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This paper systematically evaluates a pharmacokinetic compartmental model for identifying tumor hypoxia using dynamic positron emission tomography (PET) imaging with 18F-fluoromisonidazole (FMISO). A generic irreversible one-plasma two-tissue compartmental model was used. A dynamic PET image dataset was simulated with three tumor regions-normoxic, hypoxic and necrotic-embedded in a normal-tissue background, and with an image-based arterial input function. Each voxelized tissue's time activity curve (TAC) was simulated with typical values of kinetic parameters, as deduced from FMISO-PET data from nine head-and-neck cancer patients. The dynamic dataset was first produced without any statistical noise to ensure that correct kinetic parameters were reproducible. Next, to investigate the stability of kinetic parameter estimation in the presence of noise, 1000 noisy samples of the dynamic dataset were generated, from which 1000 noisy estimates of kinetic parameters were calculated and used to estimate the sample mean and covariance matrix. It is found that a more peaked input function gave less variation in various kinetic parameters, and the variation of kinetic parameters could also be reduced by two region-of-interest averaging techniques. To further investigate how bias in the arterial input function affected the kinetic parameter estimation, a shift error was introduced in the peak amplitude and peak location of the input TAC, and the bias of various kinetic parameters calculated. In summary, mathematical phantom studies have been used to determine the statistical accuracy and precision of model-based kinetic analysis, which helps to validate this analysis and provides guidance in planning clinical dynamic FMISO-PET studies.

Unlabelled: This article describes a method of assessing the biologic consequences of nonuniform dose distributions produced in tumors by biologically targeted radionuclide therapy. The analysis is based on a simple mathematical model that assumes all tumor cells are uniformly radiosensitive., Methods: Using the linear-quadratic radiobiologic model, it is possible to represent an absorbed dose distribution by a biologically effective dose (BED) volume histogram (BVH). The Laplace transform of the BVH yields an equivalent uniform biologically effective dose. This is a one-number value that fully describes the biologic effect of a nonuniform absorbed dose distribution. In this article, for the purposes of exposition, nonuniform BED distributions are represented by normal distributions., Results: Nonuniform absorbed dose distributions are inefficient in sterilizing tumors and become proportionately less effective as the mean dose increases. The loss in effectiveness is most severe for radiosensitive tumors., Conclusion: Several approaches may alleviate the consequences of dosimetric nonuniformity. These include the use of smaller targeting molecules, radionuclides with longer emission ranges, fractionated administration of biologically targeted radionuclide therapy and combined modality treatments.

Proliferation of tumour cells during radiotherapy may be a significant factor determining response to treatment. In previous work based on the linear-quadratic (LQ) model, tumour cell proliferation was assumed to be independent of both tumour size and the temporal structure of treatment. This paper examines a form of tumour cell proliferation that is exponential at small tumour sizes and Gompertzian at larger sizes. This is integrated with the LQ description of tumour cell sterilization. It is assumed that exposure to therapeutic radiation changes the state of tumour cells from viable to doomed. Doomed cells are assumed to be lost from the tumour mass with exponential kinetics. Six parameters are used to describe tumour response. Three of these are the standard 'LQ+time' (alpha, beta, Tpot) parameters. Two additional parameters are required to describe the shape of the tumour growth/regrowth curve (VG, Vmax). The sixth parameter (Ts) represents the rate of loss of doomed cells from the tumour. The model may be used to describe the effects of radiation therapy, both in terms of cure response (clonogenic cell sterilization) and also remission response (tumour regression and regrowth). An important feature of the model is that it enables the effects of temporally non-uniform treatments to be described. Preliminary modelling studies suggest that it may be possible to manipulate the temporal structures of fractionation schedules to increase the duration of remission at the expense of the probability of cure.

Auger-emitting radionuclides have potential for the therapy of cancer due to their high level of cytotoxicity and short-range biological effectiveness. Biological effects are critically dependent on the sub-cellular (and sub-nuclear) localization of Auger emitters. Mathematical modelling studies suggest that there are theoretical advantages in the use of radionuclides with short half-lives (such as 123I) in preference to those (such as 125I) with long half-lives. In addition, heterogeneity of radionuclide uptake is predicted to be a serious limitation on the ultimate therapeutic effect of targeted Auger therapy. Possible methods of targeting include the use of analogues of DNA precursors such as iodo-deoxyuridine and molecules which bind DNA such as steroid hormones or growth factors. A longer term possibility may be the use of molecules such as oligonucleotides which can discriminate at the level of DNA sequence. It seems likely that the optimal clinical role of targeted Auger therapy will be as one component of a multi-modality therapeutic strategy for the treatment of selected malignant diseases.

Unlabelled: Targeted radionuclide therapy is a new form of radiotherapy that differs in some important respects from external beam irradiation. One of the most important differences is due to the finite range of ionizing beta particles emitted as a result of radionuclide disintegration. The effects of particle range have important implications for the curability of tumors., Methods: We used a mathematical model to examine tumor curability and its relationship to tumor size for 22 beta-emitting radionuclides that may have therapeutic potential. The model assumed a uniform distribution of radionuclide throughout., Results: For targeted radionuclide therapy, the relationship between tumor curability and tumor size is different from that for conventional external beam radiotherapy. With targeted radionuclides, there is an optimal tumor size for cure. Tumors smaller than the optimal size are less vulnerable to irradiation from radionuclides because a substantial proportion of the disintegration energy escapes and is deposited outside the tumor volume., Conclusion: We found an optimal tumor size for radiocurability by each of the 22 radionuclides considered. Optimal cure diameters range from less than 1 mm for short-range emitters such as 199Au and 33P to several centimeters for long-range emitters such as 90Y and 188Re. The energy emitted per disintegration may be used to predict optimal cure size for uniform distributions of radionuclide.

Purpose: Radiobiological modeling was used to explore optimum combination strategies for treatment of disseminated malignancies of differing radiosensitivity and differing patterns of metastatic spread. The purpose of the study was to derive robust conclusions about the design of combination strategies that incorporate a targeting component. Preliminary clinical experience of a neuroblastoma treatment strategy, which is based upon general principles obtained from modelling, is briefly described., Methods and Materials: The radiobiological analysis was based on an extended (dose-rate dependent) formulation of the linear quadratic model. Radiation dose and dose rate for targeted irradiation of tumors of differing size was in part based on microdosimetric considerations. The analysis was applied to several tumor types with postulated differences in the pattern of metastatic spread, represented by the steepness of the slope of the relationship between numbers of tumors present and tumor diameter. The clinical pilot study entailed the treatment of five children with advanced neuroblastoma using a combination of 131I metaiodobenzylguanidine (mIBG) and total body irradiation followed by bone marrow rescue., Results: The theoretical analysis shows that both intrinsic radiosensitivity and pattern of metastatic spread can influence the composition of the ideal optimum combination strategy. High intrinsic radiosensitivity generally favors a high proportion of targeting component in the combination treatment, while a strong tendency to micrometastatic spread favors a major contribution by total body irradiation. The neuroblastoma patients were treated using a combination regimen with an initially low targeting component (2 Gy whole body dose from targeting component plus 12 Gy from total body irradiation). The treatment was tolerable and resulted in remissions in excess of 9 months in each of these advanced neuroblastoma patients., Conclusions: Radiobiological analysis, which incorporates simple models of metastatic spread, emphasizes the importance of the total body irradiation component in a targeting/total body irradiation combination strategy. However, the analysis favors a larger targeting component than is used in clinical practice at present. A cautious escalation of the 131I mIBG component in the combination treatment of advanced neuroblastoma appears justified.

Background: In conventional radiotherapy, proliferation of tumor cells throughout treatment is believed to be an important cause of treatment failure. For radioimmunotherapy (RAIT), tumor cell proliferation will be a significant mechanism to consider when designing therapeutic strategies., Methods: A mathematic model, based on the irradiation of a proliferating tumor cell population by an exponentially decaying dose-rate, was used to examine the effects of proliferation during RAIT., Results: Proliferation can give rise to dose-rate effects in tumors that are distinct from those attributable to repair or recovery from radiation damage. An equation for the therapeutic efficiency of RAIT was generated. The analysis showed that RAIT will be less effective on rapidly proliferating tumor cell populations. High radioresistance causes a radiation dose to produce less tumor cell sterilization. In addition, for RAIT, the proportion of the dose that is "wasted" because of proliferation will be greater for radioresistant tumors. Therapeutically, higher initial dose-rates are more effective, meaning that, dose for dose, shorter decay half-lives will be better than longer ones. The analysis indicates that the therapeutic efficiency depends on tumor size and dosimetric heterogeneity and implies that micrometastases and "cold spots" in tumors could be major foci of recurrence., Conclusions: The results of this study support the use of RAIT as part of an integrated treatment regimen featuring local radiotherapy to bulk disease, and systemic treatment with total body irradiation plus bone marrow rescue and/or chemotherapy.

Purpose: A model is presented for calculating combinations of targeted 131I and total body irradiation, followed by bone marrow rescue, in the treatment of tumors of different radiosensitivity. The model is used to evaluate the role of the total body irradiation component in the optimal combination regime as a function of the radiosensitivity of the tumor cells., Methods and Materials: A microdosimetric model was used to calculate absorbed dose in small tumors and micrometastases when uniformly targeted by the radionuclide 131I. Cell kill was calculated from absorbed dose using an extended version of the linear quadratic model. The addition of varying total doses of total body irradiation, assuming 2 Gy fractions, was also calculated using the linear quadratic model. The net cell kill from combined modality (targeted 131I and total body irradiation) was computed for varying proportions of the two components, for a range of tumor sizes, restricting the total radiation dose to within tolerance for a full-course TBI regime (approximately 14 Gy total) in all cases. The calculations were repeated for a range of presumed tumor uptakes of the targeting agent and for a range of tumor radiosensitivities, typical of those reported for tumor cells of differing type in culture. Optimal regimes were identified as those predicted to yield a high probable tumor cure rate (evaluated using a Poisson statistical model) for all tumor sizes., Results: The analysis supports earlier model studies which predicted that systemic combination treatment with targeted 131I and total body irradiation would be superior to either component used alone. The intrinsic tumor radiosensitivity is found to be a factor which influences the optimal combination of the 131I and external beam total body irradiation components. The total body irradiation component is greater in optimal regimes treating radio-resistant than radiosensitive tumors. However, an obligatory total body irradiation component is also predicted for more radiosensitive tumors; the analysis suggests that the total body irradiation component should in no circumstances be less than 2 x 2 Gy, whilst practical arguments exist in favor of higher doses., Conclusion: Total body irradiation is an obligatory component for effective systemic treatment of disseminated malignant tumors to which 131I can be selectively targeted. Clinical studies applying this strategy to the treatment of neuroblastoma by 131I targeted by meta-iodo-benguanidine (mIBG), total body irradiation and bone marrow rescue are now in progress.

A mathematical model analysis is used to address the question of optimal scheduling of combined treatments consisting of biologically targeted radiotherapy (BTR), total body irradiation (TBI), and bone marrow rescue. Radiation effects on normal tissue are described using an extension of the LQ model. Tumor effects are described using a simple model that allows for radiation-induced sterilization and exponential proliferation of tumor cells, a proportion of which completely escapes the effects of targeted radiotherapy. The effect on a tumor cell population of a set of treatment schedules, composed partly of targeted radiotherapy and partly of fractionated external beam irradiation, are calculated. Treatment schedules are chosen to be biologically equivalent, for a "late responding" organ, to a fractionated TBI schedule of 7 fractions of 2 Gy. The tumor effects of the treatment schedules depend on the specificity of targeting, represented by the ratio of initial dose-rate for the tumor cells to that in the dose-limiting organ, and the heterogeneity of targeting, represented by the proportion of tumor cells that escape irradiation by targeted radiotherapy. The main mechanism determining optimal combinations is an overkill of effectively targeted tumor cells. Treatment regiments consisting of targeted radiotherapy alone fail, due to the unimpeded growth of those tumor cells that escape targeted irradiation. Optimal schedules almost invariably consist of elements of both BTR and TBI. Although it is recognized that the model is simplistic in a number of respects, these findings provide support for the clinical use of integrated BTR, TBI, and bone marrow rescue for the treatment of systemic malignant disease.

A mathematical model has been used to investigate the relationship of curability to tumour size and cell number for spherical tumours treated with targeted 131I or 90Y, assuming uniform uptake of radionuclide throughout the tumour. The analysis shows that, for any given cumulated activity per unit mass of tumour, cure probability is greatest for tumours whose diameter is close to an optimum value which depends on the path length of the emitted beta-particle. Smaller tumours are less curable because of inefficient absorption of radiation energy, and larger tumours are less curable because of greater clonogenic cell number. The lesser curability of very small tumours is a feature of targeted radiotherapy using long-range beta-emitters which does not occur with external beam irradiation. The predicted inefficiency of sterilisation of microscopic tumours poses a problem for targeted radiotherapy which is analogous to "geographic miss" in conventional radiotherapy. The implication is that small micro-metastases could escape sterilisation by radionuclides administered at activity levels sufficient to eradicate larger tumours. It is suggested that single agent targeted radiotherapy should not be used for treatment of disseminated malignancy when multiple tumours of differing size, including micrometastases, may be present. The analysis implies that an advantage might result from the use of a panel of several radionuclides (including short-range emitters) or from combining targeted radiotherapy using long-range beta-emitters with external beam irradiation or some other modality to which microscopic tumours are preferentially vulnerable.

Targeted radiotherapy consists of biologically selective irradiation of malignant cells by means of radionuclides attached to tumour-seeking molecules. A variety of clinical strategies for targeted radiotherapy may be used, for which different normal tissues will be critical. A large number of radionuclides exist, emitting nuclear particles with a range of path lengths from nanometres to millimetres. An important feature of normal-tissue radiobiology is the dose-rate effect, which is especially marked for late-responding tissues. Radiobiological calculations imply that tolerance dose for targeted radiotherapy using low-LET emitters will depend strongly on the effective half-life of the radionuclide, which will be affected by pharmacokinetics and may vary between patients. Some strategies designed to improve the therapeutic radio (e.g. accelerated clearance of radionuclide) may have modulating effects on the tolerance dose. Tumour response will be governed by the 'four Rs' (repair, repopulation, reoxygenation, redistribution) as well as by mechanisms peculiar to targeted radiotherapy. Analysis based on the extended linear quadratic model predicts that dose-rate effects will be of major importance for only a minority of tumours. Most of the radiation dose to tumour will usually be delivered over a time-scale of a few days. This might give insufficient time for tumour reoxygenation, making the use of hypoxic sensitizers appropriate. A special feature of targeted radiotherapy is the complex relationship between tumour curability and tumour size for different radionuclides. For long-range beta-emitters, microscopic tumours may be operationally resistant because of inefficient absorption of radionuclide disintegration energy in small volumes. Short-range emitters will be more efficient in sterilization of micrometastases but sterilization of larger tumours may require an unattainable degree of homogeneity of radionuclide distribution. Optimal use of targeted radiotherapy may require it to be combined with external-beam irradiation or chemotherapy. Experimental studies will be necessary to investigate those features of targeted radiotherapy which differ from external-beam irradiation. Future directions may include targeted radiotherapy of minimal numbers of tumour cells detected by use of molecular probes. Such applications call for use of short-range alpha-emitters and Auger emitters whose radiobiology will become increasingly important.

Total body irradiation (TBI) followed by bone marrow rescue is being increasingly used in the systemic treatment of acute leukaemia and some solid tumours such as neuroblastoma. Typically, these neoplasms are radiosensitive with little or no shoulder on the in vitro survival curve (n approximately equal to 1.0, Do approximately equal to 1.0 Gy). In such cases, fractionated or low-dose-rate TBI should allow preferential sparing of normal tissues. With the appropriate choice of dose rate, low-dose-rate TBI should, in principle, be radiobiologically equivalent to fractionated TBI. Calculations based on an extension to the linear quadratic model suggest that extremely low dose rates (e.g., approximately equal to 0.5 Gy h-1) might be required for equivalence to conventionally fractionated schedules. Such low dose rates would require very long treatment times (e.g., approximately equal to 24 h), which renders them impractical. For cell survival parameters of typical radiosensitive neoplasms the effects of proliferation do not alter this conclusion. These studies suggest that fractionated TBI (with high dose rates) is preferable to low-dose-rate therapy for neoplasms such as leukaemia and neuroblastoma.