Literature Review
HI Freedman, G Belostki – “Perturbed models for cancer treatment by radiotherapy”
http://link.springer.com/content/pdf/10.1007%2Fs12591-009-0009-7.pdf
This article produces a model of radiation therapy where both healthy cells and cancerous
cells are affected by it.
They then take into account the fact that only a small number of healthy cells are going
to be affected by the radiation, and they use a little epsilon for that. This is their final model.
ηi(t, x1, x2) ≥ 0, i = 1, 2, are the controls due to radiation. Then, they give four options
for the control mechanisms right after that. One of them is a periodic step function, which
I am interested in using in my models. Next, they go into a lot of perturbation stuff. They compute
equilibria and stability for several different values plugged in for their constants.
HI Freedman, G Belostki – “Perturbed models for cancer treatment by radiotherapy”
http://ijpam.eu/contents/2005-25-4/3/3.pdf
The paper presents a model of radiation treatment for cancer where it doesn’t affect the
healthy cancer cells.
This was the building block of the previous reference. They make a no treatment
hypothesis: that in the absence of treatment, the cancer cells always win the competition with
normal cells. Then they have four control methods that that use for the radiation. They analyze
the equilibria for stability, and then they do it when they plug in hypothetical, realistic values for
their constant parameters. They do it for each control method.
Usman A, Cunningham C, Jackson T – “Application of the Mathematical Model of Tumor- Immune
Interactions for IL-2 Adoptive Immunotherapy to Studies on Patients with Metastatic Melanoma
or Renal Cell Cancer”
http://www.rose-hulman.edu/mathjournal/archives/2005/vol6-n2/paper9/v6n2-9pd.pdf
This article focuses on developing models to describe immunotherapy on a tumor. It
summarizes cancer, its causes, treatments, and assumptions of models (including the mitotic
clock hypothesis), focusing on immunotherapy mostly. The model takes into consideration:



Effector Cells – T-Lymphocytes. Cells that provide immunological functions when
activated by specific antigens.
Tumor Cells – “self” cells so they go undetected by the immune system, until they start
producing antigens that the immune system does recognize.
o Antigenicity – the measure of how different the tumor has become from self,
which increases the immune response.
Cytokines – protein cell-mediators that contribute to immunity and more. There are many
types, but the important one here is the Interleukins. These are activated by the TLymphocytes and fight the tumor.
The original model that they used is the Kirschner model, which uses the same three parameters.
The article describes the limitations and assumptions of that model. This model attempts to
remove the assumption that treatment doesn’t depend on any parameters that change over
time, and allows for the treatment to be abruptly stopped if side effects become too severe.
Isaeva OG, Osipov VA – “Different strategies for cancer treatment: Mathematical modelling”
http://arxiv.org/ftp/q-bio/papers/0605/0605046.pdf
This article models immune response to a tumor with immunotherapy, chemotherapy,
and vaccine treatment. They describe how the immune system affects tumor growth and how it
is important to incorporate the immune response into mathematical models. A history of
modeling immunotherapy and chemotherapy is given. Their model includes five populations:
tumor cells (T), CTL (L), Interleukin-2 (I2), chemo drug (C), and IFN- (I).
They then give their parameters for all the constants in their model, and they analyze
their models. They do chemo alone, immunotherapy alone, both sequentially, both concurrently,
and vaccine therapy alone. Then, they discussed which worked best. It was sequential
chemo/immunotherapy.
Mamat M, Subiyanto, Kartono A – “Mathematical Model of Cancer Treatments Using
Immunotherapy, Chemotherapy, and Biochemotherapy”
http://www.m-hikari.com/ams/ams-2013/ams-5-8-2013/mamatAMS5-8-2013-2.pdf
This article creates a mathematical model for the treatment of cancer with
chemotherapy, immunotherapy, and a combination of the two. It gives information about cancer,
treatments, and statistics. Descriptions of immunotherapy, chemotherapy, and
biochemotherapy are given. Their model is based on the de Pillis’s model and the Isaeva and
Osiopov’s model, which they cite. They give a long list of assumptions, and their model is:
Next, they describe terms and describe parameters for all the constants, which is a good
idea. There are four cell population and three drug concentration differential equations, so seven
total. They use Natural Killer cells, CD8+ T-cells, tumor cells, INF-, and more. Then, they graph
the model for hypothetical patients, which is very interesting.
Anand P, Kunnumakara AB, Sundaram C, Karikumar KB, Tharakan ST, Lai OS, Sung B, Abbarwal
BB – “Cancer is a Preventable Disease that Requires Major Lifestyle Changes”
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2515569/pdf/11095_2008_Article_9661.pdf
The article states that the majority of diseases, including cancer, come not from our genes
but from our lifestyle and environment. Cancer is caused by both internal factors like inherited
mutations, hormones, and immune conditions and external factors like tobacco, diet, radiation,
and infectious diseases. They say only 5-10% of cancer cases are a result of inherited gene
defects. It discusses the prevention of cancer.
This article has lots great statistics and several useful references.
Castellucci L – “Proton Therapy Faces High Hurdles to General Use”
http://jnci.oxfordjournals.org/content/90/23/1768.full.pdf
Proton therapy means shooting high-energy charges particles into the body, and it offers
more specificity and fewer side effects than radiation therapy. It has been in use since 1954, but
there are still very few proton therapy treatment clinics in the United States.
The goal of proton therapy (and all types of radiation therapy) is to deliver as much of the
radiation dose to the tumor and not the surrounding healthy cells. Radiation uses X-rays whose
beams travel straight through the body, depositing energy as they travel. There’s lots of
information about how radiation works.
Proton therapy proton beams have mass and are positively charged, causing them to act
completely differently from radiation. Because they have mass, they only penetrate a specific
distance into the body, which can be calculated. Unlike radiation where the largest dose is at the
surface, the maximum dosage can hit the tumor itself, which harms healthy cells less.
Lin R, Slater JD, Yonemoto LT, Grove RI, Telchman SL, Watt DK, Slater JM – “Nasopharyngeal
Carcinoma: Repeat Treatment with Conformal Proton Therapy – Dose-volume Histogram
Analysis”
http://radiology.rsna.org/content/213/2/489.short
The article discusses recurrent nasopharyngeal carcinoma, which is in the nasal cavity.
Radiation is inefficient because there are delicate structures around the nose, whose tissues do
not need to be hit with large doses of radiation. Proton-beam radiation allows for a higher dose
of radiation at the tumor and less in surrounding tissues. The Bragg peak of protons is farther
into the tissue than the Bragg peak of radiation.
Sixteen patients were treated with proton therapy for this recurring tumor. 50% survived. When
the tumor was close to critical structures, it was difficult for the dose to cover the entire tumor if
the dose to surrounding structures is to be kept the same. They give suggestions for how to fix
this, which could be combination methods that we use in our treatments that we model.
Miller AB, Hoogstraten B, Staquet M, Winkler A – “Reporting Results of Cancer Treatment”
http://onlinelibrary.wiley.com/store/10.1002/1097-0142(19810101)47:1%3C207::AIDCNCR2820470134%3E3.0.CO;26/asset/2820470134_ftp.pdf?v=1&t=hhzmk6m2&s=77f23ae37098525ca03ba22469131626ca9
b86a4
The article is a summary of what and how to report the results of treating a patient with
cancer. It has a lot of useful cancer-related terminology. It gives treatment information that
should be included, which we could use to drive our model. These could be possible variations of
our model or parameters we should consider. They also discuss reporting toxicity, response, and
recurrence.
Werner E – “Cancer Networks – A general theoretical and computational framework for
understanding cancer”
http://arxiv.org/pdf/1110.5865.pdf
The article proposes a new paradigm for describing cancer growth, with these cancerous
developmental control networks. He proposes that a pathological developmental control
network causes cancer, and to understand how cancer works, we have to understand the
networks that cause it. Mutations in developmental networks cause cancer, and cancer isn't
merely uncontrolled growth, but a highly regulated process controlled by developmental
networks.
Werner describes linear, exponential, and geometric cancer networks. He discusses a few
specific types of cancers to which these networks may apply. He describes signaling and
stochastic networks.
Chen W, Unkelback J, Trofimov A, Madden T, Kooy H, Bortfeld A, Craft D – “Including Robustness
in Multi-criteria Optimization for Intensity Modulated Proton Therapy”
http://iopscience.iop.org/0031-9155/57/3/591/pdf/0031-9155_57_3_591.pdf
The article gives and introduction to radiation. It says that intensity modulated proton
therapy (IMPT) comes closest to delivering a high dose of radiation to the tumor while sparing
surrounding organs. IMPT is more sensitive to error than IMRT because there is such a large
dosage delivered at the very end of the beam (late Bragg peak). They then discuss some other
factors that come into play when optimizing the beam. Then, they go into detail about it.
Evan GI, Vousden KH – “Proliferation, cell cycle, and apoptosis in cancer”
http://www.nature.com/nature/journal/v411/n6835/pdf/411342a0.pdf
The article discusses how diverse different types of cancers are and how it seems that
there can’t be one overall cure, but that treatment must be as diverse as the types of cancer. But
then it argues that there are underlying characteristics that unify all types of cancer. They argue
that research should be conducted to find a therapy that targets these similar points of cancer.
Then it discusses how cancer develops and that it’s only after anti-tumor mechanisms fail to stop
the cancer from spreading and developing. They say that cancers vary, but they all share the
common ability to grow beyond what limits normal cells and have suppressed apoptosis.
The cell only grows when it receives appropriate mitogenic signals. Mitogens are social
cues that allow cells to divide and reproduce only in a specific social context. They then discuss
other factors that limit cell growth. It describes cancer in terms of abnormal proliferation. It says
that some cancers may have mutated in a way that makes mitogenic signals unnecessary, that
they are not needed to give an okay for division. They say that inhibition of differentiation may
also be a contributing factor to cancer.
Apoptosis is caused by caspases, which are series of cysteine aspartyl proteases that
cleave a various intracellular substrates that trigger cell dissolution and cause cell death. Halting
these processes are important to cancer. The two most important targets for cancer therapy are
deregulated proliferation and inhibition of apoptosis.
HI Freedman and STR Pinho – “Stability criteria for the cure state in a cancer model with radiation
treatment”
http://ac.els-cdn.com/S146812180800179X/1-s2.0-S146812180800179Xmain.pdf?_tid=486cb950-d758-11e2-a5d500000aab0f27&acdnat=1371478675_6c8072adc230f995abd948dad2971c82
The article describes a system of differential equations that they created to model
treatment by radiation. They say radiation destroys cells by breaking their chromosomes, so they
can’t reproduce and will die off. Their model accounts for tumor cells and healthy cells.
They also analyze the stability of the model and calculate the equilibria.
RK Sachs, LR Hlatky, P Hahnfeldt – “Simple ODE Models of Tumor Growth and Anti-Angiogenic or
Radiation Treatment”
http://ac.els-cdn.com/S0895717700003162/1-s2.0-S0895717700003162main.pdf?_tid=b110e5f0-d75b-11e2-aa2a00000aab0f02&acdnat=1371480138_67004b16f40d4d90528e1110b8933a8f
The author of this article argues that complicated models using PDE’s and such are way
too complicated for use by biologists. The simpler ones are much more useful in the real world.
He says that though tumors often continue to grow forever, almost all tumors’ growth
rates decrease over time, so logistic growth is appropriate.
For their model of radiation, they used a linear-quadratic (LQ) model. This allowed for
them to account for damage repair and misrepair (fixing it wrong) from the radiation treatments.
1 Gy = 1 J/kg.
They state that the most important damage done by radiation is to the chromatin, where
the DNA double strand breaks apart. Many of these breaks are repaired after a half-hour or so,
and few are misrepaired. One misrepair can be enough to kill a cell the next time it tries to
undergo mitosis.
The LQ model is great because it lets us take into account the three main parameters that
are going to have the largest effect on our cancer, which glossing over other more minute details.
HD Suit – “Protons to Replace Photons in External Beam Radiation Therapy?”
http://www.sciencedirect.com/science/article/pii/S0936655502901718
The higher the dosage of radiation to the surrounding normal tissues, the worse the
treatment is for the patient. Protons are great, and he gives some facts about them. Then, he
talks about radiation. He says photons’ range is indefinite and the dose decreases exponentially
as it travels through the body. He compares and contrasts photons and protons, though he seems
biased toward proton therapy and excludes information about photon therapy (radiation).
Mu, Xiangkui et. Al – “Does electron and proton therapy reduce the risk of radiation induced
cancer after spinal irradiation for childhood medulloblastoma? A comparative treatment
planning study”
http://informahealthcare.com/doi/abs/10.1080/02841860500218819
The article compares electron therapy, proton therapy, and photon (x-ray) therapy
treatments. It gives absorbed doses for the tumor and for surrounding tissues for each, and
showed proton therapy to be the best treatment because it delivered an equal amount of
radiation to the tumor with the minimal dose absorbed by surrounding organs at risk. This could
be helpful in estimating our parameters.
Li L, Ting X – “Stem Cell Niche: Structure and Function”
http://0-ehis.ebscohost.com.library.winthrop.edu/ehost/pdfviewer/pdfviewer?sid=2ccbab8c98dc-4f0b-acd5-d04dc3f47477%40sessionmgr198&vid=1&hid=115
The article says that stem cells are unique because they can replenish themselves through
self-renewal and they can differentiate into other types of cells that have specific functions. Stem
cells are unspecialized. Stem cells are important in the regeneration of tissue, replacing cells lost
to apoptosis or injury through differentiation. They maintain a balance between self-renewal and
differentiation.
Def: Multipotent stem cell – can give rise to other stem cells but is limited in its ability to
differentiate. For example, haematopoietic stem cells can create blood cells but not brain cells,
that’s how they’re limited. Commited to producing specific cell types.
They talk a lot about stem cell niches and communication signaling pathways.
On p. 11 they start talking about epithelial stem cells’ niche in the skin. Epithelial stem
cells are multipotent. Daughter cells migrate away from the parent stem cell to go perform their
specific function.
On p. 19 they discuss the possibility of cancer stem cells. They suggest that tumors could
be caused by stem cells that somehow escaped their niche, which would mean that they are no
longer under the control of the signals from the niche environment.
A Soltysova, V. Altanerova, C. Altaner – “Cancer stem cells”
http://www.researchgate.net/publication/7483126_Cancer_stem_cells/file/9fcfd500cdeacb7e
8b.pdf
The article describes normal stem cells. They say there are three types – embryonic,
germinal, and progenitor. Symmetric cell division is when each daughter cell has the same
properties of their parent. They are the same types of cells. Asymmetric division is when one
daughter is the same as the parent cell, but the other differentiates into something different.
An important characteristic of stem cells is their ability to self-renew without losing
proliferation capacity. Stem cells can express telomerase, an enzyme that rebuilds telomeres.
This is common to cancer cells as well. Normal cells can’t divide forever because their telomeres,
which are important in preventing the loss of parts of DNA during division, are shortened with
each division. Eventually they get too short, so the cell undergoes apoptosis.
In the beginning, they say that a cancer stem cell may be caused by a normal stem cell
mutating. Cancer stem cells divide asymmetrically, creating more cancer stem cells and creating
other cells that differentiate. Not all cells in a tumor are there to support tumor growth. Tumors
consist of heterogeneous cell populations.
Cancer stem cells can be caused by a normal stem cell mutating or by a normal cell
mutating so much that it becomes a “stem” cell with the ability to self-renew.
Cancer stem cell model (StemCellModel)
The article gives some facts about cancer stem cells. It has a mathematical model that models
normal and stem cell, and normal and stem cancer cells. They give numerical approximations for
their parameters, like the cell growth and such.