Using Model Reduction to Bridge the QSP-Pharmacometrics Divide

Using Model Reduction to Bridge the QSP-Pharmacometrics Divide

Quantitative systems pharmacology (QSP) models are generally too large to be validated or fit in a traditional sense and they can become intractable to standard methods of analysis or even to the modeler’s own intuition. Model reduction can alleviate these issues of complexity by eliminating portions of a system that have minimal effect upon the outputs or time-scales of interest. In this blog, I’ll discuss how this approach can yield simplified models that still provide accurate predictions.

What is quantitative systems pharmacology?

In short, quantitative systems pharmacology seeks to unify the computational modeling of drug disposition with detailed mechanistic descriptions of target-scale dynamics of drug action.

Traditional methods such as pharmacokinetic/pharmacodynamics (PK/PD or pharmacometric) models have their own advantages and disadvantages. Their strengths include their ability to be fit to real world data and often produce simple, highly predictive models. On the downside, they have limited mechanistic explanatory power.

On the other hand, systems biology methods tend to create highly mechanistic models that enable insight into how drug action occurs. But these models are typically too complex to match to data or intuitively understand.

Why invest in QSP?

Both business and scientific rationale have driven investment in QSP. First, complex, multifaceted diseases such as dementia, diabetes, and heart disease are on the rise. For example, the worldwide incidence of dementia is expected to double over the next 30 years. We need more complex and nuanced models to understand these diseases and develop new therapeutics.

In addition, traditional drug development approaches are proving increasingly expensive. “Erooms Law” shows an exponential decline in the number of drugs developed per billion dollars in research spending since the 1950s. So, we need novel approaches to drug development to revitalize pharma productivity.

Finally, we need a solution to the problem of Phase 2 attrition—the biggest cause of drug program failure over the last 20 years. Incomplete understanding of drug efficacy is a major source of these failures. Therefore, we need to better understand how efficacy emerges from complex biological systems. Because we don’t understand the consequences of perturbing these complex systems, we’re often not picking the right drug targets. QSP uses mathematical modeling and simulation to unravel the biology behind the systems we seek to manipulate.

What’s different about QSP from the perspective of modelers from different backgrounds?

Different types of scientists—systems biologists, pharmacometricians, and mathematical biologists—approach QSP from differing perspectives. For a systems biologist, the key difference is the introduction of drugs into the biological system. In terms of modeling, we’re adding on pharmacokinetics and ADME—the absorption, the distribution, the metabolism, and the excretion of the drugs.

For the pharmacometrician, QSP introduces complex, mechanistic descriptions of the target scale dynamics. This adds significant complexity compared to traditional pharmacometric modeling approaches.

And from my perspective as a mathematical biologist, QSP could just mean more differential equations. Large models that stitch together PK and systems biology.

But in fact, the key difference is that QSP models are controlled. We are attempting to control a diseased system by administering medication. To the mathematician’s mind, this would suggest that they use control theory.

Challenges in QSP modeling

Like any method, QSP models have their own challenges including:

  • Parameterization of very large models
  • Model validation: what to include in a complex model in terms of target scale dynamics and what to leave out
  • Model identifiability
  • Model complexity

By seeking to describe target scale dynamics systemically, QSP grapples with model complexity. Other fields such as engineering and computational physics have used model reduction to address this problem.

Defining Model Reduction

Model reduction is any method designed to give a system capable of satisfactorily reproducing the dynamical behavior of the original model (under some given metric of error) while reducing the number of species, reactions, or complexes.

Model reduction can simplify QSP models and get them to the scale of pharmacometric models. It can also decrease simulation time and ameliorate the problem of parameter identifiability.

The optimal reduction depends upon your specific research questions. Model reduction has the potential to bolster QSP, and I’ve personally found it to be a useful tool.

To learn more about how model reduction can help you get more out of your models, please watch a webinar I gave on this topic.

Tom Snowden

About the Author

Tom Snowden

Research Scientist, Certara

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Tom Snowden received his PhD in applied mathematics and quantitative systems pharmacology from the University of Reading in 2015. He was then awarded and completed an EPSRC doctoral prize fellowship at the university, continuing his research at the interface of mathematics and pharmacology. In October 2016, Tom joined Certara QSP as a research scientist working on a range of QSP consultancy projects.