4.9: Measured Doc concentration versus time data from Pc-3 tumor-bearing SCID mice (circles, µ, with ±σ error bars, n = 3 mice per point) compared with mouse PBPK model predictions (lines) for the tumor compartment.