In-Silico Modellingof

Tumour GrowthDARIO PANADA

dario.panada@postgrad.manchester.ac.ukSupervised by Dr. Dawn Walker at The University of

Sheffield

Introduction & Biological BackgroundA 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 growand 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)

About TumourCancer is responsible for dozens of thousands ofdeaths 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

Cancer as a Complex System There are different stages to cancer

1. Initiation – Cells slowly acquire highly proliferative phenotypes2. Vascular Growth – Regular Growth3. Avascular Growth –Irregular and unpredictable growth on site4. 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!

In-Vivo/Vitro Challenges & In-Silico SolutionsIn-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

conditionsPossibility 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

The Problem at HandCell 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 enhancedacidity might contribute to tumour growth and expansion

If this was the case, the Warburg Effect could form a target for therapies

Our MethodWe 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 possibleto 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

Our MethodGeneral Model Schedule Cancer Cell Agent Schedule

ResultsThe 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

ResultsGrowth with Enhanced Acidity Growth without Enhanced Acidity

Future Areas of ResearchImprove 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

Future Areas of Research

Questions?