3 30 2010 Modeling Tumor Growth Group Members Meggie Erickson Daniel Lukaszewski Wesley Jackson and Gustavo Miranda Mentor Scott Hottovy 3 30 2010 Removing malignant tumors Traditional chemotherapy Radiation therapy Immunotherapy Main goal is to suppress the appropriate immune response to assist the body in combating the tumor rather than affecting it directly 3 30 2010 How tumors form Normal cells undergo malignant transformations Depends on the strength of the immune system 2 types of treatment cytokines and IL 2 s 3 30 2010 Cytokines Pro and antiinflammatory molecules in immune systems Low weight molecular protein mediators involved in cell growth inflammation immunity differentiation and repair 3 30 2010 IL 2 s Produced by T helper cells when stimulated by an infection 3 30 2010 Both needed 3 30 2010 Transforming Growth Factor Wound healing inflammation and growth stimulatory angiogenesis Present in health cells and tumor cells In tumor cells it challenges the immune system 3 30 2010 Basic tumor growth model not taking into account siRNA treatment 3 30 2010 Nondimensionalized model 3 30 2010 TGF Passive Case TGF is not present S t 0 for varying c 0 c 8 55 x 10 6 Tumor 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 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 3 30 2010 TGF Aggressive Case TGF 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 tumor However p4 value maximum value of TGF production affects behavior as well 3 30 2010 Tumor cell density Varying p4 small c Time Tumor cell density vs time for c 5 6 as the rate of TGFB production p4 increases For small c As p4 increases the max tumor cell density increases and tumor mass exceeds its normal carrying capacity 3 30 2010 Intermediate c p4 0 p4 2 84 p4 2 84 As p4 increases a Hopf bifurcation occurs Tumor behavior changes from unstable to stable oscillations cease large tumor mass results 3 30 2010 Large c 0 0035 p4 0 p4 2 84 p4 2 84 When p4 reaches the Hopf bifurcation of p4 2 84 a stable node results and a large tumor mass results 3 30 2010 Relationship between p4 and gamma Gamma the ability of TGF B to reduce c The greater the ability for TGF B to reduce c the less TGFB the tumor will have to produce to avoid detection 3 30 2010 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 The higher the antigenicity value the lower the immune response needed to control tumor growth 3 30 2010 Equations with siRNA treatment New feature How siRNA treatment suppresses the production of TGF A represents strands of siRNA f is proportion of bounded A Eq 5 describes the injection and degradation of the siRNAs Di t dose of siRNA D1 continuous infusion dose D2 multiple injection dose 3 30 2010 Non dimensional equations 3 30 2010 siRNA Treatment Consider the case where c 0 002 p 4 0 5 and 10 First case continuous infusion of siRNA D1 t D0 Second Case siRNA is administered periodically through one or more rounds of siRNA injected once a day for 11 days D2 t 3 30 2010 D1 siRNA Treatment continuous time time time 3 30 2010 D2 t siRNA Treatment Left column is one injection Right column is 2 injections Row 1 2 3 have increasing a 1 11 12 respectively 3 30 2010 Summary Dudley ME Rosenberg SA Adoptive cell transfer therapy for the treatment of patients with cancer Review 97 refs Journal Article Review Review Tutorial Nature Reviews Cancer 3 9 666 75 2003 Sep 3 30 2010 What we ll be adding Add chemotherapy at certain times Change doses of siRNA treatment number of treatments or treatment dose 3 30 2010 Citation 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