A Mathematical Model of Gene Therapy for the Treatment of Cancer - Mathematical Methods and Models in Biomedicine - page 360

In Eq. (3a), the first term represents stimulation by the tumor to generate effector
immune cells. The parameter c is known as the antigenicity of the tumor. Since
tumor cells begin as self, c represents how different the tumor cells are from self
cells (i.e., how foreign). The second term in Eq. (3a) represents natural death and
the third is the proliferative enhancement effect of the cytokine IL-2. In Eq. (3b), the
first term is a logistic growth term for tumor growth and the second is a clearance
term by the immune effector cells. In the final Eq. (3c), IL-2 is produced by effector
cells (in a Michaelis-Menten fashion) and decays via a known half-life (third term).
To capture a novel treatment approach (still in use in some clinical settings),
KP introduced three terms into their models. The first one is Adoptive cellular
immunotherapy (ACI), representing the introduction of immune cells into cancer
patients that have been stimulated to have specific anti-tumor activity [ 42 , 44 - 46 ].
T cells, also known as lymphocytes, produce cytokines that are either self-
stimulating or can stimulate (or shut down) other cells. ACI is usually performed
in conjunction with large amounts of IL-2. There are two types of immune cells
that are cultured for this purpose: (1) LAK-(lymphokine-activated killer cells): cells
taken from host and then stimulated with activating factors. These cells are then
injected back to patient. (2) TIL-(tumor infiltrating lymphocytes): Immune cells are
taken from patient, and grown with high concentrations of IL-2 before injected back
to the patient.
In the KP model, s 1 represents the treatment terms of introducing LAK and TIL
cells to the tumor site of a patient. The second term, s 2 , is a treatment term that
represents administration of the cytokine IL-2 by a physician to a patient, to again
stimulate effector cell growth and proliferation.
The KP system can exhibit chaotic behavior. The typical example of chaotic
behavior is the system of Lorenz (1963) representing a so called strange attractor.
The complete qualitative analysis of KP equations is much harder than the con-
ventional Kuznetsov model. Nevertheless, Kirschner and Panetta, using stability
analysis and modern bifurcation theory, classified representative behaviors of
solutions and stability of cancer-free equilibrium states. Description of oscillations
with long time dormant periods of illness was described in order to complete the
studies by Kuznetsov.
Arciero and colleagues [ 5 ] extended the KP equation by including a suppressive
cytokines known as TGF-

and also a simple type of gene therapy known as
siRNA [ 39 ]. The use of siRNA is an early type of gene therapy where short-
interfering RNA fragments interfere with the expression of a specific gene and
modify behaviors in a cell. In addition, they added TGF-

β

to the model, which is a
cytokine that acts to suppress immunity by inhibiting activation of effector cells and
reducing antigenicity of tumors. It also stimulates tumor growth by promoting tumor
vascularization. Their model predicts that increasing the rate of TGF-

β

production
for reasonable values of tumor antigenicity enhanced tumor growth and its ability
to escape host detection. siRNA treatment focused on the gene expression for
TGF-

β

β : it acts to suppress TGF- β production by targeting the messenger RNA that

codes for TGF- helped to rescue these negative effects to the

host. Another group also recently explored the development of a microRNA-mRNA

β . Reducing TGF- β