Division of Mathematics University of Dundee Dundee DD1 4HN Scotland 31 October 2014 Professor S

Division of Mathematics University of Dundee Dundee DD1 4HN Scotland 31 October 2014

Professor Sławomir Zadrożny, Ph.D., D.Sc.

iBS PAN,

Systems Research Institute, Polish Academy of Sciences, Newelska 6,

01-447 Warszawa, Poland

Dear Professor Zadrożny,

Doctoral dissertation: Mr. Maciej Cytowski, M.Sc.

Large Scale Computational Modelling of Cellular Biosystems

It is a pleasure to provide a report concerning the above PhD thesis. My report is overleaf. If you require any further information from me at this point, please do not hesitate to contact me.

Yours sincerely,

Professor Mark Chaplain, FRSE

Ivory Chair of Applied Mathematics

Mr. Maciej Cytowski, M.Sc.: Ph.D. Thesis

Large Scale Computational Modelling of Cellular Biosystems General Overview

This thesis presents the results of research carried out by Mr. Maciej Cytowski at the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, under the supervision of Professor Marek Niezgódka with auxiliary supervison by Dr. Zuzanna Szymańska.

The main work of the thesis is the development of a novel large scale computational model that can simulate the growth of colonies of cells in a 3-dimensional spatial domain. The model is multi-scale and through the use of high-performance computing and parallel processing, simulations of colonies of up to 10

cells are achieved.

The multiscale nature of the model allows for connections between three important biological scales of interest: the intra-cellular, the cellular and the tissue. The simulations presented in the thesis are capable of simulating a colony of cells up to around 1cm in diameter. At this scale, such colonies are palpable and the model has the potential to be of prognostic value to clinicians interested in a range of pathological situations e.g. cancer, wound healing.

This thesis is an original piece of work and contains novel and original research with very interesting and widely applicable results. It clearly satisfies the crtieria for a Ph.D. thesis.

The thesis begins with an overview in the Introduction chapter. In chapter 2, an overview of the previous mathematical modelling in this area is given followed by an overview of the state-of-the-art in HPC in chapter 3. In chapter 4 the modelling framework is described and then in chapter 5 the main computational simulation results are presented for generic growing cell colonies. In chapter 6 a specific application is made to the growth of a 3-dimensional solid tumour. Conclusions and future work are presented in the final Chapter 7.

Detailed comments:

The Introduction chapter is appropriate and clearly describes the aims and the content of the thesis.

Chapter 2, “Mathematical Modelling Background”, gives a comprehensive summary of previous work in the area and covers work on continuum-level modelling, discrete- level modelling and hybrid modelling. All relevant previous work is appropriately cited.

In chapter 3, “High Performance Computing: State of the art”, an overview of the current capability of HPC is given.

Chapter 4, “The Framework: Generic Model of Cellular Biosystems”, describes the

general multiscale mathematical model of growing cell colonies. The approach is a

force-based lattice-free model of interacting cells. Intra-cellular dynamics are

accounted for by modelling a basic four-phase cell-cycle (M-phase, G1-phase, S- phase, G2-phase). Interactions between individual cells are modelled using a modified Hertz model which accounts for the forces of attraction and repulsion between cells.

Finally external fields, such as oxygen or other nutrients, are modelled using nonlinear partial differential equations.

In chapter 5, “Main Results”, the computational simulation results are presented, preceded by a description of the computational algorithms used to obtain both high accuracy and efficient parallelization and high scalability. The results are very impressive.

In chapter 6, “Reference applications”, the general model is applied to the growth of a 3-dimensional solid tumour in normal tissue. Initial simulations focus on examining the effect of the cell-cycle time and the cell-cell adhesion forces. The final set of simulations examines the growth of the solid tumour with an external nutrient field of oxygen. This enables the modelling of the development of a quiescent region in the solid tumour and a necrotic core. The results of this chapter are novel and very exciting. For the first time, an individual-based model of cell interactions can simulate interactions at the tissue-scale. This has enormous potential for future development and genuine quantitative, predictive modelling of cancer growth, wound healing and embryogenesis.

The final chapter 7 provides a summary of the original work in the thesis and gives details of possible future developments. The references cited are entirely appropriate and satisfactory.

Summary:

The thesis of Mr. Maciej Cytowski is an original piece of work which contains novel scientific results. It is very well-written. The author has demonstrated a sound knowledge of previous work in the area and cited the relevant literature. The work of the thesis has taken multiscale mathematical modelling of cellular systems to a completely new level and has indicated several fruitful avenues for future work.

Therefore, it meets the criteria for an original piece of research that are specified in the Law of March 13

2003 concerning scientific degrees.

In conclusion, I can state that in my professional opinion the draft thesis of Mr.

Maciej Cytowski that I have reviewed above satisfies the criteria for a Ph.D. thesis and deserves to be awarded.

31.X.14