Research Interests

My research broadly involves modelling and analysing multiscale problems with applications in biology and industry.

On this page I give a few examples of my research.

Note that I haven't updated this page in several years. You can find a chronological list of my publications here, which is more likely to be kept up to date.

Synthetic biology

Synthetic biology concerns the engineering of biological systems for useful purposes. One example from my research is tissue engineering, where artificial body tissue is derived synthetically and used to repair or replace natural tissue. The general process of growing artificial tissue takes place within a bioreactor and involves transporting a nutrient-rich fluid to the tissue cells, which are placed within a porous scaffold to grow.

To model this process, is imperative to have knowledge of the fluid flow within a bioreactor, for two main reasons. Firstly, advection is the dominant nutrient transport mechanism in tissue engineering - a solely diffusive mechanism cannot penetrate far into larger tissues. Secondly, the growth of tissue cells is generally mechanosensitive, and a fluid flow induces a stress on these cells. Thus, understanding and being able to control the flow within a bioreactor is of paramount importance. In general, mathematically determining the fluid flow within these systems can be computationally expensive, especially in bioreactors where the tissue construct is free to move (in an effort to mix the depleting nutrient), yielding a moving boundary problem. I use a wide range of asymptotic methods to significantly reduce the computational effort required to determine the fluid flow in such systems for cylindrical porous scaffolds, exploiting the slender geometry of common bioreactors.

Another aspect of my synthetic biology research is carbon recycling through the metabolic engineering of microorganisms. In a typical set-up, a waste gas, such as carbon dioxide, is bubbled through a fluid containing genetically modified bacteria. The goal is for these bacteria to consume the gas and create useful chemicals, such as medicines or petroleum replacements. In a research laboratory, these systems are tested with an abundance of feed gas, with the goal of determining the viability of the microbial strain. However, the supply of nutrient is limited when these laboratory experiments are scaled up for industrial production. A key challenge is to determine how to effectively scale such experiments for industrial viability. I am interested in systematically deriving averaged (homogenized) equations for nutrient uptake over a colony of bacteria that account for the microscale uptake over individual bacteria. I am also interested in understanding how the metabolic processes within such bacteria can be most effectively modified in order to produce useful chemicals in a biosustainable manner.

Related publications:

On the boundary layer structure near a highly permeable porous interface
MP Dalwadi, SJ Chapman, SL Waters, and JM Oliver (2016)
J Fluid Mech, 798: pp 88-139 [link], [pdf]

Multi-timescale analysis in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine
MP Dalwadi, JR King, and NP Minton (2018)
J Math Biol, 77: pp 165-199 [link], [pdf]

The effect of weak inertia in rotating high-aspect-ratio vessel bioreactors
MP Dalwadi, SJ Chapman, JM Oliver, and SL Waters (2018)
J Fluid Mech, 835: pp 674-720 [link], [pdf]

Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway
MP Dalwadi, M Garavaglia, JP Webb, JR King, and NP Minton (2018)
J Theor Biol, 439: pp 39-49 [link], [pdf]

Upscaling diffusion through first-order volumetric sinks: a homogenization of bacterial nutrient uptake
MP Dalwadi, Y Wang, JR King, and NP Minton (2018)
SIAM J Appl Math, 78: pp 1300-1329 [link], [pdf]

An asymptotic analysis of the malonyl-CoA route to 3-hydroxypropionic acid in genetically engineered microbes
MP Dalwadi and JR King (2020)
Bull Math Biol, 82, 31 pages [link], [pdf]

A systematic upscaling of nonlinear chemical uptake within a biofilm
MP Dalwadi and JR King (2020)
SIAM J Appl Math, 80: pp 1723–1750 [link], [pdf]

Using singular perturbation theory to determine kinetic parameters in a non-standard coupled enzyme assay
MP Dalwadi, D Orol, F Walter, NP Minton, JR King, and K Kovács (2020)
J Math Biol, 81: pp 649–690 [link], [pdf]

Cleaning and decontamination

Filtration is a vital process in many industries, such as kidney dialysis, air purification, waste water treatment, and beer production. While the removal of contaminant occurs over the pore scale, it is incredibly computationally expensive to resolve models on this small scale over the much larger filter scale. I am interested in systematically deriving averaged (homogenized) equations for filtration that can be solved efficiently, but still account for the behaviour on the pore scale.

In addition, we are interested in modelling the decontamination of an oily toxic chemical agent by an aqueous cleanser within a porous medium. In such a scenario, it is very difficult to mix the two phases to enhance contaminant removal. I am interested in understanding how one should choose a cleanser for this clean-up process given characteristics of the toxic agent.

Related publications:

Understanding how porosity gradients can make a better filter using homogenization theory
MP Dalwadi, IM Griffiths, and M Bruna (2015)
Proc R Soc A, 471: 20150464 [link], [pdf]

A multiscale method to calculate filter blockage
MP Dalwadi, M Bruna, and IM Griffiths (2016)
J Fluid Mech, 809: pp 264-289 [link], [pdf]

Mathematical modeling of chemical agent removal by reaction with an immiscible cleanser
MP Dalwadi, D O'Kiely, SJ Thomson, TS Khaleque, and CL Hall (2017)
SIAM J Appl Math, 77: pp 1937-1961 [link], [pdf]

Optimising the flow through a concertinaed filtration membrane
VE Pereira, MP Dalwadi, E Ruiz-Trejo, and IM Griffiths (2021)
J Fluid Mech, 913, A28 [link], [pre-print]


Cryopreservation is the process of preserving biological entities by cooling to temperatures low enough to halt biochemical processes such as metabolism. This technology has a variety of uses, including fertility, tissue transplantation, food security, and the protection of endangered species. When cooling cells to preserve them during cryopreservation, cooling too quickly results in the formation of lethal intracellular ice, while cooling too slowly amplifies the toxic effects of the cryoprotective agents added to slow down ice formation. I am interested in understanding and quantifying these observations by modelling the cryopreservation process.

Related work:

A mathematical framework for developing freezing protocols in the cryopreservation of cells
MP Dalwadi, SL Waters, HM Byrne, and IJ Hewitt (2020)
SIAM J Appl Math, 80: pp 657-689 [link], [pdf]

Presentation at CRYO 2020

Beyond Boundaries 2020

Mathematical Institute Case Study

Microvascular flow

The endothelial glycocalyx is a porous coating found on the luminal surface of most blood vessels. While the macroscale details of the glycocalyx structure are fairly well known, its microscale structure is not. We are interested in understanding how differences in the microscale structure would affect the macroscale properties of plasma flow through the glycocalyx, and in using quantities observed on the macroscale to infer details about the microscale structure.

Related publications:

A mathematical model to determine the effect of a sub-glycocalyx space
MP Dalwadi, JR King, RJ Dyson, and KP Arkill (2020)
Phys Rev Fluids, 5: 043103, 24 pages [link], [pdf]