Applying radiobiological plan ranking methodology to VMAT prostate SBRT.

The impact of a rectal spacer and an increased near maximum target dose in VMAT prostate SBRT is studied. For a group of 11 patients (35Gy-in-five-fractions VMAT prostate SBRT) a set of 4 plans were generated, namely two VMAT plans, with D2%⩽37.5Gy (Hom) and with D2%⩽40.2Gy (Het), were created for each of two CT scans taken before (NoSpc) and after (Spc) transperineal spacer insertion. Consequently the methodology for parameter invariant TCP (tumor control probability) plan ranking was applied for comparison of the plans in terms of tumor control. NTCPs (normal tissue complication probabilities) were calculated for rectum and bladder using Lyman's model. For all 11 patients the TCP plan ranking has shown that the Het plans would perform considerably better in TCP terms than the Hom ones. The plans without rectal spacer were ranked worse compared to those with rectal spacer except for one set of Hom plans. The calculated NTCPs for rectum produced by the Het plans were quite similar to the NTCPs of the Hom ones. The rectal NTCPs of the Hom Spc plans were always lower than the NTCPs of the Hom NoSpc plans. The NTCP values for bladder were extremely low in all cases. The use of rectal spacer leads in general to lower risk of rectal complications, as expected, and even to better tumor control. Plans with increased near maximum target dose (D2%⩽40.2Gy) are expected to perform much better in terms of tumor control than those with D2%⩽37.5Gy.

Confidence limits of the probability of success in animal experiments and clinical studies: a Bayesian approach.

PURPOSE: To determine from the number of trials, n, and the number of observed successes, k the most probable value, the variance and the confidence limits of the probability of success, p, in animal experiments and clinical studies subject to binomial statistics. METHOD: In such experiments the probability of success is an unknown parameter. The Bayesian approach to the problem is advocated, based on constructed distribution of the probability of success. RESULTS: A simple Matlab code for the calculation of the confidence limits according to the proposed method is provided. The most probable, the mean, the variance and the confidence limits are calculated applying the usual definitions of these characteristics. CONCLUSION: The proposed method works for any number of trials--large and small and all possible values of the number of successes, including k=0 and k=n, providing exact formulae for the calculation of the confidence limits in all cases.

Effect of epoetin zeta for correction of renal anemia in hemodialysis patients with thalassemia minor.

Two patients with thalassemia minor and end-stage renal failure on hemodialysis were treated with epoetin zeta (Silapo, Retacrit; STADA, Germany), a medicinal product that was developed and registered as biosimilar to epoetin alfa. Dosing was titrated individually for two patients to achieve a stable hemoglobin (Hb) concentration of 10.5-12.0 g/dL. One patient was treated intravenously with epoetin zeta; the other patient was treated subcutaneously. After 12 weeks of therapy both patients achieved Hb levels within the target range, confirming the effi cacy of epoetin zeta in patients with thalassemia minor.

A study on the magnetic resonance imaging (MRI)-based radiation treatment planning of intracranial lesions.

The aim of this study is to develop a magnetic resonance imaging (MRI)-based treatment planning procedure for intracranial lesions. The method relies on (a) distortion correction of raw magnetic resonance (MR) images by using an adaptive thresholding and iterative technique, (b) autosegmentation of head structures relevant to dosimetric calculations (scalp, bone and brain) using an atlas-based software and (c) conversion of MR images into computed tomography (CT)-like images by assigning bulk CT values to organ contours and dose calculations performed in Eclipse (Philips Medical Systems). Standard CT + MRI-based and MRI-only plans were compared by means of isodose distributions, dose volume histograms and several dosimetric parameters. The plans were also ranked by using a tumor control probability (TCP)-based technique for heterogeneous irradiation, which is independent of radiobiological parameters. For our 3 T Intera MRI scanner (Philips Medical Systems), we determined that the total maximum image distortion corresponding to a typical brain study was about 4 mm. The CT + MRI and MRI-only plans were found to be in good agreement for all patients investigated. Following our clinical criteria, the TCP-based ranking tool shows no significant difference between the two types of plans. This indicates that the proposed MRI-based treatment planning procedure is suitable for the radiotherapy of intracranial lesions.

Limitations of a TCP model incorporating population heterogeneity.

The variation between individuals in their dose-response characteristics complicates attempts to extract estimates of radiobiological parameters (e.g. alpha, beta, etc) from fits to clinical dose-response data. The use of 'population' dose-response models that explicitly account for this variability is necessary to avoid obtaining skewed parameter estimates. In this work, we evaluated an example of a 'population' tumour control probability (TCP) model in terms of its ability to provide reliable parameter estimates. This was accomplished by performing fits of this population model to 'pseudo' data sets, which were generated with Monte Carlo techniques and based on preset values for the various radiobiological parameters. The fitting exercises illustrated considerable correlations between the model parameters. Especially significant was the large correlation observed between the parameter mu=alpha/sigmaalpha used to characterize the level of population heterogeneity in radiosensitivity and the alpha/beta parameter typically used to describe the response to fractionation. The results imply that fits to clinical data may not be able to distinguish between tumours exhibiting a high degree of heterogeneity and a strong beta-mechanism and those containing little heterogeneity and having a weak beta-mechanism. One implication is that basing the design of optimal fractionation regimes on such fitting results may be error-prone. If in vitro assays are to be used to independently determine biologically reasonable ranges for parameter values, an accurate knowledge of the relationship between in vitro and in vivo dose-response characteristics is required.

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 of in vitro tumour 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.

Investigating the effect of clonogen resensitization on the tumor response to fractionated external radiotherapy.

In this work we further develop the modeling of tumor dynamics by proposing a mechanism of tumor resensitization that is based on the process of reoxygenation. Reoxygenation is modeled using the concept of nonstationary diffusion of oxygen. This leads to the derivation of an explicit expression for the radiosensitivity parameter that predicts a radiosensitivity that increases with time. To account for the resensitization mechanism, the time-dependent expression for the radiosensitivity is then incorporated within a tumor control probability (TCP) model that already includes tumor cell repopulation and repair. We fit a set of experimental animal TCP curves corresponding to several different fractionation regimes using both the modified (with resensitization) and unmodified (without resensitization) versions of the TCP model. In comparison to the unmodified model, the modified model produces statistically superior fits, and is able to describe an "inverse" dose-fractionation behavior present in the data.

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.

Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy.

In this work we study the descriptive power of the main tumor control probability (TCP) models based on the linear quadratic (LQ) mechanism of cell damage with cell recovery. The Poisson, binomial, and a dynamic TCP model, developed recently by Zaider and Minerbo are considered. The Zaider-Minerbo model takes cell repopulation into account. It is shown that the Poisson approximation incorporating cell repopulation is conceptually incorrect. Based on the Zaider-Minerbo model, an expression for the TCP for fractionated treatments with varying intervals between two consecutive fractions and with cell survival probability that changes from fraction to fraction is derived. The models are fitted to an experimental data set consisting of dose response curves that correspond to different fractionation regimes. The binomial TCP model based on the LQ mechanism of cell damage solely was unable to fit the fractionated response data. It was found that the Zaider-Minerbo model, which takes tumor cell repopulation into account, best fits the data.

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.

On the implementation of dose-volume objectives in gradient algorithms for inverse treatment planning.

A method that allows a straightforward implementation of dose-volume constraints in gradient algorithms for inverse treatment planning is presented. The method is consistent with the penalty function approach, which requires the formulation of an objective function with penalty terms proportional to the magnitudes of constraint violations. Dose constraints with respect to minimum and maximum target dose levels are incorporated in quadratic, dose-penalty terms. Analogously, quadratic volume-penalty terms in the objective function reflect the violation of dose-volume constraints imposing limits on the fractions of healthy organ volumes that can be irradiated above specified dose levels. It has been demonstrated that within the framework of this formulation neither modified objective functions nor finite difference gradient calculations are necessary for the incorporation of gradient minimization algorithms. As an example, a simple steepest descent algorithm is presented along with its application to illustrate prostate and lung cases.

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.

Surgical correction of funnel chest.

AIM: To present our experience in surgical treatment of funnel chest. MATERIAL AND METHODS: Seven patients (6 males and 1 female) aged 13 to 18 years were treated in the Department using Rathke-Schlegel's modification of Ravitch operative technique. In 2 patients the corrected deformity status was maintained by 2 Kirschner's pins that were placed substernally and attached bilaterally to the adjacent ribs. In one patient a direct traction through the sternum was applied and in 4 patients the fixation was achieved by fastening the sternum with wire loops to an overlying AO plate. RESULTS: Very good results were achieved in 4 patients (57.14%) and a good outcome was evaluated in 3 patients with 30% recurrence of the deformity. There was no lethal outcome. Three complications were encountered: in one patient hemothorax occurred that was cured by a single punction aspiration, in other patient one of the Kirschner's pins slipped into the thoracic cavity. The pin but did not injure intrathoracic organs and was promptly removed. In the third patient earlier removal of the plate was required because suppuration developed. CONCLUSION: The presented method for correction of chest deformity is successful if the implants are kept in place from 6 to 12 months. This time is sufficient for formation of a solid callus that prevents recurrence of the deformity.

Dynamic follow-up of the intact parathormone levels in hemodialysis patients treated with Rocaltrol and calcium.

UNLABELLED: The object of the present study was to follow prospectively the serum levels of intact parathormone (PTH) of hemodialysis patients and the subsequent changes following the oral administration of 1.25(OH)D3 and calcium. METHODS: We studied 30 chronic renal failure hemodialysis patients--16 men and 14 women, aged 20-70 years. Twenty-one of them were on hemodialysis with duration of up to 5 years (Group 1) and nine--up to 10 years (Group 2). All patients received oral supplementation therapy with 1.0 elemental calcium and Rocaltrol (Roche) 0.25 microgram/day. We measured the serum calcium, ionized calcium, serum phosphorus, alkaline phosphatase and the intact serum PTH levels in intervals of 12 months. RESULTS: Patients with duration of dialysis of up to 5 years had a significantly lower baseline PTH level of 392.5 +/- 94.7 pg/ml versus 896.4 +/- 160.7 pg/ml for those from the second group (P < 0.01). The intact PTH levels showed a tendency towards decrease--at the end of the study they were as follows: 372.02 +/- 76.9 for group 1 versus a significant increase for those from group 2--serum PTH levels of 1793.65 +/- 290.3 (P < 0.02). The differences in alkaline phosphatase and serum phosphorus levels at the end of the study period failed to reach statistical significance. Serum calcium levels were increased in both groups following the initiation of treatment but the difference was statistically significant only for group 2. A significant positive correlation was observed between the duration of hemodialysis treatment and the intact serum PTH levels. CONCLUSIONS: 1. Long-term low-dose conventional calcitriol therapy in combination with calcium supplementation could slow the progression of secondary hyperparathyroidism in some hemodialysis patients. 2. Low-dose therapy with active vitamin D-metabolites is effective only in hemodialysis patients with baseline serum PTH levels below 500 pg/ml and without pronounced hyperphosphatemia.

A study of objective functions for organs with parallel and serial architecture.

An objective function analysis when target volumes are deliberately enlarged to account for tumour mobility and consecutive uncertainty in the tumour position in external beam radiotherapy has been carried out. The dose distribution inside the tumour is assumed to have logarithmic dependence on the tumour cell density which assures an iso-local tumour control probability. The normal tissue immediately surrounding the tumour is irradiated homogeneously at a dose level equal to the dose D(R) delivered at the edge of the tumour. The normal tissue in the high dose field is modelled as being organized in identical functional subunits (FSUs) composed of a relatively large number of cells. Two types of organs--having serial and parallel architecture are considered. Implicit averaging over intrapatient normal tissue radiosensitivity variations is done. A function describing the normal tissue survival probability S0 is constructed. The objective function is given as a product of the total tumour control probability (TCP) and the normal tissue survival probability S0. The values of the dose D(R) which result in a maximum of the objective function are obtained for different combinations of tumour and normal tissue parameters, such as tumour and normal tissue radiosensitivities, number of cells constituting a normal tissue functional unit, total number of normal cells under high dose (D(R)) exposure and functional reserve for organs having parallel architecture. The corresponding TCP and S0 values are computed and discussed.

Acute renal failure--etiologic and therapeutic considerations. A five-year experience at a single institution.

In the present study we highlight the epidemiology, etiologic spectrum, and evaluation of ARF in adults. We then expand on the pathophysiologic mechanisms of renal failure and discuss the rationale for current therapeutic strategies in ARF patients. A total of 79 patients (45 male, female 34), aged 18-75 years (median age 51.2 +/- 17.7 years) with acute renal failure were studied in 5 years (January 1990 through October 1995). Emergency hemodialysis sessions following an acute anuric episode were instituted in 39 cases (49.3% of all patients). The median number of hemodialysis procedures per patient treated at our institution was 3.2 +/- 1.9. The total number of acute interstitial nephritis-associated ARF was 40. In 30 of them (75%) the acute renal insult included a combination of several therapeutic antimicrobial agents, in 2 cases (5%) ARF followed the administration of nonsteroidal anti-inflammatory drugs, in 1 (2.5%) it resulted from a combined therapeutic regimen and in the remaining 5 (12.5%) from the application of a single drug. Acute interstitial nephritis developed in 2 patients following a viral infection. In the hemodialysis-treated ARF group 12 patients (29.77%) had interstitial nephritis and 2 patients (5.13%) presented with renal impairment for an unspecified period of time preceding the development of overt ARF. In a subset of this group of patients, ARF occurred in 7 patients (17.95%) following an urologic intervention, in 8 patients (20.51%) as a consequence of thermal or mechanical trauma or intoxication and in 3 cases (7.69%) it resulted from fever of unknown origin. Three patients with postoperative peritonitis and 4 other (10.26%) with postoperative complications were encountered in our series. No cases of septic abortion-related or obstetric-related ARF were recorded. 92.3% of all hemodialysis-treated patients seen at our Institution had received a combination of antibiotics and only 2 patients had been pre-treated with a single antimicrobial agent. Our results underscore the strong tendency towards diversity in the etiologic spectrum of clinical entities causing ARF and the increase in the number of acute interstitial nephritis. These factors highlight the importance of precise dosing and administration of drugs, especially antibiotics, as well as the duration of antibiotic treatment.