In-Silico Modelling of Tumour Growth DARIO PANADA [email protected] Supervised by Dr. Dawn Walker at The University of Sheffield
In-Silico Modellingof
Tumour GrowthDARIO PANADA
[email protected] 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?