1. In-Silico Modelling
of
Tumour Growth
DARIO PANADA
dario.panada@postgrad.manchester.ac.uk
Supervised by Dr. Dawn Walker at The University of Sheffield

2. Introduction & Biological Background
A cell is the smallest unit capable of reproducing independently
 They are sometimes referred to as the “building block of life”
Complex organisms – including us humans – are made up of trillions of cells
 In multicellular organisms cells specialize to better perform specific functions (Eg: Neurons, Immune Cells, Gametes)
 Hence, it is necessary for cells to coordinate, successful functioning of organisms is dependent upon cells
doing the right thing at the right time
Tissues and organs are made up by cells. In order for them to grow
and repair it is necessary that cells undergo division
 Cellular division, mitosis, results in the formation of two identical daughter
cells
 The cell-cycle illustrates the growth of a cell, ultimately leading to
division or death
 Cell division is a highly regulated phenomenon to ensure that there is
always exactly the needed number of cells
But, things don’t always go according to plans
 Unregulated cell duplication leads to resource depletion and ultimately
organ failure
 When a sufficiently large number of cells is undergoing unregulated division
we identify a tumour mass (cancer)

3. About Tumour
Cancer is responsible for dozens of thousands of
deaths each year
Causes of tumour aren’t fully understood yet
 Genetic predisposition
 Environmental/Lifestyle factors
Cancer cells
 Physically invade healthy tissues
 Block contact with blood vessels, diffusion of
nutrients and absorption of waste products,
hence starving healthy cells
 Can spread to other sites (metastasis)
 Ultimately cause key organs (Eg: Heart, Kidneys)
to fail resulting in the patient’s death
There is no definitive cure for cancer
 Existing therapies are invasive, meaning that they also affect healthy tissues and negatively impact on health
 Even in cases where the original tumour is successfully removed, there is a risk of relapse due to malignant cells having
spread to other sites or survived therapy

4. Cancer as a Complex System
 There are different stages to cancer
1. Initiation – Cells slowly acquire highly proliferative phenotypes
2. Vascular Growth – Regular Growth
3. Avascular Growth –Irregular and unpredictable growth on site
4. Metastasis – Tumour spreads to various parts of the body, nearly impossible to cure
 Therapies focus on preventing cancer from reaching stage 4
 Furthermore, tumour growth relies on multiple intercellular and intracellular processes and mechanisms
 Over-expression/Under-expression of specific genes
 Failure of the immune system to identify tumour antigens
 Ability to promote vessel growth (Angiogenesis)
 Successful targeting of any of these can form a viable therapy!

5. In-Vivo/Vitro Challenges & In-Silico Solutions
In-Vivo/Vitro Challenge In-Silico Solution
It’s hard to isolate tumours, measurements are often
approximate
Exact measurements, possibility to ‘look’ at tumour in high
definition and from multiple perspectives
Tumours behave differently in petri-dishes and animals than
they do in humans
Possibility of replicating tumour microenvironment/niche that
would be found in humans
Tests affect the end-results (Eg: To sample the inner section of
the tumour we have to break its outer membrane)
Tests do not affect the end-results
Each experiment only tells us about one behaviour of cancer
cells. Cancer cells can have different behaviours in different
conditions
Possibility of repeating experiments under different
conditions with no or minimal additional setup
Wetware experiments have large operation costs
Minimal operation costs, simulations can often run on normal
laptops

6. The Problem at Hand
Cell metabolism is the process whereby cells extract energy from nutrients
Healthy cells perform aerobic respiration
 A chemical reaction with converts sugars (Eg: Glucose) and Oxygen into energy available for cellular processes
 Carbon dioxide is a by-product of the reaction. It is absorbed in the blood and released in the lungs from where
it is then expelled
Cancer cells perform anaerobic respiration
 This is similar to its aerobic counterpart, but instead of carbon dioxide it produces H+ positive ions
 These cannot be absorbed by the blood as easily, and have the effect of lowering the pH of the tumour
microenvironment. That is, they make the local environment more acid
 In addition, anaerobic respiration also produces several molecules useful for cell division
This is known as the Warburg Effect
Cancer cells are more resistant to acid than healthy tissues, it has therefore been hypothesized that enhanced
acidity might contribute to tumour growth and expansion
If this was the case, the Warburg Effect could form a target for therapies

7. Our Method
We propose a model to simulate tumour growth in the presence and absence of enhanced acidity
We propose that by comparing average growth curves under these two conditions it will be possible
to infer the extent to which enhanced acidity contributes to tumour growth
Our model represents a tissue seeing the beginning of tumour vascular growth
 Space is discretized as a 2D grid, each cell represents a space of 40μmx40μm, approximately the space occupied by 10
cells
 Time is discretized as time-steps, where each time-step corresponds to two hours, approximately the length of the
shortest process in the cell-life cycle
Our model takes the form of a discrete agent-based model
 Each individual cell is an agent
 At each time-step, each agent independently makes a decision on what to do next. This decision is based on its current
state (intra-cellular factors) and on its local environment (extra-cellular factors)
 Possible actions include preparing for division, dividing, migrating, etc.
 All cells are updated simultaneously (synchronous updating)
 We use glucose to represent all resources, we assume constant concentration throughout the tissue
 In parallel, diffusion of positive ions is also simulated

8. Our Method
General Model Schedule Cancer Cell Agent Schedule

9. Results
The model was initially seeded with a small core
of cancer cells surrounded by healthy tissues
pH was set at a neutral 7.5 across the tissue
We allowed the simulation to progress for 200
time-steps, approximately equivalent to 2.5
weeks
At each time-step, we recorded the number of
cancer cells in the simulation, results were
averaged across 10 trials
We used polynomial regression to fit the
average growth curves
We used a t-test to compare polynomial
coefficients
Results suggest that the two rates of growth are
not statistically different
Error bars show standard error

10. Results
Growth with Enhanced Acidity Growth without Enhanced Acidity

11. Future Areas of Research
Improve the diffusion model
Include additional intra-cellular and inter-cellular processes
Progress model beyond 2.5 weeks including phenomena such as angiogenesis and metastasis
Include additional properties of the tumour micro-environment

12. Future Areas of Research
Questions?