A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling.

1. Mathematical Modelling
of Adaptive Therapy for
brain cancer
Name: Fatimah Al shehri
Reg.No: p126935
Supervisor’s Name: Dr.Mohd Almie bin Alias

2.  Introduction
 Problem Statement
 Research Question
 Research Objectives
 Literature Review
 Methodology
 Expected Results
 Gantt Chart
 References

3.  Cancer is a type of disease that can lead to death after a heart attack, The number of
deaths reached 10 million in the world in 2020.
 One of the main problems with cancer is that it is very invasive and disappear and come
back offer, which makes treatment difficult.
 Continuous therapy (CT) is a standard way of cancer treatment method involving consistent
drug dosages.
 Recently, Adaptive therapy (AT) has emerged as an innovative strategy, when treatment is
planned to stop when the cancer burden decreasing to specific value, and treatment restarts
when the burden returns to its initial point.

4. • While existing models often use (ODEs), this study propos advanced 1D and 2D continuous spatial
models with (PDEs) to capture spatial heterogeneity within cancer.
• Mathematical modles for (AT) are not a lot ,we need models condition under which situations (AT) is
better than (CT). Recent attempts to incorporate spatial distribution using 2D agent-based and hybrid
cellular automaton models have fallen short.
• lacking the ability to accurately represent the heterogeneity of drug nutrients, and other materials within a
tumor. There is a need for advanced modeling approaches that address these limitations and provide a
more realistic depiction of tumor dynamics
• Our problem statement focuses on developing 1D and 2D continuous spatial models using (PDEs),
specifically advection-reaction-diffusion equations.
• These equations will account for changes in drug-resistant cells, drug-sensitive cells, drug concentration,
and nutrient concentration within a tumor.This study will allow for a more accurate representation of the
effectiveness of (AT) over (CT)

5.  How can mathematical models be developed that provide continuous
representation and incorporate spatial variation in the distribution of
nutrients, drugs, and tumor cells?
 What are the methods that can be used to measure the effectiveness
of drug administration?
 How does competition between tumor cells modulate the relationship
between spatial variation in cell, nutrient and drug administrated
through (AT) and (CT)?
 What are the spatial conditions where (AT) can be more effective than
(CT)?

6.  To develop 1D and 2D continuous mathematical models with spatial variations in
the distribution of nutrient, drug, and tumor cells.
 To investigate the effects spatial variations (in the distribution of nutrients, drugs,
and tumor cells) on (i) time to progression of tumors and (ii) total drug doses
administered for both (CT) and (AT).
 To investigate how the nature and strength of competition between tumor cells
modulates the effects of spatial variations (in the distribution of nutrient, drug, and
tumor cells) on (i) time to progression of tumors and (ii) total drug doses
administered for both(AT) and (CT).
 To determine the spatial conditions where (AT) is more effective than (CT).

7.  Spatial variations in the distribution of tumor cells, nutrient and drug could affect
time to progression of tumor and total drug doses administered for both (AT) and
(CT).
 The nature and strength of tumor cell competition could change the effects of
spatial variations in the distribution of tumor cells, nutrient and drug on time to
progression of tumor and total drug doses administered for both (AT) and (CT).
 (AT) is more effective than (CT) when the competition between drug-resistant and
drug-sensitive cancer cells is increased by spatial variations in the distribution of
tumor cells, nutrient and drug.

8. Result
Topic
Researcher
Create 1D and 2D
continuous spatial modles
Areaction Diffusion model of cancer
invasion
Gatenby (1996)
Inability to represent the
heterogeneity of drug and...
2D Agent hybrid modles.
Anderson (1998)
A specific drug is
administrated to apatient can
affect the efficiency
Adaptive therapy
Frieden (2009)
This strategy offers anti-
cancer benefits and may
lessen drug resistance
Combination therapy in combating
cancer.
Mokhtari (2017)

9. Result
Topic
Researcher
Optimising cancer treatment
strategies
Recognise the spatial- temporal
complexities within the tumor is crucial
Norton (2019)
Influencing the efficacy of
(AT) and (CT)
The spatial distributation of cancer cells,...
Wang (2022)

10. • Development of general-Dimensional models
General methods
A continuous
Mathematical
models
(PDEs)

11. • Solving a 1D mathematical model:
Rewritten in one
dimension or not
Analytically and
numerically

12. • Solving 2D mathematical model
Numerical Finite difference
method
The general
Dimensional
Mathematical models

13.  Mathematical Model Development:
 Development 1D and 2D continuous spatial models based on (PDEs) for advection-reaction-diffusion
equations, account spatial variations in drug-resistant cells, drug-sensitive cells, drug concentration, and
nutrient concentration within tumors.
 Also, develop 1D and 2D continuous spatial models using PDEs to represent the heterogeneity of materials
within tumors.
 We need advanced modelling approaches that address these limitations.
 Provide a more realistic depiction of tumor dynamics.
 This study will allow for a more accurate representation of the effectiveness (AT) over (CT).
 Compare the result with output from experimental studies obtained from the reported tumor volume.
 We will also compare our output with those of the discrete models hybirid discrete models and ODEs.
 By altering parameter values obtained through estimation based methods, one can achieve the effects of
spatial variations in tumor cells, nutrients, and drugs.
 Incorporate (AT) for brain cancer and benefit MRI data contributes to the development of treatment
strategies for brain cancer.

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