- letters to the editor
- radiation therapy physics
- radiation imaging physics
- radiation measurement physics
- nuclear medicine physics
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Index of content:
Volume 30, Issue 8, August 2003
- RADIATION THERAPY PHYSICS
Dependence of radiochromic film optical density post-exposure kinetics on dose and dose fractionation30(2003); http://dx.doi.org/10.1118/1.1587611View Description Hide Description
Radiochromic film (RCF) has been shown to be a precise and accurate secondary planar dosimeter for acute exposure radiation fields. However, its application to low dose-ratebrachytherapy has been questioned because of possible dose-rate effects. To address this concern, we have measured the optical density (OD) of Model 55-2 RCF as a function of time (interval between the completion of irradiation and densitometry using a 633 nm laser scanner) following exposure (from less than 1 hour to 90 days) for single and split doses from 1 Gy to 100 Gy. Our work demonstrates that film darkening as a function of post-irradiation time depends significantly on total dose, with films exposed to lower doses developing faster than films given higher doses. At 1 Gy, the OD 90 days after exposure is 200% larger than that measured 1 h after exposure compared to a 20% increase over 90 days for doses larger than 20 Gy. An empirical model with time-independent, fast and slow growth terms was used to fit single exposure data. The dependence of the resulting best-fit parameters on dose was investigated. Splitting the dose into two fractions (20 Gy followed by doses of 1–80 Gy 24 h later) results in modest post-irradiation time-dependent changes in the total optical density (at most 15% at small doses), which dissipates within 20 hours following the second exposure. This experimental finding is consistent with the predictions of a simple cumulative dose superposition model. Overall, both experimental and empirical modeling suggest that dose-rate effects may be relatively small despite the strong dependence of film darkening kinetics on total dose. However, more experimental evaluation of radiochromic film response dependence on dose rate and dose-time-fractionation patterns is needed.
30(2003); http://dx.doi.org/10.1118/1.1590436View Description Hide Description
The dose from photon-induced nuclear particles (neutrons,protons, and alpha particles)generated by high-energy photonbeams from medical linacs is investigated. Monte Carlo calculations using the MCNPX code are performed for three different photonbeams from two different machines: Siemens 18 MV, Varian 15 MV, and Varian 18 MV. The linac head components are simulated in detail. The dose distributions from photons,neutrons,protons, and alpha particles are calculated in a tissue-equivalent phantom. Neutrons are generated in both the linac head and the phantom. This study includes (a) field sizeeffects, (b) off-axis dose profiles, (c) neutron contribution from the linac head, (d) dose contribution from capture gamma rays, (e) phantom heterogeneity effects, and (f) effects of primary electron energy shift. Results are presented in terms of absolute dose distributions and also in terms of DER (dose equivalent ratio). The DER is the maximum dose from the particle (neutron,proton, or alpha) divided by the maximum photon dose, multiplied by the particle quality factor and the modulation scaling factor. The total DER including neutrons,protons, and alphas is about 0.66 cSv/Gy for the Siemens 18 MV beam The neutron DER decreases with decreasing field size while the proton (or alpha) DER does not vary significantly except for the field. Both Varian beams (15 and 18 MV) produce more neutrons,protons, and alphas particles than the Siemens 18 MV beam. This is mainly due to their higher primary electron energies: 15 and 18.3 MeV, respectively, vs 14 MeV for the Siemens 18 MV beam. For all beams,neutrons contribute more than 75% of the total DER, except for the field The total DER is 1.52 and 2.86 cSv/Gy for the 15 and 18 MV Varian beams respectively. Media with relatively high- elements like bone may increase the dose from heavy charged particles by a factor 4. The total DER is sensitive to primary electron energy shift. A Siemens 18 MV beam with 15 MeV (instead of 14 MeV) primary electrons would increase by 40% the neutron DER and by 210% the DER. Comparisons with measurements (neutron yields from different materials and neutron dose equivalent) are also presented. Using the NCRP risk assessment method, we found that the dose equivalent from leakage neutrons (at 50-cm off-axis distance) represent 1.1, 1.1, and 2.0% likelihood of fatal secondary cancer for a 70 Gy treatment delivered by the Siemens 18 MV, Varian 15 MV, and Varian 18 MV beams, respectively.
Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. I. The effect of shift invariance30(2003); http://dx.doi.org/10.1118/1.1589492View Description Hide Description
Convolution methods have been used to model the effect of geometric uncertainties on dosedelivery in radiation therapy. Convolution assumes shift invariance of the dose distribution. Internal inhomogeneities and surface curvature lead to violations of this assumption. The magnitude of the error resulting from violation of shift invariance is not well documented. This issue is addressed by comparing dose distributions calculated using the Convolution method with dose distributions obtained by Direct Simulation. A comparison of conventional Static dose distributions was also made with Direct Simulation. This analysis was performed for phantom geometries and several clinical tumor sites. A modification to the Convolution method to correct for some of the inherent errors is proposed and tested using example phantoms and patients. We refer to this modified method as the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over different beam arrangements in the various phantom examples) was 21% with the Static dose calculation, 9% with Convolution, and reduced to 5% with the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over four clinical examples) was 9% for the Static method, 13% for Convolution, and 3% for Corrected Convolution. While Convolution can provide a superior estimate of the dosedelivered when geometric uncertainties are present, the violation of shift invariance can result in substantial errors near the surface of the patient. The proposed Corrected Convolution modification reduces errors near the surface to 3% or less.
Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. II. The effect of a finite number of fractions30(2003); http://dx.doi.org/10.1118/1.1589493View Description Hide Description
Convolution methods can be used to model the effect of geometric uncertainties on the planned dose distribution in radiation therapy. This requires several assumptions, including that the patient is treated with an infinite number of fractions, each delivering an infinitesimally small dose. The error resulting from this assumption has not been thoroughly quantified. This is investigated by comparing dose distributions calculated using the Convolution method with the result of Stochastic simulations of the treatment. Additionally, the dose calculated using the conventional Static method, a Corrected Convolution method, and a Direct Simulation are compared to the Stochastic result. This analysis is performed for single beam, parallel opposed pair, and four-field box techniques in a cubic water phantom. Treatment plans for a simple and a complex idealized anatomy were similarly analyzed. The average maximum error using the Static method for a 30 fraction simulation for the three techniques in phantoms was 23%, 11% for Convolution, 10% for Corrected Convolution, and 10% for Direct Simulation. In the two anatomical examples, the mean error in tumor control probability for Static and Convolution methods was 7% and 2%, respectively, of the result with no uncertainty, and 35% and 9%, respectively, for normal tissue complication probabilities. Convolution provides superior estimates of the delivered dose when compared to the Static method. In the range of fractions used clinically, considerable dosimetric variations will exist solely because of the random nature of the geometric uncertainties. However, the effect of finite fractionation appears to have a greater impact on the dose distribution than plan evaluation parameters.
30(2003); http://dx.doi.org/10.1118/1.1587431View Description Hide Description
To realize the accelerator-based boronneutron capture therapy (BNCT) at the Cyclotron and Radioisotope Center of Tohoku University, the feasibility of a cyclotron-based BNCT was evaluated. This study focuses on optimizing the epithermal neutron field with an energy spectrum and intensity suitable for BNCT for various combinations of neutron-producing reactions and moderator materials. Neutrons emitted at from a thick (stopping-length) Ta target, bombarded by 50 MeV protons of 300 μA beam current, were selected as a neutron source, based on the measurement of angular distributions and neutron energy spectra. As assembly composed of iron, and lead was chosen as moderators, based on the simulation trials using the MCNPX code. The depth dose distributions in a cylindrical phantom, calculated with the MCNPX code, showed that, within 1 h of therapeutic time, the best moderator assembly, which is 30-cm-thick iron, 39-cm-thick and 1-cm-thick lead, provides an epithermal neutron flux of This results in a tumor dose of 20.9 Gy-eq at a depth of 8 cm in the phantom, which is 6.4 Gy-eq higher than that of the Brookhaven Medical Research Reactor at the equivalent condition of maximum normal tissue tolerance. The beam power of the cyclotron is 15 kW, which is much lower than other accelerator-based BNCT proposals.
30(2003); http://dx.doi.org/10.1118/1.1590437View Description Hide Description
VIPAR polymergels and 3D MRI techniques were evaluated for their ability to provide experimental verification of 3D dose distributions in a simulation of a prostate monotherapy clinical application. A real clinical treatment plan was utilized, generated by post-irradiation, CT based calculations derived from Plato™ BPS and Swift™ treatment planning systems. The simulated treatment plan involved the use of 10 catheters and 39 source positions within a glass vessel of appropriate dimensions, homogeneously filled with the VIPAR gel. 3D high resolution MR scanning of the gel produced relaxation time maps, from which 3D dose distributions were derived via an appropriate calibration procedure. Results were compared to corresponding dose distributions obtained from the Plato and Swift treatment planning systems. Quantitative comparison, on a point by point basis, was based on user adopted acceptance criteria of 5% dose-difference and 3 mm distance-to-agreement. Significant deviations between experimental and calculated dose distributions were found for doses lower than 50% due to the reduced dose resolution of the method in the low dose, low dose gradient region. Measurement errors were observed at 1.0–1.5 mm around each catheter due to MR imaging susceptibility artifacts. For most remaining points the acceptance criteria were fulfilled. Systematic offsets of the order of 1–2 mm, observed between measured and corresponding calculated isocontours at specific segments, are attributed to the 1 mm uncertainty in catheter reconstruction and 1 mm uncertainty in the alignment of the MR and CTimaging planes.
30(2003); http://dx.doi.org/10.1118/1.1591991View Description Hide Description
Treatment planning involves selecting delivery parameters that distribute the dose to nontumor tissue in such a way as to minimize the risk of complications. This work studied the relationship between nontumor integral dose (NTID), the fractional energy deposited in nontumor tissue, and a variety of delivery parameters for three clinical cases: nasopharynx, pancreas, and prostate. Integral dose for an organ of uniform density is simply the product of the organ density, volume, and mean dose. For each case, conventional plans were generated with 2, 4, 8, 12 and 36 equally spaced beams. All plans were normalized to the same tumor mean dose which is equivalent to the same tumor integral dose. For the pancreas and prostate cases, the patients were assumed to be uniform density. For the nasopharynx case, bones and air cavities were outlined and each assigned a uniform non-unit density. With four or more beams and clinical margin values, the variation in NTID was as a function of number of beams. With eight or more beams, the variation was Reducing the beam margin decreased the NTID because less normal tissue was irradiated. However, the effect of the number of beams on NTID was independent of margin size. Higher energy beams reduced the NTID, as expected, and the effect was independent of the number of beams. With four or more beams, variation in beam direction changed NTID by less than 1.5%. Changing beam weights changed NTID by for plans with four to eight beams. For the body sites studied, the majority of energy was deposited in nontumor tissue, ranging from 72% in the nasopharynx case to 97% for the prostate case. The NTID decreased with increasing tumor size for similar anatomic sizes and increased with increasing size of anatomical region for similar tumor size. Finally, the effect of heterogeneity-corrected doses on the NTID was found to be for the nasopharynx case. These data support the hypothesis that the NTID is approximately independent of beam orientation or relative weighting when many beams are used. Optimization, therefore, can only find the best distribution of dose; it cannot reduce the energy imparted. NTID may be useful in establishing an upper bound on the quality of plan that can be achieved by optimization.
30(2003); http://dx.doi.org/10.1118/1.1592896View Description Hide Description
A quality assurance method is developed for measuring, verifying and analyzing intensity modulated radiation fields. It is applicable for rotational and fixed-beam intensity modulated radiation therapy(IMRT)treatments. A gantry-mount device was constructed to measure the transmission dose of an IMRT field using radiographicfilms. A double-exposure technique with optimal kernel estimate method was developed to minimize the errors from measurements. A confidence level test method was developed to detect the discrepancies between measured and prescribed IMRT fluence distributions. Our method was tested for rotational and fixed-beam IMRTtreatment verifications. The method was found insensitive to the hardware-related parameters for rotational and fixed-beam IMRTdeliveries. The confidence level test was found to be more sensitive than linear correlation method in detecting relative small errors for cases with a few segments or narrow regions of interest. In conclusion, we demonstrated a quantitative method for verifying and analyzing IMRTtreatmentdeliveries.
30(2003); http://dx.doi.org/10.1118/1.1589612View Description Hide Description
Microdosimetric measurements have been performed at the clinical beam intensities in two epithermal neutron beams, the Brookhaven Medical Research Reactor and the M67 beam at the Massachusetts Institute of Technology Research Reactor, which have been used to treat patients with BoronNeutron Capture Therapy (BNCT). These measurements offer an independent assessment of the dosimetry used at these two facilities, as well as provide information about the radiation quality not obtainable from conventional macrodosimetric techniques. Moreover, they provide a direct measurement of the absorbed dose resulting from the BNC reaction. BNC absorbed doses measured within this study are approximately 15% lower than those estimated using foil activation at both MIT and BNL. Finally, an intercomparison of the characteristics and radiation quality of these two clinical beams is presented. The techniques described here allow an accurate quantitative comparison of the physical absorbed dose as well as a measure of the biological effectiveness of the absorbed dose delivered by different epithermal beams. No statistically significant differences were observed in the predicted RBEs of these two beams. The methodology presented here can help to facilitate the effective sharing of clinical results in an effort to demonstrate the clinical utility of BNCT.
Ultrasound tomography imaging of radiation dose distributions in polymer gel dosimeters: Preliminary study30(2003); http://dx.doi.org/10.1118/1.1590751View Description Hide Description
A novel imaging system for investigation of absorbed dose distributions in radiotherapypolymergeldosimeters using ultrasound is introduced. A prototype transmission ultrasoundcomputed tomography (UCT) imaging system is developed and evaluated. The imaging capabilities of the system are assessed through investigation of an irradiated polyacrylamide gel test phantom. Images based on transmitted signal amplitude and time of flight (TOF) of the ultrasonic signal through the phantom are reconstructed using a filtered backprojection technique. In general, the reconstruction of the square field in the TOF image was superior to the transmission image, however, transmission images displayed superior contrast to TOF images. The image quality achieved with this prototype system is promising and could be significantly enhanced through improvements, in particular through the development of more sophisticated experimental equipment. It is concluded that UCT is a viable technique for imaging absorbed dose distributions in polymergeldosimeters and investigations are continuing to further improve the system.
Diamond detector versus silicon diode and ion chamber in photon beams of different energy and field size30(2003); http://dx.doi.org/10.1118/1.1591431View Description Hide Description
The aim of this work was to test the suitability of a PTW diamonddetector for nonreference condition dosimetry in photon beams of different energy (6 and 25 MV) and field size (from to Diamond behavior was compared to that of a Scanditronix p-type silicondiode and a Scanditronix RK ionization chamber. Measurements included output factors (OF), percentage depth doses (PDD) and dose profiles. OFs measured with diamonddetector agreed within 1% with those measured with diode and RK chamber. Only at 25 MV, for the smallest field size, RK chamber underestimated OFs due to averaging effects in a pointed shaped beam profile. Agreement was found between PDDs measured with diamonddetector and RK chamber for both 6 MV and 25 MV photons and down to field size. For the field size, at 25 MV, RK chamber underestimated doses at shallow depth and the difference progressively went to zero in the distal region. PDD curves measured with silicondiode and diamonddetector agreed well for the 25 MV beam at all the field sizes. Conversely, the nontissue equivalence of silicon led, for the 6 MV beam, to a slight overestimation of the diode doses in the distal region, at all the field sizes. Penumbra and field width measurements gave values in agreement for all the detectors but with a systematic overestimate by RK measurements. The results obtained confirm that ion chamber is not a suitable detector when high spatial resolution is required. On the other hand, the small differences in the studied parameters, between diamond and silicon systems, do not lead to a significant advantage in the use of diamonddetector for routine clinical dosimetry.
30(2003); http://dx.doi.org/10.1118/1.1592031View Description Hide Description
Techniques for reconstruction of electron spectra from the depth-dose curves used to date have ignored the angular distribution of incident electrons scattered at large angles. The approximation adopted is to employ a database of monoenergetic depth-dose curves generated for normal incidence of electrons at the surface. This approximation is acceptable for direct electrons with small angular spread. However, electrons scattered from the treatment head and collimating system may have large average angles of incidence which affects the depth-dose distribution significantly at shallow depths by increasing energy deposition close to the surface. We show that ignoring the electron incident angular distribution leads to systematic errors in the low energy region of reconstructed electron spectra. We propose a simple 1-D model to correct for these systematic errors using only electron angular distribution at the central beam axis. This model provides reconstructed spectra in excellent agreement with Monte Carlo simulation in the low energy region.
Accounting for high Z shields in brachytherapy using collapsed cone superposition for scatter dose calculation30(2003); http://dx.doi.org/10.1118/1.1587411View Description Hide Description
Common clinical brachytherapytreatment planning algorithms perform at best one-dimensional corrections for high Z heterogeneities that will be inaccurate for intermediate energies (60–100 keV). The development of fast methods for a three-dimensional dose calculation to account for high Z materials in this energy range is important, e.g., to fully utilize the potential of patient individualized shields using isotopes such as and In this work we use the collapsed cone superposition algorithm to calculate the scatterdose contribution around partly lead-shielded point sources at 60, 100, and 350 keV. Methods to scale point kernels for water into kernels for high Z materials are derived. The scaling accounts for scatteredphoton spectral differences between materials and thus goes beyond the common density scaling approach. Compared to Monte Carlo simulations, the results of our algorithm yield agreements on the unshielded side to within 3% at 350 and 60 keV and to within 7% at 100 keV out to distances of 8 cm from the source. The effect of the shield in the center of the unshielded region is small at 350 keV but significant and occurs at short distances at 100 and 60 keV. At 60 keV, the shield causes a dose reduction of around 10%, 1 cm from the source on the unshielded side. At 100 keV, the reverse effect is seen, the insertion of shields leading to the total dose being increased by about 10% at 1 cm. That one-dimensional algorithms are incapable of predicting these changes shows the importance of accounting for the full three-dimensional geometry in correctly determining the scatterdose contribution.
30(2003); http://dx.doi.org/10.1118/1.1589495View Description Hide Description
In clinical radiation physics chart checking, the dose calculation results generated by computertreatment planningsoftware are usually verified by an independent computerized monitor unit calculation routine, or by “hand calculation” using percent depth dose (PDD), tissue phantom ratio (TPR), scatter factors, and the machine calibration factors. For intensity-modulated radiosurgery (IMRS) or intensity-modulated radiation therapy(IMRT), the “hand calculation” becomes not feasible due to the sophisticated multileaf collimator(MLC) segments created for intensity-modulated dosedelivery. Therefore, an independent computerized dose calculation routine is needed for fast and reliable dose verification. In this work, a point dose calculation routine for IMRS/IMRT plan verification is developed by directly applying Clarkson’s method. The method includes preparing data table by measuring TPRs for circular fields with diameters ranging 6 to 98 mm, extrapolating TPR for the zero field size (TPR0) from measured data and generating scatter phantom ratio (SPR) for each individual circular field. The segmented MLC sequences created by IMRS/IMRT inverse planning are converted into irregular fields for Clarkson’s calculation. This method has been tested using 29 IMRS/IMRT cases. The results indicate that it is reliable, fast, and accurate. The average time to calculate one field is about 2 s with a 300 Mhz CPU.
30(2003); http://dx.doi.org/10.1118/1.1592017View Description Hide Description
Intensity modulated radiation therapy(IMRT) with a dynamic multileaf collimator (DMLC) requires synchronization of DMLC leaf motion with dosedelivery. A delay in DMLC communication is known to cause leaf lag and lead to dosimetric errors. The errors may be exacerbated by gated operation. The purpose of this study was to investigate the effect of leaf lag on the accuracy of dosesdelivered in gated IMRT. We first determined the effective leaf delay time by measuring the dose in a stationary phantom delivered by wedge-shaped fields. The wedge fields were generated by a DMLC at various dose rates. The so determined delay varied from 88.3 to 90.5 ms. The dosimetric effect of this delay on gated IMRT was studied by delivering wedge-shaped and clinical IMRT fields to moving and stationary phantoms at dose rates ranging from 100 to 600 MU/min, with and without gating. Respiratory motion was simulated by a linear sinusoidal motion of the phantom. An ionization chamber and films were employed for absolute dose and 2-D dose distribution measurements. Discrepancies between gated and nongated delivery to the stationary phantom were observed in both absolute dose and 2-D dose distribution measurements. These discrepancies increased monotonically with dose rate and frequency of beam interruptions, and could reach 3.7% of the total dosedelivered to a ion chamber. Isodose lines could be shifted by as much as 3 mm. The results are consistent with the explanation that beam hold-offs in gated delivery allowed the lagging leaves to catch up with the delivered monitor units each time that the beam was interrupted. Low dose rates, slow leaf speeds and low frequencies of beam interruptions reduce the effect of this delay-and-catch-up cycle. For gated IMRT it is therefore important to find a good balance between the conflicting requirements of rapid dosedelivery and delivery accuracy.
Dose linearity and uniformity of a linear accelerator designed for implementation of multileaf collimation system-based intensity modulated radiation therapy30(2003); http://dx.doi.org/10.1118/1.1592640View Description Hide Description
The dose linearity and uniformity of a linear accelerator designed for multileaf collimation system- (MLC) based IMRT was studied as a part of commissioning and also in response to recently published data. The linear accelerator is equipped with a PRIMEVIEW, a graphical interface and a SIMTEC IM-MAXX, which is an enhanced autofield sequencer. The SIMTEC IM-MAXX sequencer permits the radiation beam to be “ON” continuously while deliveringintensity modulated radiation therapy subfields at a defined gantry angle. The dosedelivery is inhibited when the electron beam in the linear accelerator is forced out of phase with the microwave power while the MLC configures the field shape of a subfield. This beam switching mechanism reduces the overhead time and hence shortens the patient treatment time. The dose linearity, reproducibility, and uniformity were assessed for this type of dosedelivery mechanism. The subfields with monitor units ranged from 1 MU to 100 MU were delivered using 6 MV and 23 MV photon beams. The doses were computed and converted to dose per monitor unit. The dose linearity was found to vary within 2% for both 6 MV and 23 MV photon beam using high dose rate setting (300 MU/min) except below 2 MU. The dose uniformity was assessed by delivering 4 subfields to a Kodak X-OMAT TL film using identical low monitor units. The optical density was converted to dose and found to show small variation within 3%. Our results indicate that this linear accelerator with SIMTEC IM-MAXX sequencer has better dose linearity, reproducibility, and uniformity than had been reported.
- RADIATION IMAGING PHYSICS
30(2003); http://dx.doi.org/10.1118/1.1590315View Description Hide Description
Comprehensive analyses and measurements of computed tomography(CT) single-scan dose profiles were performed for several scanners and operating conditions. Measurements were made using two types of thermoluminescent dosimeters, LiF:Mg,Cu,P and and two CTdosimetry phantoms, head and body. Analyses of CT single-scan dose profiles were made in terms of a Gaussian function for primary radiation and a Lorentzian function for scattered radiation. This function was used to investigate several common descriptions of the CT dose, including the computed tomography dose index(CTDI) and the multiple scan average dose. The relative percentage of scatter versus primary radiation to the contribution of CTDI at the central and peripheral locations was determined and analyzed. The correlation between CTDI of thermoluminescent dosimeter measurements and pencil-shaped ionization chamber measurements was determined. A method for estimating organ dose from CT was developed and compared to organ-dose estimates from Monte Carlo simulations.
Selective enhancement filters for nodules, vessels, and airway walls in two- and three-dimensional CT scans30(2003); http://dx.doi.org/10.1118/1.1581411View Description Hide Description
Computer-aided diagnostic(CAD) schemes have been developed to assist radiologists in the early detection of lungcancer in radiographs and computed tomography(CT)images. In order to improve sensitivity for nodule detection, many researchers have employed a filter as a preprocessing step for enhancement of nodules. However, these filters enhance not only nodules, but also other anatomic structures such as ribs, blood vessels, and airway walls. Therefore, nodules are often detected together with a large number of false positives caused by these normal anatomic structures. In this study, we developed three selective enhancement filters for dot, line, and plane which can simultaneously enhance objects of a specific shape (for example, dot-like nodules) and suppress objects of other shapes (for example, line-like vessels). Therefore, as preprocessing steps, these filters would be useful for improving the sensitivity of nodule detection and for reducing the number of false positives. We applied our enhancement filters to synthesized images to demonstrate that they can selectively enhance a specific shape and suppress other shapes. We also applied our enhancement filters to real two-dimensional (2D) and three-dimensional (3D) CTimages to show their effectiveness in the enhancement of specific objects in real medical images. We believe that the three enhancement filters developed in this study would be useful in the computerized detection of cancer in 2D and 3D medical images.