1. A Mathematical Explanation to Tumor’s Response to Perfusion and Hypoxic Fraction after Radiation
Y. Yan1, V. Adhikarla1, M.W. Kissick1,2, D. Campos1, D. H. Zhao1, S. Jacques3, J. Bussink4 and A. Van der Kogel1
1. University of Wisconsin – Madison, WI Morgridge Institute for Research, Madison, WI Oregon Health & Science University, Portland, OR Radboud University, Nijmegen, The Netherlands
Poster SU-E-T-841, Joint AAPM/COMP, Charlotte, NC, USA, July 29-August 2, 2012
Purpose & Expanded Statement of Innovation and Impact: Hypoxia and microvascular changes are considered to be important factors for the outcome of the treatment. Characterizing and quantifying the relationship between the oxygen distribution within the tumor and tissue metabolism, tissue diffusivity, anatomical structure of blood vessels as well as oxygen gradients is very promising to make more effective treatment. (Dalah et al). Unfortunately, patient specific theoretical model for treatment response is still elusive. We propose a mathematical model to explain the experimental results provided by Bussink et al’s group (Bussink et al 2000). A more sophisticated model is also discussed in this presentation.
Fig. 1: Representative of our compartment model. The dotted box indicate the dynamic changes of the tumor cell.
Results: Theoretical: The value of this theoretical calculation is that it points out (see Fig. 4) where in relative frequency (period) space one should be located so that PO will be efficacious. One should be in a regime of ‘pure blurring.’ that will happen when the relative frequencies are an order of magnitude different from each other. If they are close, it may still work, as with HT: we saw no interference (‘interplay’) in the experiment in any frequency range (see Fig. 3)!
Fig. 4: An illustration of the interference dose error response function caused by an aspect of the modulation (a single gantry rotation in this case) having coherence with a sinusoidal tumor motion. The tumor motion (breathing in this case) is assumed to remain within a plane, and so the gantry angle modulation in this case is just the projection angle variation between tumor motion and gantry motion. The phases are chosen to correspond to a registration to the long time average position. At large differences between these two periods, phase becomes less important to the magnitude of the dose error. In our real case with a low pitch, the gantry rotation overlaps by a factor of three. Pitch is not included in these simulations.
Fig. 3: Dynamic behavior of the of the perfusion fraction (up) and hypoxic fraction (down). The experimental data is obtained from Bussink et al’s paper (Bussink et al 2000). The error bar indicates the uncertainties in the statistics of the experiment.
Conclusion & Clinical Implications: Given that we are already optimizing for IMRT; and given that most patients will not have motion management (tracking or gating, etc.); and given that it is possible with IMRT to sample motion well (with HT at least it is), then we suggest that probablistic optimization (PO) should be considered for HT and further explored for other forms of IMRT. Acknowledgements: Thanks to Scott Johnson (phantom) and NIH/NCI grant K25 CA
References:
Bortfeld et al., 2002 Effects of Intra-fraction Organ Motion on the Delivery of Dynamic Intensity Modulation, Phys. Med. Biol
Brahme et al., 1982 Solution of an integral equation encountered in rotation therapy Phys. Med. Biol
Kissick et al., 2008 On the impact of longitudinal breathing motion randomness for tomotherapy delivery Phys. Med. Biol
Kissick M W, Mackie T R 2009 Correspondence: Task Group 76 Report on ‘The Management of Respiratory Motion in Radiation Oncology [Med. Phys. 33, (2006)] Med. Phys
Kissick et al., 2010 A Phantom Model demonstration of tomotherapy dose painting delivery, including managed respiratory motion without motion management Phys. Med. Biol
Unkelbach J, Oelfke U 2005 Incorporating organ movements in IMRT treatment planning for prostate cancer: minimizing uncertainties in the inverse planning process Med. Phys
Yu CX, Jaffray DA, Wong JW 1998 The effects of intra-fractional organ motion on the delivery of dynamic intensity modulation Phys. Med. Biol
Contact: Michael Kissick, Assistant Professor, Department of Medical Physics,
Wisconsin Institutes for Medical Research (WIMR) Building,
University of Wisconsin – Madison, School
1111 Highland Avenue, Madison, WI ,