Optimization of tumour control probability for heterogeneous tumours in fractionated radiotherapy treatment protocols.

We find the dose distribution that maximizes the tumour control probability (TCP) for a fixed mean tumour dose per fraction. We consider a heterogeneous tumour volume having a radiation response characterized by the linear quadratic model with heterogeneous radiosensitivity and repopulation rate that may vary in time. Using variational calculus methods a general solution is obtained. We demonstrate the spatial dependence of the optimal dose distribution by explicitly evaluating the solution for different functional forms of the tumour properties. For homogeneous radiosensitivity and growth rate, we find that the dose distribution that maximizes TCP is homogeneous when the clonogen cell density is homogeneous, while for a heterogeneous initial tumour density we find that the first dose fraction is inhomogeneous, which homogenizes the clonogen cell density, and subsequent dose fractions are homogeneous. When the tumour properties have explicit spatial dependence, we show that the spatial variation of the optimized dose distribution is insensitive to the functional form. However, the dose distribution and tumour clonogen density are sensitive to the value of the repopulation rate. The optimized dose distribution yields a higher TCP than a typical clinical dose distribution or a homogeneous dose distribution.

A model for optimizing normal tissue complication probability in the spinal cord using a generalized incomplete repair scheme.

The purpose of this study was to determine the treatment protocol, in terms of dose fractions and interfraction intervals, which minimizes normal tissue complication probability in the spinal cord for a given total treatment dose and treatment time. We generalize the concept of incomplete repair in the linear-quadratic model, allowing for arbitrary dose fractions and interfraction intervals. This is incorporated into a previously presented model of normal tissue complication probability for the spinal cord. Equations are derived for both mono-exponential and bi-exponential repair schemes, regarding each dose fraction and interfraction interval as an independent parameter, subject to the constraints of fixed total treatment dose and treatment time. When the interfraction intervals are fixed and equal, an exact analytical solution is found. The general problem is nonlinear and is solved numerically using simulated annealing. For constant interfraction intervals and varying dose fractions, we find that optimal normal tissue complication probability is obtained by two large and equal doses at the start and conclusion of the treatment, with the rest of the doses equal to one another and smaller than the two dose spikes. A similar result is obtained for bi-exponential repair. For the general case where the interfraction intervals are discrete and also vary, the pattern of two large dose spikes is maintained, while the interfraction intervals oscillate between the smallest two values. As the minimum interfraction interval is reduced, the normal tissue complication probability decreases, indicating that the global minimum is achieved in the continuum limit, where the dose delivered by the "middle" fractions is given continuously at a low dose rate. Furthermore, for bi-exponential repair, it is seen that as the slow component of repair becomes increasingly dominant as the magnitude of the dose spikes decreases. Continuous low-dose-rate irradiation with dose spikes at the start and end of treatment yields the lowest normal tissue complication probability in the spinal cord, given a fixed total dose and total treatment time, for both mono-exponential and bi-exponential repair. The magnitudes of the dose spikes can be calculated analytically, and are in close agreement with the numerical results.

Use of three-dimensional spiral computed tomography imaging for staging and surgical planning of head and neck cancer.

We compare four different three-dimensional (3D) reconstruction methods of spiral computed tomography (CT) data for head and neck cancer to establish the method best suited for specific uses, eg, staging of lymph nodes and viewing of spatial relationships between the tumor, fascial spaces, adjacent soft tissues, and others structures. We evaluated a series of 10 patients (six men and four women), aged 32 to 60 years. Of these, five were histologically diagnosed with squamous cell carcinoma, two with lymphoma, one with thyroid cancer, one with Kikuchi's disease or necrotizing lymphadenitis, and one with esthesioneuroblastoma. All scans were obtained using high-resolution spiral CT (General Electric Medical Systems, Milwaukee, WI). The collimations used were 3 mm and 5 mm, matrix 512 x 512, and reconstruction interval not more than 3 mm. Scanning was performed from the skull base to the aortic arch. Iodinated contrast medium was injected so that the blood vessels were clearly differentiated from nodes. Different techniques of three-dimensional reconstruction were employed, including shaded surface display (SSD), multiplanar reconstructions (MPR), maximum intensity projection (MIP), 3D volume rendering (VR), and combined techniques. The reconstructions were performed in a variety of planes, including sagittal, coronal, and oblique views. In our series of selected patients, the technique of 3D VR showed potential advantages over other techniques. The MIP technique was useful in analyzing the patency of vessels and to exclude thrombus, compression, or displacement by tumor. The use of combined techniques such as SSD and MPR, accurately demonstrated the levels of lymph nodes and the relationship between the tumor projection of interest and various anatomic structures. In conclusion, 3D reconstruction of CT data is useful in the localization and staging of neck tumors and assists in surgical planning and radiation treatment.

Effect of incomplete repair on normal tissue complication probability in the spinal cord.

PURPOSE: To incorporate the effects of repair into a model for normal tissue complication probability (NTCP) in the spinal cord. METHODS AND MATERIALS: We used an existing model of NTCP for the spinal cord, based on a critical volume concept, into which we incorporated an incomplete repair (IR) scheme. Values for the repair half time were taken from existing experimental data. Repair corrections were expanded to account for the possibility of biphasic repair, namely the existence of long and short components of repair. RESULTS: We found that the model predicts complete repair to occur at approximately 15 hours, consistent with experimental data. The dependence of the model on the value of the dose per fraction was also studied. It was found that there is a sparing effect as the dose per fraction is decreased below 2 Gy. Surface plots of the NTCP as a function of both the interfraction interval (IFI) and the dose per fraction were generated. We investigated "iso-NTCP" curves, which may allow freedom in choice of treatment plans in terms of the optimal IFI and dose per fraction. As for biphasic repair, as the relative weights of the long and short components of repair were varied, the NTCP changed as well. The model showed little difference between mono- and bi-exponential repair in the time to complete repair, due to a dominance of the long component at long IFIs. CONCLUSIONS: Incorporating IR into NTCP modeling of the spinal cord is consistent with current experimental data. The concept of iso-NTCP curves is an approach which may be clinically useful.