Critical volume model analysis of lung complication data from different strains of mice

The critical volume (CV) normal tissue complication probability (NTCP) model was used to fit experimental data on radiation pneumonitis in mice to test the model and determine the values of the model parameters characterizing the lung structure: relative critical volume and cell radiosensitivity. The entire lungs of mice from ten different strains were irradiated acutely and homogeneously to different doses. The experimental animals from the different strains expressed different radiation sensitivities, forming ten well-defined dose-response curves. The most widely accepted biological NTCP model (the individual CV NTCP) readily applicable to cases of acute uniform irradiation was used to fit all the individual dose-response curves simultaneously. To account for the apparent difference in the response of the different strains, it was assumed that the strains differed in their (cell) radiosensitivity. The maximum likelihood method of fitting was used. The obtained fit was statistically highly acceptable. The best-fit value of the relative critical volume, mu, was 78%, which is extremely close to the histologically observed value of around 72%. The values of radiosensitivity, alpha, ranged between 0.26 and 0.37 Gy(-1) for the different strains. The best-fit numbers of functional subunits (FSU) constituting the lung, N, and the number of cells in an FSU, N(o), were implausibly low: N = 9 and N(o) = 23, respectively. The best-fit value of N(o)N was a very small number that was unlikely to correspond to the total number of cells comprising the lung, suggesting that a different interpretation of N and N(o) was required. The individual CV model provided a simultaneous description of the individual responses of different mouse strains through assumed interindividual variability in alpha only. A new interpretation is given to the entities corresponding to N(o) and N. N(o)N is interpreted as the number of certain elementary structures. These structures are considered to be equivalent to the classical functional subunit, which is much larger than a cell and plays a fundamental role in determining the radiation response of the organ. N is identified as the number of the few large subdivisions of the lungs, M = microN is the number that have to be damaged for the lung to fail. N(o) is interpreted as the mean number of elementary structures (FSU) per large subdivision. This imposes a picture of damage to large, contiguous subdivisions containing many FSU, which is consistent with the histological appearance of the lungs of mice in respiratory distress. This picture is in marked contrast to the random distribution of small areas of damage expected for the small size of an FSU. This random distribution is characteristic of earlier stages of the development of radiation pneumonitis, suggesting that some additional process spreads injury from damaged FSU to adjacent, undamaged FSU during the terminal phase.

Radiation damage, repopulation and cell recovery analysis ofin vitrotumour cell megacolony culture data using a non-Poissonian cell repopulation TCP model

The effects of radiation damage, tumour repopulation and cell sublethal damage repair and the possibility of extracting information about the model parameters describing them are investigated in this work. Previously published data on two different cultured cell lines were analysed with the help of a tumour control probability (TCP) model that describes tumour cell dynamics properly. Different versions of a TCP model representing the cases of full or partial cell recovery between fractions of radiation, accompanied by repopulation or no repopulation were used to fit the data and were ranked according to statistical criteria. The data analysis shows the importance of the linear-quadratic mechanism of cell damage for the description of the in vitro cell dynamics. In a previous work where in vivo data were analysed, the employment of the single hit model of cell kill and cell repopulation produced the best fit, while ignoring the quadratic term of cell damage in the current analysis leads to poor fits. It is also concluded that more experiments using different fractionation regimes producing diverse data are needed to help model analysis and better ranking of the models.

Inverse treatment planning by physically constrained minimization of a biological objective function

In the current state-of-the art of clinical inverse planning, the design of clinically acceptable IMRT plans is predominantly based on the optimization of physical rather than biological objective functions. A major impetus for this trend is the unproven predictive power of radiobiological models, which is largely due to the scarcity of data sets for an accurate evaluation of the model parameters. On the other hand, these models do capture the currently known dose-volume effects in tissue dose-response, which should be accounted for in the process of optimization. In order to incorporate radiobiological information in clinical treatment planning optimization, we propose a hybrid physico-biological approach to inverse treatment planning based on the application of a continuous penalty function method to the constrained minimization of a biological objective. The objective is defined as the weighted sum of normal tissue complication probabilities evaluated with the Lyman normal-tissue complication probability model. Physical constraints specify the admissible minimum and maximum target dose. The continuous penalty function method is then used to find an approximate solution of the resulting large-scale constrained minimization problem. Plans generated by our approach are compared to ones produced by a commercial planning system incorporating physical optimization. The comparisons show clinically negligible differences, with the advantage that the hybrid technique does not require specifications of any dose-volume constraints to the normal tissues. This indicates that the proposed hybrid physico-biological method can be used for the generation of clinically acceptable plans.

Derivation of the expressions for gamma50 and D50 for different individual TCP and NTCP models

This paper presents a complete set of formulae for the position (D50) and the normalized slope (gamma50) of the dose-response relationship based on the most commonly used radiobiological models for tumours as well as for normal tissues. The functional subunit response models (critical element and critical volume) are used in the derivation of the formulae for the normal tissue. Binomial statistics are used to describe the tumour control probability, the functional subunit response as well as the normal tissue complication probability. The formulae are derived for the single hit and linear quadratic models of cell kill in terms of the number of fractions and dose per fraction. It is shown that the functional subunit models predict very steep, almost step-like, normal tissue individual dose-response relationships. Furthermore, the formulae for the normalized gradient depend on the cellular parameters alpha and beta when written in terms of number of fractions, but not when written in terms of dose per fraction.

Modelling the dose-volume response of the spinal cord, based on the idea of damage to contiguous functional subunits

PURPOSE

To investigate the response of the spinal cord of experimental animals to homogeneous irradiation, the main purpose being to propose a new version of the Critical Volume Normal Tissue Complication Probability (NTCP) model, incorporating spatial correlation between damaged functional subunits (FSU).

METHOD

The standard Critical Volume NTCP model and its modified version, the Contiguous Damage model promoted here, are described in mathematical terms. Also, a fiber-like structure of the spinal cord is considered, which is a more complex structure than the standard Critical Volume NTCP model assumes. It is demonstrated that the Contiguous Damage model predicts different responses to two-segment irradiation and to single-segment irradiation to the same combined length as observed in experiments on rats, a result that cannot be described by the standard Critical Volume NTCP model.

RESULTS AND CONCLUSIONS

Both the Critical Volume model and the Contiguous Damage model, are fitted to two sets of canine spinal cord radiation data corresponding to two different fractionation regimes of irradiation. Whole-organ irradiation as well as partial irradiation to different lengths are considered, allowing the investigation of dose-volume effects. Formal goodness-of-fit investigation shows that both models fit the canine spinal cord data equally well.

Generalization of a model of tissue response to radiation based on the idea of functional subunits and binomial statistics

This work investigates the existing biological models describing the response of tumours and normal tissues to radiation, with the purpose of developing a general biological model of the response of tissue to radiation. Two different types of normal tissue behaviour have been postulated with respect to its response to radiation, namely critical element and critical volume behaviour. Based on the idea that an organ is composed of functional subunits, models have been developed describing these behaviours. However, these models describe the response of an individual, a particular patient or experimental animal, while the clinically or experimentally observed quantity is the population response. There is a need to extend the models to address the population response, based on the ideas we have about the individual response. We have attempted here to summarize and unify the existing individual models. Finally, the population models are investigated by fitting to pseudoexperimental sets of data and comparing them with each other in terms of goodness-of-fit and in terms of their power to recover the values of the population parameters.

Binding of ketoprofen to human serum albumin studied by circular dichroism

The protein binding of ketoprofen has been studied using circular dichroism titration method as well as the new algorithm proposed by the authors for the treatment of data obtained. The quantitative parameters association constants (k) and number of binding sites (N) have been determined. It is proved that the protein binding of Ketoprofen is going through separate stages and the number of binding sites probably arises. It is acceptable that a high affinity binding takes place primarily (kI = 3.8 x 10(6) l.mol-1). Later, due to the conformational changes in the protein molecule the binding areas are modified and the number of binding sites considerably arises (NI = 3.5 and NII = 14), while the binding affinity reduces 100-fold (kII = 5.10(4) l.mol-1). The number of binding sites has been studied and an identification of the chromophore taking part in the drug-protein interaction has been performed on the base of UV- and CD spectra. A mechanism of the interaction is proposed which coincides with the stepwise binding model.

Binding of sulindac to human serum albumin studied by circular dichroism

The protein binding of sulindac (CAS 38194-50-2) was studied using circular dichroism (CD). By the new algorithm for the analysis of proposed data the association constants (k) and number of binding sites (N) were determined. The binding was found to go through separate stages, where the binding affinity tends to become lower; the first step characterized by kI = 7.6 x 10(6) l.mol-1 and NI = 1.4; while for the second step kII = 1.7 x 10(6) l.mol-1 and NII = 6.6. On the basis of the CD-data and using UV-spectra the nature of binding sites was studied. It may be stated that the binding sites are situated in the region of asymmetrically perturbed chromophore of the drug, which made a positive contribution to the Cotton effect. The results obtained suggest a mechanism of interaction which is consistent with the stepwise binding model.

New algorithm for analysis of data obtained by means of circular dichroism titration method

A new method for analysis of circular dichroism titration data used for drug-protein binding investigations is proposed. A square equation between molar ellipticity change and total drug concentration is obtained which is examined analytically. A new minimization algorithm for determining the binding sites and association constants of each type of drug-protein complexes is applied.