• Hybrid modeling
• colorectal cancer
• lung cancer

Cancer is a multi-scale disease and its overwhelming complexity depends upon the multiple
interwind events occurring at both molecular and cellular levels, making it very difficult
for therapeutic advancements in cancer research. The resistance to cancer drugs is a
significant challenge faced by scientists nowadays. The roots of the problem reside not
only at the molecular level, due to multiple type of mutations in a single tumor, but also
at the cellular level of drug interactions with the tumor. Tumor heterogeneity is the term
used by oncologists for the involvement of multiple mutations in the development of a
tumor at the sub-cellular level. The mechanisms for tumor heterogeneity are rigorously
being explored as a reason for drug resistance in cancer patients. It is important to observe
cell interactions not only at intra-tumoral level, but it is also essential to study the drug
and tumor cell interactions at cellular level to have a complete picture of the mechanisms
underlying drug resistance.
The multi-scale nature of cancer drug resistance problem require modeling approaches
that can capture all the multiple sub-cellular and cellular interaction factors with respect to
dierent scales for time and space. Hybrid modeling offers a way to integrate both discrete
and continuous dynamics to overcome this challenge. This research work is focused on the
development of hybrid models to understand the drug resistance behaviors in colorectal
and lung cancers. The common thing about the two types of cancer is that they both have
dierent mutations at epidermal growth factor receptors (EGFRs) and they are normally
treated with anti-EGFR drugs, to which they develop resistances with the passage of time.
The acquiring of resistance is the sign of relapse in both kind of tumors.
The most challenging task in colorectal cancer research nowadays is to understand the
development of acquired resistance to anti-EGFR drugs. The key reason for this problem is
the KRAS mutations appearance after the treatment with monoclonal antibodies (moAb).
A hybrid model is proposed for the analysis of KRAS mutations behavior in colorectal
cancer with respect to moAb treatments. The colorectal tumor hybrid model is represented
as a single state automata, which shows tumor progression and evolution by means of
mathematical equations for tumor sub-populations, immune system components and drugs
for the treatment. The drug introduction is managed as a discrete step in this model.
To evaluate the drug performance on a tumor, equations for two types of tumors cells
are developed, i.e KRAS mutated and KRAS wild-type. Both tumor cell populations
were treated with a combination of moAb and chemotherapy drugs. It is observed that
even a minimal initial concentration of KRAS mutated cells before the treatment has the ability to make the tumor refractory to the treatment. Moreover, a small population of
KRAS mutated cells has a strong influence on a large number of wild-type cells by making
them resistant to chemotherapy. Patient's immune responses are specifically taken into
considerations and it is found that, in case of KRAS mutations, the immune strength does
not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy)
drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated
cells. Results show that this combined treatment could be only effective for patients with
high immune strengths and it should not be recommended as first-line therapy for patients
with moderate immune strengths or weak immune systems because of a potential risk of
relapse, with KRAS mutant cells acquired resistance involved with them.
Lung cancer is more complicated then colorectal cancer because of acquiring of multiple
resistances to anti-EGFR drugs. The appearance of EGFR T790M and KRAS mutations
makes tumor resistant to a geftinib and AZD9291 drugs, respectively. The hybrid model for
lung cancer consists of two non-resistant and resistant states of tumor. The non-resistant
state is treated with geftinib drug until resistance to this drug makes tumor regrowth
leading towards the resistant state. The resistant state is treated with AZD9291 drug for
recovery. In this model the complete resistant state due to KRAS mutations is ignored
because of the unavailability of parameter information and patient data. Each tumor state
is evaluated by mathematical differential equations for tumor growth and progression. The
tumor model consists of four tumor sub-population equations depending upon the type
of mutations. The drug administration in this model is also managed as a discrete step
for exact scheduling and dosages. The parameter values for the model are obtained by
experiments performed in the laboratory. The experimental data is only available for
the tumor progression along with the geftinib drug. The model is then fine tuned for
obtaining the exact tumor growth patterns as observed in clinic, only for the geftinib
drug. The growth rate for EGFR T790M tumor sub-population is changed to obtain the
same tumor progression patterns as observed in real patients. The growth rate of mutations
largely depends upon the immune system strength and by manipulating the growth rates
for different tumor populations, it is possible to capture the factor of immune strength of
the patient. The fine tuned model is then used to analyze the effect of AZD9291 drug
on geftinib resistant state of the tumor. It is observed that AZD9291 could be the best
candidate for the treatment of the EGFR T790M tumor sub-population.
Hybrid modeling helps to understand the tumor drug resistance along with tumor
progression due to multiple mutations, in a more realistic way and it also provides a way
for personalized therapy by managing the drug administration in a strict pattern that
avoid the growth of resistant sub-populations as well as target other populations at the
same time. The only key to avoid relapse in cancer is the personalized therapy and the
proposed hybrid models promises to do that.