The aim of the present study was to evaluate model identifiability when minimal physiologically-based pharmacokinetic (mPBPK) models are integrated with target mediated drug disposition (TMDD) models in the tissue compartment. Three quasi-steady-state (QSS) approximations of TMDD dynamics were explored: on (a) antibody-target complex, (b) free target, and (c) free antibody concentrations in tissue. The effects of the QSS approximations were assessed via simulations, taking as reference the mPBPK-TMDD model with no simplifications. Approximation (a) did not affect model-derived concentrations, while with the inclusion of approximation (b) or (c), target concentration profiles alone, or both drug and target concentration profiles respectively deviated from the reference model profiles. A local sensitivity analysis was performed, highlighting the potential importance of sampling in the terminal pharmacokinetic phase and of collecting target concentration data. The a priori and a posteriori identifiability of the mPBPK-TMDD models were investigated under different experimental scenarios and designs. The reference model and QSS approximation (a) on antibody-target complex were both found to be a priori identifiable in all scenarios, while under the further inclusion of QSS approximation (b) target concentration data were needed for a priori identifiability to be preserved. The property could not be assessed for the model including all three QSS approximations. A posteriori identifiability issues were detected for all models, although improvement was observed when appropriate sampling and dose range were selected. In conclusion, this work provides a theoretical framework for the assessment of key properties of mathematical models before their experimental application. Attention should be paid when applying integrated mPBPK-TMDD models, as identifiability issues do exist, especially when rich study designs are not feasible.

译文

:本研究的目的是在组织隔室中将基于最小生理学的药代动力学(mPBPK)模型与目标介导的药物处置(TMDD)模型集成时,评估模型的可识别性。探索了TMDD动力学的三种准稳态(QSS)近似值:(a)抗体-靶标复合物,(b)游离靶标和(c)组织中的游离抗体浓度。通过模拟评估了QSS近似值的影响,并以mPBPK-TMDD模型作为参考,没有进行任何简化。近似值(a)不会影响模型得出的浓度,而包含近似值(b)或(c)时,仅目标浓度曲线,或药物和目标浓度曲线都分别偏离参考模型曲线。进行了局部敏感性分析,突出了在最终药代动力学阶段进行采样和收集目标浓度数据的潜在重要性。在不同的实验场景和设计下,对mPBPK-TMDD模型的先验和后验可识别性进行了研究。发现在所有情况下参考模型和抗体-靶标复合物的QSS近似值(a)都是先验可识别的,而在进一步包含QSS近似值(b)的情况下,需要保留目标浓度数据才能保留先验可鉴定性。无法评估包括所有三个QSS近似值的模型的属性。尽管选择了适当的采样和剂量范围,观察到了改善,但所有模型均检测到后验可识别性问题。总之,这项工作为数学模型在实验应用之前评估其关键特性提供了理论框架。在应用集成的mPBPK-TMDD模型时应引起注意,因为确实存在可识别性问题,尤其是在无法进行丰富的研究设计时。

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