Refinements to the boundary transformation vector representation of attractor shape deformation to enhance system parameter identification.

A new method of quantifying parameter changes in chaotic systems using estimates of how the boundaries of Poincare sections deform was recently developed. Refinements that improve the number and quality of the boundary transformation vectors produced by this method are proposed and analyzed here. Collectively, these refinements offer the ability to better match closely spaced linear segments of Poincare sections typical of fractal geometry, better handle boundary gaps, and more uniformly sample the boundary, resulting in additional data. The refinements are tested using Poincare sections constructed in three ways for five different dynamical systems and are shown to enhance results in all cases.

A medical needle drive for the study of interstitial implant mechanics.

We describe the construction and test performance of a computer-controlled medical needle drive. The drive represents one facet of a larger project whose aim is to investigate experimentally the mechanics of needle introduction in radioactive 'seed' prostate implants, with a view to identifying ways of making incremental improvements in needle placement accuracy. It is capable of mimicking a range of motions imparted to a needle by a clinical practitioner, and of monitoring the compressive force at the needle tip in real time via an in-line load cell. Tests involving driving needles into porcine gelatin samples using a variety of velocity profiles confirm intended operation. The drive will permit us to introduce needles in a controlled and reproducible manner into a realistic prostate phantom currently being designed.

Experimental determination of the anisotropy function and anisotropy factor for model 6711 I-125 seeds.

Model 6711 125I seeds are commonly used in permanent brachytherapy implants. While recommended dose distribution parameters for these sources have been published by AAPM TG-43, several investigators have recently questioned the presence of seemingly unphysical fluctuations in the anisotropy function data. Seeking to understand these, we measured the dimensions of eight model 6711 seeds radiographically, and made a new experimental determination of the anisotropy function and factor using thermoluminescent dosimeters (TL-100 chips and minicubes) in a solid water phantom. It was found that variations in seed capsule end weld thickness, and movement within the capsule of the Ag rod onto which the 125I is adsorbed, were present for all sources and thus contributed to experimental uncertainty. Averaging results from two different sources, from data acquired at the same time from diametrically opposed quadrants of the phantom, and from repeated measurements yielded anisotropy function values similar to those of TG-43 but characterized by greater precision (< or = 3% for radial distance r < or = 3 cm and < or = 1% for r > or = 4 cm), an absence of sharp fluctuations, and reduced magnitudes at r = 1 cm. The measured values can be well represented by an analytic function similar to that proposed by Furhang and Anderson to fit the TG-43 data. Values of the anisotropy factor derived from this function by integration exhibit little variation with r, in agreement with earlier diode data but in contrast to TG-43 data, and can also be represented by an analytic function. Finally, a difference in TLD chip and minicube reproducibility, observed here and by earlier investigators, is explained by reference to recent work (done concurrently with ours) as stemming from variations in dosimeter orientation and automated reader positioning/heating for minicubes.

Combined experimental and Monte Carlo verification of 137Cs brachytherapy plans for vaginal applicators.

Dose rates in a phantom around a shielded and an unshielded vaginal applicator containing Selectron low-dose-rate 137Cs sources were determined by experiment and Monte Carlo simulation. Measurements were performed with thermoluminescent dosimeters in a white polystyrene phantom using an experimental protocol geared for precision. Calculations for the same set-up were done using a version of the EGS4 Monte Carlo code system modified for brachytherapy applications into which a new combinatorial geometry package developed by Bielajew was recently incorporated. Measured dose rates agree with Monte Carlo estimates to within 5% (1 SD) for the unshielded applicator, while highlighting some experimental uncertainties for the shielded applicator. Monte Carlo calculations were also done to determine a value for the effective transmission of the shield required for clinical treatment planning, and to estimate the dose rate in water at points in axial and sagittal planes transecting the shielded applicator. Comparison with dose rates generated by the planning system indicates that agreement is better than 5% (1 SD) at most positions. The precision thermoluminescent dosimetry protocol and modified Monte Carlo code are effective complementary tools for brachytherapy applicator dosimetry.

Monte Carlo dosimetry of the VariSource high dose rate 192Ir source.

The purpose of the work is to calculate basic dosimetry data for a VariSource high dose rate 192Ir source in water. These basic dosimetry data, expressed in the dose calculation formalism endorsed by the Interstitial Collaborative Working Group and AAPM Task group 43, include the dose rate constant, the radial dose function, and the anisotropy function. A modified version of the EGS4 Monte Carlo code was used to calculate (1) the transverse-axis dose distribution at radial distances from 0.1 to 14 cm, (2) the two-dimensional dose distribution for axial and radial distances from 0.1 cm to 10 cm, and (3) the air-kerma strength, for the VariSource high dose rate 192Ir source. From these Monte Carlo results the basic dosimetry data were derived. The calculated dose rate constant for the high dose rate source is 1.044 +/- 0.2% cGy h-1 per unit air-kerma strength. The anisotropy function exhibits 40%-60% deviations from isotropy at positions on the long axis. The radial dose function for the source is nearly identical to that for a microSelectron high dose rate 192Ir source, except at radial distances smaller than 0.5 cm where values for VariSource are 1.7%-2.8% smaller. These basic dosimetry data were compared with corresponding results from other authors for high and low dose rate 192Ir sources, as well as with Meisberger's fitting formula.

Influence of source geometry and materials on the transverse axis dosimetry of 192Ir brachytherapy sources.

Monte Carlo dose rates on the transverse axis in water and air kerma strengths normalized to unit source activity were calculated for a low dose rate steel-clad 192Ir source. MicroSelectron high dose rate and pulsed dose rate 192Ir sources, and a VariSource high dose rate 192Ir source, as well as five other hypothetical cylindrical 192Ir source designs. Based on these results, the dependence of dose rate and air kerma strength on source geometry and materials was analysed. Source geometry and attenuation in the core material are the important factors determining basic dosimetric characteristics. Core length, h, only affects the dose rate on the transverse axis at radial distances r < 4 h, over which the dose rate decreases nonlinearly with increasing core length. By comparison, core diameter, d, influences the air kerma strength and dose rate at all radial distances; these decrease linearly with increasing core diameter. Based on their dosimetric characteristics, pertinent dosimetry modelling for four actual 192Ir sources is suggested, and similarities and differences in the dose rate constant and radial dose function between these sources are explained.

Influence of catheter materials and tissue composition on low dose rate iridium-192 seed implant dosimetry.

PURPOSE: To quantify the perturbing influence of catheter materials and tissue composition on the dose distribution in water around a low dose rate, steel encapsulated Ir-192 seed. METHODS AND MATERIALS: The EGS4 Monte Carlo code was used to estimate point doses in a bounded phantom within a cylinder with a radius of 3 cm surrounding the source. Simulations were performed in water and soft tissue media for an unadorned seed, and then in soft tissue for a nylon-ribbon-encased seed inside steel and nylon catheters. The latter simulations were repeated including inactive seeds on either side of the source at spacings of 1.0 and 0.5 cm. Sufficient numbers of photon histories were run to reduce the relative statistical uncertainty of most dose estimates to <0.1%. Contributions from primary and scattered photons were scored separately. RESULTS: For the unadorned source, doses in soft tissue were uniformly approximately 1% lower than in water. Introduction of either catheter perturbed the dose in soft tissue by <0.4% along the transverse source axis, r. In the long axis direction, d, dose in soft tissue for the steel catheter relative to the unadorned source fell with increasing distance and decreasing radius, r, and trended oppositely for the nylon catheter. Neighboring seeds did not affect the dose distribution except at r = 0.2 cm for seeds spaced at 0.5 cm, where dose fell approximately 8% in the interval d = 4-7 cm. For several Paris system implant geometries, the presence of catheters altered basal doses in a systematic manner. CONCLUSION: Perturbations of the dose distribution for LDR Ir-192 seeds in water introduced by treatment catheters and tissue composition are small but systematic. If desired, they can be accounted for in clinical volumes of interest by simple adjustment of dose calculation parameters.

Linear accelerator photon beam quality at off-axis points.

Transmitted intensity through water was measured in a narrow-beam geometry for different energy x-ray beams from commercial accelerators. In order to accurately obtain the attenuation coefficient of the incident beam using transmission data, a novel formula was developed based on consideration of beam hardening in phantom. The value of the attenuation coefficient obtained by fitting transmission data to this formula was found to be independent of the absorber thickness used in experiments, whereas the attenuation coefficient obtained from the traditional formula, I(x) = I0 exp(-mux), changed by up to 7% with absorber thickness for a given beam. The beam hardening coefficient obtained from our formula indicates that the attenuation coefficient in water changes by about 0.33% per cm near the surface for the high-energy photon beams studied. Variations in beam quality with off-axis distance were subsequently investigated using the new formula. Results show that the attenuation coefficient at the water surface increased by about 15% for 15 and 18 MV beams, and by 11%-13% for 6 MV beams, when the off-axis distance at 100 cm from the source was changed from 0 to 18 cm. Consideration of the physics of bremsstrahlung production suggests that these variations should be mainly determined by the shape of the flattening filter, i.e., by the path length of rays traversing the filter in different directions. This expectation was confirmed by observing that the attenuation coefficient at the phantom surface can be related to the ray path of the beam in the flattening filter using the new transmission formula.

Effect of beam blocking on linac head scatter factors.

PURPOSE: This study aimed to investigate the influence of beam blocking on head scatter within the context of a two-component x-ray source model. METHODS AND MATERIALS: Head scatter factors were measured for open rectangular fields defined by X and Y jaws and for fields blocked by a multileaf collimator (MLC) for a 6-MV photon beam from a Varian 2300CD accelerator. A simple formula based on consideration of linac head geometry and an x-ray source model was derived to determine when the head scatter factor for a shaped field depends only on jaw settings and when it is influenced by the blocking (cerrobend blocks or MLC) itself. RESULTS: Experimental data demonstrate that the assumption that head scatter is unaffected by the introduction of beam blocking is not always acceptable, particularly for fields blocked by an MLC. The ratios of open to blocked field dimensions were compared with simple functions characterizing the accelerator head geometry to predict changes in the behavior of head scatter factors observed experimentally. CONCLUSION: A simple formula can be used to determine when head scatter factors are influenced by beam blocking (cerrobend blocks or MLC).

EGS4 dosimetry calculations for cylindrically symmetric brachytherapy sources.

Computer algorithms for electron binding correction to Compton scattering and for detailed simulation of K-edge characteristic x-ray production were incorporated into EGS4 unix version 2.0. Based on detailed modelling of the internal structures of sources, the modified version was used to calculate dose rate constants, radial dose functions, and anisotropy functions on the long axis for an 125I model 6711 source, 169Yb Type 5 and Type 8 sources, and a stainless steel clad (SS) 192Ir source. The geometry of these sources is cylindrically symmetric. Calculated results are generally in good agreement with corresponding values recommended by TG-43 and Monte Carlo results published by other authors. The influence of electron binding in Compton scattering on the calculated dose distribution for an 125I model 6711 source in water, and of different characteristic x-ray production models for 125I model 6711 and 192Ir SS sources, were also studied.

Measurement of photon beam backscatter from collimators to the beam monitor chamber using target-current-pulse-counting and telescope techniques.

Backscattered radiation (BSR) arising from field-defining collimators and entering the beam monitor chamber (BMC) may contribute to observed variations in medical linear accelerator photon beam output with collimator setting. Measuring the magnitude of such contributions for particular accelerators under specified operating conditions is therefore important when attempting to understand and model accelerator head scatter. The present work was conducted to confirm some backscatter measurements for collimating jaws reported previously and to extend these to include other accelerators and a multileaf collimator (MLC). BSR reaching the BMC from the jaws of Clinac 600C, 2100C and 2300CD accelerators and from an MLC on the 2300CD was investigated using both target-current-pulse-counting and telescope methods. Our measurements show that for the Clinac 600C BSR-dependent output variations are negligible. However, for the 2100C and 2300CD BSR-dependent relative output increased in an almost linear fashion, by up to 2.4% for 15 and 18 MV beams, and by up to 1.7% for 6 MV beams, as the field size varied from 5 x 5 cm2 to 40 x 40 cm2. The magnitude of BSR dependent upon collimator location in the head, as expected, thereby contributing to the collimator exchange effect. An earlier study at our centre using the telescope method had reported higher BSR levels. This discrepancy was resolved when corrections for telescope block and room scatter, previously assumed negligible, were made.

Optimized low dose rate pellet configurations for intravaginal brachytherapy.

PURPOSE: The objective was to identify configurations of low dose rate pellet sources that optimize short treatment length brachytherapy dose distributions for a set of four intravaginal applicators. METHODS AND MATERIALS: The method of simulated annealing was used. Dose rates at calculation points on the surface of 2.0, 2.5, 3.0, and 3.5 cm diameter applicators along a fixed 3.0 cm treatment length were optimized for Cs-137 sources of strengths 0.74 and 0.63 GBq in trains having maximum lengths of 3.0, 3.5 and 4.0 cm. Variations in the optimization algorithm involving two different objective functions and different combinations of selectable parameters were investigated in an effort to standardize the approach. RESULTS: An objective function based on the maximum dose rate difference at the calculation points in conjunction with a single parameter set proved suitable for all applicators. Optimized solutions involving both a single configuration of sources and a combination of two such configurations were successfully identified. The latter consistently afforded superior dose rate uniformity, particularly for the smaller diameter applicators. A maximum source train length of 3.5 cm was found to provide a good compromise between attaining dose rate uniformity along the 3.0 cm treatment length and minimizing irradiation of adjacent normal tissues. For each applicator, an optimized 3.5 cm pellet train yielded better surface dose rate uniformity than a corresponding optimum-length linear source. CONCLUSION: Pellet configurations that optimize dose distributions for intravaginal brachytherapy applicators can be reliably identified with modest computational effort using the method of simulated annealing. The method is therefore suitable for use in routine clinical treatment planning for this site.

Optimization of brachytherapy dose distributions by simulated annealing.

An algorithm based on the method of simulated annealing is presented for optimizing brachy-therapy dose distributions. The algorithm accommodates either static configurations of multiple sources or single stepping sources, hence in principle can be used to optimize both low- and high-dose rate treatments delivered with remote afterloading equipment. Required inputs include the specification of target dose rates and dose rate limits, expressed in absolute or relative terms, at operator selected points near the treatment site. The influence of the dose rate limits can be adjusted continuously through the use of one or more penalty factors. The algorithm generates a set of integer weights, one for each available source position, which are interpreted in terms of configuration occupancy numbers for static source arrangements and relative dwell times for stepping sources. Application is made to several variations of a hypothetical low-dose rate vaginal vault planning problem involving one rectal and six applicator calculation points. The algorithm's performance for different source strengths, annealing schedules, target dose rates, dose rate limits, and values of a single penalty factor lambda was examined. With a simple annealing schedule and value of lambda = 25, the algorithm found solutions of high quality for all problem variants. The CPU time required for optimization on a Vax 11/750 computer ranged from 2 min for a single configuration to 25 min for a solution consisting of four configurations. These results support the use of simulated annealing for clinical planning of low dose rate vaginal treatments, and encourage investigation of other applications in brachytherapy.

Vector implementation of Chang's attenuation correction method for single photon emission computed tomography.

A vector version of Chang's attenuation correction method for single photon emission computed tomography accommodating arbitrary convex body contours is presented and its implementation on a general purpose array processor described. For a constant linear attenuation coefficient mu = 0.10 cm-1 and contour shapes similar to those encountered in clinical work, correction factors calculated with the vector algorithm are the same to within a few percent as those obtained using the original Chang method. Typical execution speed of the new algorithm is 0.01 s/correction factor for a 64 point contour.

Subtraction of simultaneously acquired dual radionuclide images.

The physical aspects of a simultaneous dual radionuclide technique incorporating computer subtraction for the diagnosis of infection using 67Ga citrate and 99mTc methylene diphosphonate (MDP) or sulfur colloid are considered. The efficacy of the data acquisition protocol and the interpretation of the subtracted images are shown to depend significantly on fundamental imaging system parameters. Measurement of these parameters using simple phantoms and their role in elucidating the technique is detailed. Subtracted images produced by three variations of the basic method arising from different normalization algorithms in current usage are compared. Simple phantoms are again used in assessing the accuracy of each variation. Clinical results are reported elsewhere.

A dynamic quality control phantom for radionuclide cardiology.

A three-dimensional dynamic cardiac phantom suitable for quality control of equilibrium gated nuclear cardiographic procedures is described. Its flexible microprocessor based design provides an absolute standard for ejection fraction determination, ventricular volume quantitation, and physiologically gated single photon emission computed tomography. The cost of the phantom is comparable to that of commercially available phantoms suitable for ejection fraction quality control alone.