Dosimetric consequences of pancreatic tumor motion when predetermined treatment margins are employed during intensity-modulated radiation therapy.

PURPOSE: To quantify the dosimetric consequences of pancreatic tumor motion on the pancreatic intensity-modulated radiation therapy (IMRT) plans. METHODS: Dose map of IMRT plans for 5 patients with pancreatic cancer were measured using a 2D diode array placed on a computer-controlled platform to simulate 2D pancreatic tumor motion. Dosimetric analysis was then performed to obtain IMRT quality assurance (QA) passing rates. The convolution method, which used a motion kernel to simulate 2D pancreatic motion, was also applied to the treatment and phantom verification plans for a wide range of magnitudes of motion (0.8-2.0 cm). The resulting motion-convolved verification dose maps (VDMs) were compared with the dynamic measurements to evaluate IMRT QA passing rates as well as the dose-volume histogram, the V95% of the planning target volume (PTV) and V98% of the clinical target volume (CTV). RESULTS: While CTV coverage was maintained when the simulated pancreatic tumor drifted inside the PTV with magnitudes of 1.0 cm and 1.5 cm, the V95% of the PTV was reduced by 10% and 17%, respectively. We also found that the differences between the measurements and the static VDMs increased proportional to the amplitude of motion, while the agreement between the measurements and the motion-convolved VDMs was excellent for any magnitude of motion. CONCLUSIONS: When the 4D technique is not available, predetermined margins must be used carefully to avoid possible under-dose to the target. Additionally, the phantom results show that the kernel convolution method provides an accurate evaluation of the dosimetric impact due to tumor motion and it should be employed in the planning process.

SU-E-T-523: Modeling Beam Data for Flattening Filter Free (FFF) Photon Beams.

PURPOSE: For flattening-filter free (FFF) photon beams, conventional algorithm based on equivalent-square to calculate dose per MU is invalid because of the non-uniform profile. In this study, an empirical algorithm is developed to calculate the dose accurately, which can be used for secondary MU check for IMRT using FFF beams. METHODS: A kernel-based algorithm based on three parameters (a0, w0, d0) is used to quantify the phantom scatter characteristics of the photon beam. The model is modified to quantify the shape of the FFF at off-axis locations by fitting the primary off-axis ratio (POAR) by a linear function 1 - br, where b is a constant and r is the radial distance. The resulting parameters are used in a kernel-based dose calculation algorithm for dose calculation. RESULTS: It is found that the proposed model can fit the product of the fractional depth doses (FDD) and phantom scatter factors (Sp) for field sizes between 2 and 40 cm and depth between 0 and 40 cm to a max and standard deviations of 1.7% and 0.01% and 1.8% and 0.01%, respectively, for 6 and 10 MV FFF beams. The value of b is 0.025 and 0.0323 for 6 MV and 10 MV photons, respectively, from fitting the POAR. The resulting phantom scatter parameters are consistent with those obtained from MC simulation. If the slope is not taken into account (b = 0), then the model cannot fit the central-axis Sp*FDD accurately and resulted in a maximum error of 3% and 4% for 6 and 10 MV, respectively. CONCLUSIONS: We have demonstrated that the shape of POAR from FFF beam will impact on the dose calculation on the central-axis. Conventional equivalent square law concept will not be applicable for dose calculation for FFF beams.

Preliminary results of interstitial motexafin lutetium-mediated PDT for prostate cancer.

BACKGROUND AND OBJECTIVES: Interstitial photodynamic therapy (PDT) is an emerging modality for the treatment of solid organ disease. Our group at the University of Pennsylvania has performed extensive studies that demonstrate the feasibility of interstitial PDT for prostate cancer. Our preclinical and clinical experience is herein detailed. STUDY DESIGN/MATERIALS AND METHODS: We have treated 16 canines in preclinical studies, and 16 human subjects in a Phase I study, using motexafin lutetium-mediated PDT for recurrent prostate adenocarcinoma. Dosimetry of light fluence, drug level and oxygen distribution for these patients were performed. RESULTS: We demonstrate the safe and comprehensive treatment of the prostate using PDT. However, there is significant variability in the dose distribution and the subsequent tissue necrosis throughout the prostate. CONCLUSIONS: PDT is an attractive option for the treatment of prostate adenocarcinoma. However, the observed variation in PDT dose distribution translates into uncertain therapeutic reproducibility. Our future focus will be on the development of an integrated system that is able to both detect and compensate for dose variations in real-time, in order to deliver a consistent overall PDT dose distribution.

Photodynamic therapy with motexafin lutetium for rectal cancer: a preclinical model in the dog.

PURPOSE: Local recurrence of rectal cancer remains a significant clinical problem despite multi-modality therapy. Photodynamic Therapy (PDT) is a cancer treatment which generates tumor kill through the production of singlet oxygen in cells containing a photosensitizing drug when exposed to laser light of a specific wavelength. PDT is a promising modality for prevention of local recurrence of rectal cancer for several reasons: tumor cells may selectively retain photosensitizer at higher levels than normal tissues, the pelvis after mesorectal excision is a fixed space amenable to intra-operative illumination, and PDT can generate toxicity in tissues up to 1 cm thick. This study evaluated the safety, tissue penetration of 730 nm light, normal tissue toxicity and surgical outcome in a dog model of rectal resection after motexafin lutetium-mediated photodynamic therapy. METHODS: Ten mixed breed dogs were used. Eight dogs underwent proctectomy and low rectal end to end stapled anastomosis. Six dogs received the photosensitizing agent motexafin lutetium (MLu, Pharmacyclics, Inc., Sunnyvale, CA) of 2 mg/kg preoperatively and underwent subsequent pelvic illumination of the transected distal rectum of 730 nm light with light doses ranging from 0.5 J/cm(2) to 10 J/cm(2) three hours after drug delivery. Two dogs received light, but no drug, and underwent proctectomy and low-rectal stapled anastomosis. Two dogs underwent midline laparotomy and pelvic illumination. Light penetration in tissues was determined for small bowel, rectum, pelvic sidewall, and skin. Clinical outcomes were recorded. Animals were sacrificed at 14 days and histological evaluation was performed. RESULTS: All dogs recovered uneventfully. No dog suffered an anastomotic leak. Severe tissue toxicity was not seen. Histological findings at necropsy revealed mild enteritis in all dogs. The excitation light penetration depths were 0.46 +/- 0.18, 0.46 +/- 0.15, and 0.69 +/- 0.39 cm, respectively, for rectum, small bowel, and peritoneum in dogs that had received MLu. For control dogs without photosensitizer MLu, the optical penetration depths were longer: 0.92 +/- 0.63, 0.67 +/- 0.10, and 1.1 +/- 0.80 cm for rectum, small bowel, and peritoneum, respectively. CONCLUSION: Low rectal stapled anastomosis is safe when performed with MLu-mediated pelvic PDT in a dog model. Significant tissue penetration of 730 nm light into the rectum and pelvic sidewall was revealed without generation of significant toxicity or histological sequelae. Penetration depths of 730 nm light in pelvic tissue suggest that microscopic residual disease of less than 5 mm are likely to be treated adequately with MLu-mediated PDT. This approach merits further investigation as an adjuvant to total mesorectal excision and chemoradiation for rectal cancer.

Characteristics of bremsstrahlung in electron beams.

Clinical electron beams contain an admixture of bremsstrahlung produced in structures in the accelerator head, in field-defining cerrobend or lead cutouts, and in the irradiated patient or water phantom. Accurate knowledge of these components is important for dose calculations and treatment planning. In this study, the bremsstrahlung components are separated for electron beams (energy 6-22 MeV, diameter 0-5 cm) using measurements in water and calculations. The results show that bremsstrahlung from the accelerator head dominates and increases with field size for electron beams generated by accelerators equipped with scattering foils. The bremsstrahlung from the field-defining cerrobend accounts for 10% to 30% of the total bremsstrahlung and decreases with increasing beam radius. The bremsstrahlung is softer than the x-ray beams of corresponding nominal energy since the latter are hardened by the flattening filter. For the 6, 12, and 22 MeV electron beams, the effective attenuation coefficients in water for the bremsstrahlung are 0.058, 0.050, and 0.043 cm(-1). The depths of maximum dose at 100 cm SSD are 0.8, 1.7, and 3.0 cm. The position of the virtual source of the bremsstrahlung shifts downstream from the nominal source position by 20, 13, 5.6 cm, respectively. The lateral bremsstrahlung dose distribution is more forward-peaked for higher electron energy. The bremsstrahlung components could be described for any machine by a set of simple measurements and can be modeled by an analytical expression.

Modeling the output ratio in air for megavoltage photon beams.

The output ratio in air, OR, for a high-energy x-ray beam describes how the incident central axis photon fluence varies with collimator setting. For field sizes larger than 3 x 3 cm2, its variation is caused by the scatter of photons in structures in the accelerator head (primarily the flattening filter and the wedge, if one is used) and by the backscatter of radiation into the monitor ionization chamber. The objective of this study was to evaluate the use of an analytical function to parametrize OR for square collimator setting c: OR = (1 + a1.c).[1 + a2.erf(c/lambda)2].H0. For open beams, these parameters can be attributed to explicit physical meanings within the systematical uncertainty of the model: a1 accounts for backscatter into the monitor, a2 is the maximum scatter-to-primary ratio for head-scattered photons, and lambda represents the effective width of the "source" of head-scatter photons. H0 is a constant that sets OR = 1 for c = 10 cm. This formula also fits OR for wedge beams and a Co-60 unit, although the fitting parameters lose their physical interpretations. To calculate the output ratio for a rectangular field, cx x cy, an equivalent square can be used: c = (1 + k).cy x cx/(k.cx + cy), where k is a constant. The study included a number of different accelerators and a cobalt-60 unit. The fits for square fields agreed with measurements with a standard deviation (SD) of less than 0.5%. Using k = lx.(f - ly)/ly.(f - lx), where lx and ly are the source-to-collimator distances and f is the source-to-detector distance, measurements and calculations agreed within a SD of 0.7% for rectangular fields. Sufficient data for the three parameters are presented to suggest constraints that can be used for quality assurance of the measured output ratio in air.

Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy.

BACKGROUND AND OBJECTIVE: On-line monitoring of light fluence during intraperitoneal photodynamic therapy (IP PDT) is crucial for safe light delivery. A flat photodiode-based dosimetry system is compared with an isotropic detector-based system in patients undergoing IP PDT. STUDY DESIGN/MATERIALS AND METHODS: Flat photodiodes and spherical detectors were placed side by side in the abdomen, for simultaneous light dosimetry in 19 patients. Tissue phantom experiments were performed to provide a preliminary estimate of the tissue optical properties of the peritoneum. RESULTS: The conversion factor between systems for 630-nm light was found to be 1.7 +/- 0.12. The mu(eff) of the tissues in the abdomen is estimated to vary between 0.5 cm(-1) to 1.4 cm(-1) assuming a mu(s)' = 7 cm(-1). CONCLUSIONS: The measured conversion factor should allow for comparison of light fluences with future clinical protocols that use an isotropic-based detector system. Differences in the optical properties of the underlying tissues may contribute to the variability in light measurements.

The impact of primary tumor volume on local control for oropharyngeal squamous cell carcinoma treated with radiotherapy.

BACKGROUND: A study was needed to determine the effect of primary tumor volume on local control of oropharyngeal carcinoma treated with radiation therapy, with or without induction chemotherapy. METHODS: Between July 1983 and April 1995, 114 patients with T2-T4 squamous cell carcinoma of the oropharynx were treated for cure with radiation therapy, with or without induction chemotherapy, and had a pretreatment CT scan available for retrospective review. All scans were reviewed by a single radiologist (A. A. M.) to determine the tumor volume of the primary lesion. Volume was measured with a computer digitizer for each CT slice showing the primary lesion. RESULTS: A large variation in tumor volume within a given T stage was found. Multivariate analysis demonstrated T stage to be the most significant factor affecting local control. Tumor volume marginally influenced local control (p =.10). CONCLUSIONS: Primary tumor volume varies significantly within a given T stage and has a marginal impact on the likelihood of local control after radiotherapy.

A generalized solution for the calculation of in-air output factors in irregular fields.

Three major contributors of scatter radiation to the in-air output of a medical linear accelerator are the flattening filter, wedge, and tertiary collimator. These were considered separately in the development of an algorithm to be used to set up an in-air output factor calculation formalism for open and wedge fields of irregular shape. A detector's eye view (DEV) field defined at the source plane was used to account for the effects of collimator exchange and the partial blockage of the flattening filter by the tertiary collimator in the determination of head scatter. An irregular field determined at the source plane by a DEV was segmented and mapped back into the detector plane by a field-mapping method. Field mapping was performed by using a geometric conversion factor and equivalent field relationships for head scatter. The scatter contribution of each segmented equivalent field at the detector plane was summed by Clarkson integration. The same methodology was applied for determining both tertiary collimator and wedge scatter contribution. However, the field size that determined the amount of scatter contribution was not the same for each component. For tertiary collimator scatter and external wedge scatter, a field projected to the detector plane was used directly. Comparisons of calculated and measured values for in-air output factors showed good agreement for both open and external wedge fields. This algorithm can also be used for multileaf collimator (MLC) fields irrespective of the position of the MLC (i.e., whether the MLC replaces one secondary collimator or is used as a tertiary collimator). The measurement and parameterization of tertiary collimator scatter is necessary to account for its contribution to the in-air output. Because a source-plane field is mapped into the detector plane, no additional dosimetric data acquisition is necessary for the calculation of head scatter.

Photon beam skin dose analyses for different clinical setups.

A comprehensive set of data on skin dose for 8 MV and 18 MV photon beams from a medical linear accelerator was measured using a parallel-plate chamber to document the effect of field size, source-to-surface distance (SSD), off-axis distance, acrylic block tray, wedge (external standard wedge), Lipowitz's metal block, multileaf collimator (MLC), and dynamic wedge. The skin dose increased as field size increased from 5 X 5 cm2 to 40 X 40 cm2 (6% to 38% for 8 MV and 5% to 44% for 18 MV beam). With the use of an acrylic block tray, the skin dose increased for all field sizes (7% to 59% for 8 MV and 5% to 62% for 18 MV beam), but the increase was minimal for small fields. The skin dose with a wedge showed a much more complex trend. It was generally lower than the dose for an open field, but higher in the case of large fields and higher degree wedges. When both wedge and block tray were used, the tray was a major contributor to the skin dose because some of the contaminant electrons from the wedge assembly were absorbed by the block tray. Field-shaping blocks increased the skin dose, but, interestingly, the block tray reduced the skin dose for small blocked fields treated with a high-energy photon beam. The effect of an MLC on skin dose was very similar to that of a Lipowitz's metal block, but its magnitude was less. The skin dose was higher for dynamic wedge fields than it was for standard wedge fields. As SSD decreased, the skin dose increased, and this effect was dominant in larger field sizes. The SSD effect was enhanced in the presence of an acrylic block tray. The skin dose off-axis was the same as at the central axis, or smaller. A similar pattern of behavior of the skin dose is expected for photon beams from other linear accelerators.

The equivalent square concept for the head scatter factor based on scatter from flattening filter.

The equivalent field relationship between square and circular fields for the head scatter factor was evaluated at the source plane. The method was based on integrating the head scatter parameter for projected shaped fields in the source plane and finding a field that produced the same ratio of head scatter to primary dose on the central axis. A value of sigma/R approximately equal to 0.9 was obtained, where sigma was one-half of the side length of the equivalent square and R was the radius of the circular field. The assumptions were that the equivalent field relationship for head scatter depends primarily on the characteristics of scatter from the flattening filter, and that the differential scatter-to-primary ratio of scatter from the flattening filter decreases linearly with the radius, within the physical radius of the flattening filter. Lam and co-workers showed empirically that the area-to-perimeter ratio formula, when applied to an equivalent square formula at the flattening filter plane, gave an accurate prediction of the head scatter factor. We have analytically investigated the validity of the area-to-perimeter ratio formula. Our results support the fact that the area-to-perimeter ratio formula can also be used as the equivalent field formula for head scatter at the source plane. The equivalent field relationships for wedge and tertiary collimator scatter were also evaluated.

Electron contamination in 8 and 18 MV photon beams.

The contribution from contaminant electrons in the buildup region of a photon beam must be separated when calculating the dose using a photon convolution kernel. Their contribution can be extrapolated from fractional depth dose (FDD) data using the fractional depth kerma (or the "equilibrium dose") derived from measured quantities such as beam attenuation with depth, phantom scatter factor as a function of field size and depth, and inverse-square law for the incident photon beam. Good agreement is observed between the extrapolated and the EGS4 Monte Carlo simulated, primary dose-to-kerma ratios in the surface region for the photon beams, excluding electron contamination. The FDD was measured using a Scanditronix photon diode and was normalized to a reference depth far beyond maximum range of contaminant electrons. An analysis for the 8 and 18 MV photon beams from a Varian 2100CD indicates that at a source-to-surface distance (SSD) of 100 cm, the maximum electron contaminant dose (relative to its maximum FDD) varies from 1% to 33% for 8 MV and 2% to 44% for 18 MV, for square collimator settings ranging from 5 to 40 cm (defined at 100 cm from the source). This value at a depth of maximum dose (2 cm for 8 MV and 3.5 cm for 18 MV) can reach 1% for 8 MV and 2.3% for 18 MV. This contaminant electron dose is almost independent of SSD for 8 MV and starts to fall off for 18 MV at SSDs larger than 120 cm. Compared with the open beam, the contaminant electron dose increases when a solid tray is used, and the magnitude of increase increases with field size, reaching 19% and 16% for a 40 x 40 cm2 field for 8 and 18 MV photons, respectively. The contaminant electron dose increases slightly for a blocked beam compared with an open beam of the same field size if a tray is used in both cases. The contaminant electron dose for the wedged field is less than that for an open field. However, the reduction is less significant at larger collimator settings (c = 20 cm) and may increase slightly for 8 MV photons.

An equivalent square field formula for determining head scatter factors of rectangular fields.

A simple formula is derived for the calculation of an equivalent square field that gives the same head scatter factor as a given rectangular field. This formula is based strictly on the configuration of a medical linear accelerator treatment head. The geometric parameters used are the distances between the target and the top of each field-defining aperture. The formula accounts for both the effect of field elongation and the collimator exchange effect. This method predicts the output to within 1% accuracy for both open and wedged fields and does not require any new measured data other than the field size dependence of head scatter for a range of square field sizes. Interestingly, the formula we derived has the same format as the formula that was empirically obtained by Vadash and Bjärngard [Med. Phys. 20, 733-734 (1993)].

Concurrent platinum-based chemotherapy and hyperfractionated radiotherapy with late intensification in advanced head and neck cancer.

PURPOSE: To determine whether a course of hyperfractionated radiation therapy concomitant with escalated radiosensitizing platinum compounds can be administered with acceptable morbidity and achieve a high rate of loco-regional control for Stage III and IV head and neck cancer and whether the patients can be tumor free at the primary site after initial therapy and cured by the additional chemoradiation without radical resection of the primary tumor. METHODS AND MATERIALS: Patients with Stage III/IV head and neck cancer were treated in this multicenter Phase II Study with 1.8 Gy fraction radiotherapy for 2 weeks, with escalation to 1.2 Gy b.i.d. hyperfractionation to 46.8 Gy. Concomitant continuous infusion cisplantinum (CDDP) 20 mg per meter square on day 1 to 4 and 22 to 25 was given. Reassessment by biopsy of primary and nodes was done. Patients with a complete response continued with hyperfractionated radiotherapy to 75.6 Gy with simultaneous carboplatinum (Carbo), 25 mg per meter square b.i.d. for 12 consecutive treatment days. Patients with residual disease at 46.8 Gy required curative surgery. Seventy-four patients were treated at the three institutions; 20 were Stage III and 54 were Stage IV. All patients had daily mouth care, nutritional, and psychosocial support. RESULTS: This regime was well tolerated. Eighty-five percent of toxicities were Grade 1 or 2 and there was only one Grade 4 hematologic toxicity. Late toxicities included xerostomia in 25 patients, dysphasia in 18, and mild speech impediment in 11. Biopsies of primary site were done after the first course of treatment in 59 patients. Neck dissections were performed in 35 patients. Forty-four of 59 (75%) primary sites and 16 of 35 (46%) lymph nodes had pathologically complete response (CR). Of the 74 patients, only 12 required surgical resection of the primary site. Thirty-five of the 50 node positive patients had neck dissections, 16 of these were CRs at surgery. At 4 years (median follow-up of 26 months), disease-specific survival is 63%. The actuarial survival for all patients is 51%. Patients with pathological CR after initial treatment have disease specific survival of 73% at 4 years vs. 48% of patients with partial response (PR) only. CONCLUSION: This study, developed on the basis of radiobiological and cell kinetic precepts, produced results that compare favorably with other reports of management of patients with advanced head and neck cancer. In comparison with our previous study, these results are comparable, not impressively better. The associated morbidity was somewhat worse.

Commissioning of enhanced dynamic wedge on a ROCS RTP system.

The enhanced dynamic wedge (EDW) is clinically commissioned on a ROCS RTPS (Version 5.03) in a manner similar to that used for any standard physical wedge. The required data set for implementation includes central axis depth dose, and open and wedge beam profiles at several depths and output factors. The features distinguishing the EDW from the physical wedge are a sharp change in output with field size in the wedge plane and a primary intensity difference at the end of the wedge field because the moving jaw stops 0.5 cm short of the fixed jaw position for all field sizes, for safety reasons. The monitor unit (MU) calculation for an EDW field in ROCS is based on scaling factors that are derived from a normalized golden STT (NGSTT). This approach requires no change in the data file structure of ROCS. It was found that the output for EDW is very sensitive to the value of final moving jaw position. Every 0.5 cm difference between planned and set value can cause 3.5% error.

Performance evaluation of a diode array for enhanced dynamic wedge dosimetry.

The performance of a diode array (Profiler) was evaluated by comparing its enhanced dynamic wedge (EDW) profiles measured at various depths with point measurements using a 0.03 cm3 ionization chamber on a commercial linear accelerator. The Profiler, which covers a 22.5 cm width, was used to measure larger field widths by concatenating three data sets into a larger field. An innovative wide-field calibration technique developed by the manufacturer of the device was used to calibrate the individual diode sensitivity, which can vary by more than 10%. Profiles of EDW measured with this device at several depths were used to construct isodose curves using the percentage depth dose curve measured by the ionization chamber. These isodose curves were used to check those generated by a commercial treatment planning system. The profiles measured with the diode array for both 8 and 18 MV photon beams agreed with those of the ionization chamber within a standard deviation of 0.4% in the field (defined as 80% of the field width) and within a maximum shift of less than 2 mm in the penumbra region. The percentage depth dose generally agreed to within 2% except in the buildup region. The Profiler was extremely useful as a quality assurance tool for EDW and as a dosimetry measurement device with tremendous savings in data acquisition time.

Electron disequilibrium in high-energy x-ray beams.

The ratio between scatter dose and scatter kerma for points on the central axis of 15-MV x-ray beams has been examined by Monte Carlo calculations. This ratio, beta'S, behaves differently from that between the primary dose and kerma, beta'p. Both the primary and scatter components of beta' undergo an initial rapid buildup, however, beta'S begins from a much higher surface value. In addition, the depth required for longitudinal electron equilibrium is larger for beta'S than for beta'P. The variation of beta'S with field size and depth is attributed to the spatial variation of scatter kerma in the photon beam. The approximation beta'S = 1 is accurate enough for clinical dose-calculation purposes, leading to less than 0.5% error in total dose, while the assumption beta'S = beta'p may cause up to 2.5% error, relative to the maximum dose, near the surface at 15 MV.

Characterizing output for dynamic wedges.

The output factor for the dynamic wedge, unlike that for the physical wedge, is a complex function of the field dimension along the moving jaw and wedge angle. The large change in output (varying as much as 40% for 45 degrees and 60 degrees wedge angles) can be attributed clearly to the segmented treatment tables (STTs), which specify cumulative monitor unit weighting as a function of jaw position, y. We found that the output factor (in air or water) on the central axis for the dynamic wedge can be characterized by multiplying the output factor (in air or water) for an open field by a normalization factor, which is determined from the STTs, thus indicating that collimator scatter is similar for both the dynamic wedge field and the open field. The introduction of the normalization factor decreases the commissioning time for dynamic wedges significantly and is useful for quality assurance.

Tissue-phantom ratios from percentage depth doses.

When converting fractional (percentage) depth doses to tissue-phantom ratios, one must use a factor that accounts for the different source-to-point distances. Two minor correction factors are also involved. One is the ratio of total to primary dose at the two different distances from the source, for the same depth and field size. This factor is usually ignored. It was determined experimentally that this can introduce up to 1.5% error at 6 MV. The second correction factor reflects differences related to scattered photons and electrons at the depth of normalization in the two geometries. This correction is accounted for in published conversion procedures. It was found to be less than 1% provided the normalization depth is sufficient for electron equilibrium, which occurs first well beyond the depth of maximum dose. One may avoid electron-equilibrium problems by using an interim normalization depth that provides electron equilibrium with some margin, renormalizing to a shallower depth if desired. With this precaution, the accuracy when measured fractional depth doses were converted to tissue-phantom ratios was comparable to that of directly measured tissue-phantom ratios even when the correction factors were ignored.

Experimental determination of the dose kernel in high-energy x-ray beams.

A semiempirical method to characterize the pencil-beam dose kernel is presented. Results from measurements are described by mathematical models of the applicable physical processes. The measurements were made with 6 and 25 MV x-ray beams from a linear accelerator. Broad-beam notations were used consistently, and the pencil-beam quantities were obtained by differentiation. The results were compared to pencil-beam kernels calculated by Monte Carlo techniques. The analysis of the measured data included a number of approximations. It was assumed that all the constituent pencil beams in the field are parallel, i.e., the divergence is ignored. Furthermore, the lateral variations of the incident photon fluence and the energy spectrum were disregarded. Monte Carlo calculations, on the other hand, are based on an average energy spectrum over the field, and are free from divergence and variations in the incident photon fluence. Measured and Monte Carlo calculated pencil beams nevertheless agreed well, and the approximations mentioned caused at maximum 2.7% discrepancies for the largest field size at 6 MV.