Applying mathematics to 3Rs problems

Mathematical modelling is an important tool for solving biological questions and providing new insights that can benefit science and medicine. These models provide the opportunity to vary the experimental parameters involved and to predict what effects different parameters will have on the system.

We have used different approaches to link mathematicians and biologists to provide new ways of reducing the use of animals in research and development:

Increasing investment in mathematical modelling in toxicology

We have invested £750k in a strategic funding call to address mathematical challenges which develop new, or apply exisiting mathematical models to toxicology research and safety testing with the aim of:

  • Providing more scientifically relevant information for human and environmental safety assessment.
  • Reducing reliance on animals.

The call was co-funded by the EPSRC. 

Four awards were made in October 2012. 

Supporting collaboration between mathematical modellers and biologists

Maths study groups bring together mathematicians and academic and industrial researchers working within the life sciences.  The biologists present research problems to a group of mathematicians who then brainstorm the problem during a week long study group.  This focussed approach very quickly leads to new insights to the research problems that can benefit science and the 3Rs.

2013 Maths Study Group

Working with the EPSRC-funded Maths in Medicine Study Group, we hosted the first NC3Rs Maths Study Group to solve biological problems or questions which if addressed could help to replace or reduce the use of animals. 

Four problems were presented:

  • Mathematical modelling of steroid responsiveness in severe asthma and COPD - workshop report
    Prof Ian Adcock, Imperial College London 
  • Modelling heart rate changes in the mouse as a system of delayed, weakly coupled oscillators - workshop report
    Dr Mark Christie, King's College London
  • Using mathematical modelling to optimise work flow in the Sanger Mouse Genetics Project  - workshop report
    Dr Chris Lelliott, Wellcome Trust Sanger Institute
  • Mathematical modelling of chronic drug infusion for toxicity assessment - workshop report
    Dr Dominic Williams, University of Liverpool

A blog entitled ‘The power of modelling: using maths to reduce animal experiments’ describes the week.

2014 Maths Study Group

Working with the EPSRC-funded POEMS Network (Predictive mOdelling for hEalthcare technology through MathS), and supported by the Turing Gateway to Mathematics, we hosted a study group where the focus was on solving medicine and healthcare problems to advance the 3Rs.

Five problems were presented:

​Mathematical modelling and open innovation

We are also demonstrating the utility of mathematical modelling in our CRACK IT open innovation platform through the IVIVE and Virtual Infectious Disease Research Challenges, both of which require considerable modelling to solve.

Accelerating acceptance of mathematical modelling in efficacy and safety decision making

Working with the international Health and Environmental Sciences Institute (HESI) we hosted a two day workshop in September 2016 to explore the challenges and opportunities in accelerating acceptance of evidence provided from mathematical models to improve the predictivity of efficacy and safety testing for drugs and chemicals. 

The meeting brought together more than 80 scientists and regulators from across sectors and disciplines to:

  • Highlight capabilities and opportunities in mathematical modelling in the biosciences;
  • Hear from other industry sectors as to how mathematical modelling supports their decision making;
  • Connect life scientists with mathematicians to encourage collaboration in model development;
  • Define a future landscape for supporting the acceptance of mathematical modelling in safety and efficacy decision making.

The meeting agenda, with links to the speaker presentations, can be downloaded below. Posters from the workshop can also be downloaded below.


Back to the top

Chernyavsky IL et al (2014) The Role of Inflammation Resolution Speed in Airway Smooth Muscle Mass Accumulation in Asthma: Insight from a Theoretical Model. PLOS One 9: e90162 doi:10.1371/journal.pone.0090162

Back to top
Office-led project



NC3Rs Scientist

Dr Anthony Holmes

Primary 'R'



Mathematical and computer modelling