Modeling Tumor GrowthGroup Members: Meggie Erickson,Daniel Lukaszewski, Wesley Jackson, and 3/30/2010Daniel Lukaszewski, Wesley Jackson, and Gustavo MirandaMentor: Scott HottovyRemoving malignant tumors• Traditional chemotherapy• Radiation therapy• Immunotherapy3/30/2010Main goal is to suppress the appropriate immune response to assist the body in combating the tumor, rather than affecting it directly.How tumors form:• Normal cells undergo malignant transformations• Depends on the strength of the immune system.3/30/2010system.• 2 types of treatment: cytokines and IL-2’sCytokines• Pro and anti-inflammatory molecules in immune systems•Low weight molecular 3/30/2010protein mediators involved in cell growth, inflammation, immunity, differentiation and repair.IL-2’s• Produced by T-helper cells when stimulated by an infection 3/30/2010Both needed3/30/2010Transforming Growth Factor-β• Wound healing, inflammation and growth stimulatory angiogenesis •Present in health cells 3/30/2010•Present in health cells and tumor cells• In tumor cells it challenges the immune systemBasic tumor growth model not taking into account siRNA treatment3/30/2010Nondimensionalized model3/30/2010TGF-β Passive Case• TGF-β is not present: S(t)=0 for varying c• 0 < c < 8.55 x 10-6Tumor has grown to carrying capacity undetected by body’s immune system• 8.55 x 10-6< c < 0.0032 Tumor mass oscillates from very high to very low values. As c increases, 3/30/2010very high to very low values. As c increases, amplitude and period of oscillations decrease• .0032 ≤ c Tumor mass experiences damped oscillations until becoming small and dormant. • c=0.0032 is the lowest value for the immune system to control tumor growth initially.• TGF-β is produced: S(t) ≠ 0 • Increase in the growth rate as well as greater ability to avoid detection from immune system•Behavior of tumor cell similar to that of passive TGF-β Aggressive Case3/30/2010•Behavior of tumor cell similar to that of passive tumor• However, p4 value (maximum value of TGF-βproduction) affects behavior as wellVarying p4: small c• Tumor cell density vs time for c=5^-6 as the rate of TGF-B production, p4, increases.•For small c, As Tumor cell density3/30/2010•For small c, As p4 increases the max tumor cell density increases and tumor mass exceeds its normal carrying capacityTumor cell densityTimeIntermediate c• As p4 increases, a Hopf bifurcation occurs. Tumor behavior p4=03/30/2010behavior changes from unstable to stable, oscillations cease, large tumor mass results.p4=2.84 p4>2.84Large c (0.0035) • When p4 reaches the Hopf bifurcation of p4=2.84, a stable 3/30/2010p4=0a stable node results and a large tumor mass results. p4=2.84 p4>2.84Relationship between p4 and gamma• Gamma (γ)-the ability of TGF-B to reduce c• The greater the ability for TGF-B to 3/30/2010the ability for TGF-B to reduce c, the less TGF-B the tumor will have to produce to avoid detection.Effects of parameter “a”• “a”- the strength of the immune response to the tumor • Only realistic values for “a” are 0.1 < a < 0.3 3/30/2010are 0.1 < a < 0.3 • The higher the antigenicity value, the lower the immune response needed to control tumor growthEquations with siRNA treatment• New feature: How siRNA treatment suppresses the production of TGF-β. • “A” represents strands of siRNA (f is proportion of bounded A).3/30/2010• Eq. 5 describes the injection and degradation of the siRNAs. Di(t) = dose of siRNA • D1 = continuous infusion dose • D2 = multiple injection dose.Non-dimensional equations3/30/2010siRNA Treatment• Consider the case where c = 0.002, p_4 = 0.5, and γ = 10• First case: continuous infusion of siRNA D(t)=D3/30/2010D1(t)=D0• Second Case: siRNA is administered periodically through one or more rounds of siRNA injected once a day for 11 days. D2(t)D1siRNA Treatment (continuous)time3/30/2010timetimeD2(t) siRNA Treatment• Left column is one injection• Right column is 2 injections3/30/2010injections• Row 1,2,3 have increasing a: .1, .11, .12 respectivelySummary3/30/2010Dudley ME. Rosenberg SA. Adoptive-cell-transfer therapy for the treatment ofpatients with cancer. [Review] [97 refs] [Journal Article. Review. Review,Tutorial] Nature Reviews. Cancer. 3(9):666-75, 2003 Sep.What we’ll be adding• Add chemotherapy at certain times• Change doses of siRNA treatment (number of treatments or treatment dose)3/30/2010Citation:Arciero, JC, TL Jackson, and DE Kirschner. "A Mathematical Model of Tumor-Immune Evasion and siRNA Treatment." Discrete and Continuous Dynamical Systems Series B. 4.1 (2004): 39-58. Print.