Issues with virtual populations when applied to nonlinear QSP models


Quantitative systems pharmacology (QSP) models describe the clinical pharmacological properties of a drug.  They are typically described as systems of linear mass-balance and nonlinear mass-action of drugs.  One of the purposes of QSP models is to simulate potential outcomes from virtual clinical trials. This approach is predicated on generating virtual populations of patients (a virtual patient is a vector of parameter values).  Since most QSP models contains nonlinearities in the ODEs then the systems are only locally defined and the behaviour in unexplored regions of the parameter space remain unknown.  In this work we explore potential issues with generating virtual populations of patients.


QSP models of drug actions are essentially constructed of modules. There are two common modular constructs based on feedback mechanisms: (1) damping and (2) positive gain (amplification).  The damping modular systems are designed to maintain the system in homeostasis, e.g. glucose-insulin control. Drugs that perturb damping systems essentially overcome ability of the system to resist change.  Positive-gain systems are designed to amplify a signal to cause an event to occur that would otherwise not normally be needed or desirable, e.g. formation of a clot.  All systems should respond in a timely manner and return back to basal activity once complete.  We constructed two example simplified system modules, a damping module consisting of 3 states and 9 parameters and an amplification module consisting of 6 states and 13 parameters.   We generated 1000 virtual patients separately for each modules.  Only 2 parameters were randomly generated for each module (the remaining parameters were fixed at their original values.  The ability of the system to return back to basal conditions was evaluated for each virtual patient for both modules.


The original set of parameter values for the damping and amplification modules yielded appropriate response relationships in relation to a perturbation of the system.  In the damping case the system quickly overcame the effect of the perturbation and returned to basal activity. In the amplification setting the system quickly accelerated production of the reactive species and then returned to basal activity once the stimulus was exhausted.  When the virtual patients were generated and evaluated in the damping module, 25% yielded a post-perturbation basal activity was different from the starting activity (i.e. did not return to normal).   For the amplification module 10% did not rapidly accelerate production of the reactive species and also did not return to pre-perturbation basal activity.


Even simple nonlinear systems, as depicted in these two examples can produce implausible response outcomes when evaluating using virtual populations.   Generating virtual patients should be viewed with caution when evaluating and applying QSP models.