The Modeling and Simulation group at Novartis provides a wide range of services to researchers, including simulating biological systems using mathematical models to prioritize and select drug candidates and recommend dosage for clinical studies.

“We use models to make predictions in humans when we cannot do a direct measurement,” says Anna Georgieva, senior scientist at Novartis. “This is a way to incorporate existing data and guide clinical trials.”

The models typically include a set of known parameters, such as tissue volume and blood flow rate, and an unknown set, such as rate of absorption and partition coefficients. For Novartis, getting useful results depends on developing accurate models, finding values for unknown parameters, and estimating their uncertainty.

To accomplish their goals, the group required a flexible, integrated modeling environment to enable rapid simulation, optimization, and statistical analysis. This environment had to provide easy access to a wide range of capabilities, including tools for symbolic math and ordinary differential equations.

Novartis uses MATLAB^® and Simulink^® to create physiologically based pharmacokinetic (PBPK) models that describe the uptake and distribution of a drug given to animal species or humans over time.

They create these PBPK models using a system of ordinary differential equations, with an associated set of variables and parameters.

“For solving our systems of ordinary differential equations, the algorithms in MATLAB are more robust than other software packages I’ve used,” explains Stoll, who adds that Simulink simplifies the model development process and facilitates collaboration. “With Simulink, you can graphically organize the organs of the body physiologically. This makes it easier to explain what we’ve done to someone with expertise in biology.”

Finding values for the unknown parameters in PBPK models is a three-step process. First, the team generates predictions from the models using educated guesses for the unknown parameters. Next, they use Global Optimization Toolbox and Optimization Toolbox™ to compare those predictions to experimentally measured data and find the best values for the parameters that describe the data. Once they find the best parameter values, they use Statistics and Machine Learning Toolbox™ to conduct parameter positivity and uncertainty analyses.

The Novartis team sees the role of MathWorks tools in the drug development process potentially expanding over the next few years.

“We have support for the integration of computational modeling into various aspects of the drug development process,” Stoll says. “The adaptability and versatility of MathWorks products are a definite advantage. These products enable us to address a wide range of challenges as they arise.”