Modeling & Simulation Services

Fit-for-Purpose Modeling Unique to Your Project

We identify the right modeling approach and, working collaboratively, help groups answer many different types of questions specific for each project, such as:

  • How do I prioritize my experiments?
  • What are optimal drug properties?
  • What is the predicted efficacious dose for my therapeutic?
  • How do we differentiate our candidate from competitors?

Contact Us To Discuss Your Project

Fei Hua and model diagram

Understanding the Modeling Spectrum

Part of identifying the right approach for your project is knowing which type of model to use. While this chart is not comprehensive, and we fully understand different groups use different terminology, we hope to delineate the approaches in an understandable way. 


Classical PK/PD



Mechanistic PK/PD



Less complex




More complex

Ideal Application

Characterizing measured PK/PD data; interpolate PK/PD responses within dose range tested

To study the variability in drug exposure and response among individuals

Mechanistically predicting drug dynamics in blood and various organs by describing the physiological properties of the body and physical/chemical properties of the compound.

Focusing on drug PK and mechanism of action (MOA) of the drug. It can be used to tease out key parameters for drug with complex MOA; species and indication translation

Expanding from mechanistic PKPD to include disease biology. It can be used to investigate exposure-response relationship for many therapeutics, identify potential biomarkers, and understand variability in treatment responses

Quantitative Systems Pharmacology

Models are built on the principle that the effect of a therapeutic may not be the result of one specific interaction, but rather a network of interactions. In doing so, QSP bridges the gap between biology and pharmacology to arrive at a quantitative math model that characterizes the therapeutic pharmacology in the context of a complex biological system and disease processes with the complexity of the therapeutic mechanism of action (MOA). 

At Applied BioMath we use QSP to describe a comprehensive model that uses detailed descriptions of the underlying biological mechanisms paired with descriptive pharmacology of the drug mechanism of action. Note, however, we realize that one type of model does not fit all questions and timelines, therefore we develop fit-for-purpose QSP models as well as platform models. 

Quantitative Systems Pharmacology Summit

Applied BioMath is dedicated to fostering a community of industry and academic participants interested in applying computational biology and mathematical modeling approaches, including QSP,  to therapy research and development (R&D). Since 2015, we've held events in various forms in Cambridge, San Francisco, and virtually to bring together this community.

Join us at the Next QSP Summit!
October 13th-14th, 2021

Register and Learn More

Photo collage of QSP Summit throughout the years.

Platform/Disease Models

We consider disease or modality platform models a subset of QSP, as it takes on a wider platform approach to building the model. It may span a range of drugs and relevant questions, but most often focuses on a disease area or indication. This broadens the scope of scientific questions that can be asked of the model.

Within these comprehensive platforms, a range of therapeutics may be tested to combat the disease. Recently, the concept of platform modeling has also been used to consider drugs, themselves, as the platform. These are models meant to describe a large class of molecules—class centric therapeutic models. If time and budget allow, these more robust models can yield further answers with added confidence as they incorporate the system and implement a more encompassing model of the disease processes.

As part of our NIH grant, we developed a platform model describing the molecular mechanisms of plaque formation in AD as well as the mechanism of action for four anti-Aβ drugs, two b-site amyloid precursor protein cleaving enzyme (BACE) inhibitor drugs, and one g-secretase inhibitor.

Model Diagram

Lin et al (2019) ACoP10

Quantitative Systems Toxicology

Quantitative Systems Toxicology (QST) is an approach to quantitatively understand the mechanisms of toxic effects on a living organism through the integration of computational and experimental methods. Similar to QSP,  it uses systems biology to gain a quantitative understanding of how drugs modulate cellular systems at the molecular level, and how therapeutic/toxic effects integrate across multiple layers of biological complexity to impact human pathophysiology. QST models include drug pharmacokinetics, a cell/organ systems physiology model, mechanism of toxicity, toxicodynamic biomarkers, and a projection of an adverse drug reaction.

P. Bloomingdale, C. Housand, J. Apgar, B. Millard, D. Mager, J. Burke, D. Shah
Quantitative Systems Toxicology
Current Opinion in Toxicology, Volume 4, 2017, Pages 79-87, Article

QST model

Bloomingdale et al (2017). Current Opinion in Toxicology

Mechanistic PK/PD

Mechanistic or Semi-mechanistic PK/PD modeling is the addition of biophysics of the therapeutic MOA and relevant target biology to the classical PK/PD modeling. 

By incorporating biophysics, the model includes enough mechanism to describe the primary pharmacology of the drug in question and link it to key biomarkers. In this way, the model distinguishes between biological system-specific and drug-specific parameters, giving it improved extrapolation capabilities to more accurately predict drug efficacy and safety in humans further down the pipeline.

Unsure of how modeling could be used for your project?

Contact Us

Translational Modeling

The importance of selecting a safe starting dose for a first-in-human (FIH) trial cannot be overstated, but at the same time the dose must not be so low that escalation to therapeutic doses takes a prohibitively long time. To strike the right balance, accurate translations of the preclinical pharmacokinetic and pharmacodynamic data must be achieved. Empirical PK/PD modeling provides a foundation for selecting an appropriate FIH starting dose, and establishing a reasonable dose escalation scheme.  

In the meantime translational modeling based on mechanistic PK/PD modeling or QSP modeling tends to provide a more accurate translation taking into consideration of quantitative and mechanistic differences between preclinical species and human. This approach will also provide more robust support for human starting dose selection and efficacious dose prediction.

Classical PK/PD

Classical Pharmacokinetics/Pharmacodynamics (PK/PD) modeling is an empirical approach that relates drug concentration (pharmacokinetics) and drug effect (pharmacodynamics) based on observed data. The selection of mathematical expressions is driven by the observed data. The model is often used to provide simulations of new dose levels or dosing regimen between the doses with data available. Classical PK/PD can be used to compare two studies and ask, “what are the differences in drug exposure between the two studies?”

Although PK/PD modeling can provide an unambiguous answer to this question (e.g., group one had a greater drug exposure with a confidence of 95%),  it will not explain why the exposure was different  or which process was responsible for that difference. To obtain this greater understanding, PBPK modeling is used.

Physiologically Based Pharmacokinetic (PBPK) Models

Physiologically Based Pharmacokinetic (PBPK) models are an extension of the classical PK/PD model, putting them a step closer to mechanistic modeling. Built on a similar mathematical framework as PK models, PBPK models also incorporate known anatomy and physiology in the form of biochemistry and fluid dynamics. They are multicompartment models in which each compartment corresponds to a tissue or organ predefined by parameter values.

PBPK models provide a way to think about PK/PD in each compartment in the body and inter/intra fluid circulation while taking into account the route of administration of the drug. This grants PBPK models an enhanced capacity for extrapolation. PBPK models can range in complexity and incorporate only a few compartments (in a simple model) or many compartments (for a more complex model).

PBPK model diagram

Shah and Betts (2012). J Pharmacokinet Pharmacodynam

PBPK modeling does not provide further insight into the pharmacodynamics of a drugs, but instead focuses on the absorption, distribution, metabolism and excretion of a dug in every tissue of the body. The prediction of target distribution kinetics is possible for drugs with intracellular targets. Modeling of barriers between compartments is also possible.

Incorporating data on tissue structure, volume and composition make PBPK modeling a better approach to allometric scaling. It may take a longer time to develop due to the implementation of these numerous parameters. This robust method, although still constrained by simplified assumptions, is more computationally expensive than classical PK/PD modeling as it requires considerably more data for model development.

Population PK, PKPD, and Exposure Response Modeling

Population modeling approaches are a means to inform optimal dose and regimen selection. By characterizing the relationship between dose, exposure, and response, the effect of new doses and regimens that have not been studied clinically can be predicted and used to choose the most appropriate doses for further study.

Determining sources of variability in PK, PD, and response can also be achieved through population modeling. Patient characteristics (or covariates) like body weight, age, gender, ethnicity, kidney and liver function status, or disease state can affect exposure and response. Choosing a dose that maximizes response for all patients, or implementing dose adjustments in particular populations, is critical to the success of new drugs. Understanding how these characteristics impact PKPD and response is also important when bridging between different patient populations.  

Population modeling can also help overcome challenges in clinical trials involving pediatric patients from the selection of an appropriate dose in these patients to problems collecting sufficient samples to characterize PK and PD due to limitations in the blood volumes that can be withdrawn from these patients. 

Additionally, comprehensive covariate analysis conducted as part of a population modeling effort may even preclude the need to conduct dedicated clinical pharmacology studies. These analyses inform not only internal decision-making but also decisions by regulatory agencies, who have come to expect population modeling support to support decisions from early drug development through submission and beyond.

Exposure-response models developed in adults can then be used to link exposures in pediatrics to outcomes, with adjustments made for differences in disease pathophysiology in children compared to adults.  Tiered fixed and fixed dosing regimens can be explored, and optimal sampling methods can be applied to determine sparse sampling schemes that ensure appropriate information is obtained to characterize PKPD in children and adolescents. Regulatory agencies expect such analyses to support pediatric drug development, and internal decision-making can be improved by the use of such approaches.  

Clinical Trial Simulations

Clinical trial simulations can be used to compare the characteristics of different designs, and maximize the probability of success for a trial.  A model-based approach to sample size determination offers advantages over traditional power-based analyses by accounting for differences in patient characteristics between trials, disease progression, and nonlinear exposure-response relationships. The probability of false positive or false negative results associated with particular clinical trial designs can also be probed through simulation of population PK, PKPD, and ER models, and the risks of these outcomes can be minimized.  

The impact of increasing or decreasing the dose or frequency of administration and route of administration can be assessed. Doses, regimens, and sampling times can be chosen such that the information gleaned from the trial is maximized, facilitating better future trials. 

What Scientific Questions Are You Trying to Answer?

We'll put you in touch with the right person on our team. 

Contact Us