Quantitative assessment of full-width at half-maximum and detector energy threshold in X-ray imaging systems.

BACKGROUND: The response function of imaging systems is regularly considered to improve the qualified maps in various fields. More the accuracy of this function, the higher the quality of the images. METHODS: In this study, a distinct analytical relationship between full-width at half-maximum (FWHM) value and detector energy thresholds at distinct tube peak voltage of 100 kV has been addressed in X-ray imaging. The outcomes indicate that the behavior of the function is exponential. The relevant cut-off frequency and summation of point spread function S(PSF) were assessed at large and detailed energy ranges. RESULTS: A compromise must be made between cut-off frequency and FWHM to determine the optimal model. By detailed energy range, the minimum and maximum of S(PSF) values were revealed at 20 keV and 48 keV, respectively, by 2979 and 3073. Although the maximum value of FWHM occurred at the energy of 48 keV by 224 mm, its minimum value was revealed at 62 keV by 217 mm. Generally, FWHM value converged to 220 mm and S(PSF) to 3026 with small fluctuations. Consequently, there is no need to increase the voltage of the X-ray tube after the energy threshold of 20 keV. CONCLUSION: The proposed FWHM function may be used in designing the setup of the imaging parameters in order to reduce the absorbed dose and obtain the final accurate maps using the related mathematical suggestions.

Improving signal-to-noise ratio by maximal convolution of longitudinal and transverse magnetization components in MRI: application to the breast cancer detection.

PURPOSE: The extraction of information from images provided by medical imaging systems may be employed to obtain the specific objectives in the various fields. The quantity of signal to noise ratio (SNR) plays a crucial role in displaying the image details. The higher the SNR value, the more the information is available. METHODS: In this study, a new function has been formulated using the appropriate suggestions on convolutional combination of the longitudinal and transverse magnetization components related to the relaxation times of T1 and T2 in MRI, where by introducing the distinct index on the maximum value of this function, the new maps are constructed toward the best SNR. Proposed functions were analytically simulated using Matlab software and evaluated with respect to various relaxation times. This proposed method can be applied to any medical images. For instance, the T1- and T2-weighted images of the breast indicated in the reference [35] were selected for modelling and construction of the full width at x maximum (FWxM) map at the different values of x-parameter from 0.01 to 0.955 at 0.035 and 0.015 intervals. The range of x-parameter is between zero and one. To determine the maximum value of the derived SNR, these intervals have been first chosen arbitrarily. However, the smaller this interval, the more precise the value of the x-parameter at which the signal to noise is maximum. RESULTS: The results showed that at an index value of x = 0.325, the new map of FWxM (0.325) will be constructed with a maximum derived SNR of 22.7 compared to the SNR values of T1- and T2-maps by 14.53 and 17.47, respectively. CONCLUSION: By convolving two orthogonal magnetization vectors, the qualified images with higher new SNR were created, which included the image with the best SNR. In other words, to optimize the adoption of MRI technique and enable the possibility of wider use, an optimal and cost-effective examination has been suggested. Our proposal aims to shorten the MRI examination to further reduce interpretation times while maintaining primary sensitivity. SIGNIFICANCE: Our findings may help to quantitatively identify the primary sources of each type of solid and sequential cancer.

Estimation of optimized timely system matrix with improved image quality in iterative reconstruction algorithm: A simulation study.

The system matrix (SM) being a main part of statistical image reconstruction algorithms establishes relationship between the object and projection space. The aim was to determine it in a short duration time, towards obtaining the best quality of contrast images. In this study, a new analytical method based on Cavalieri's principle as subdividing common regions has been proposed in which the precision of the amounts of estimated areas was improved by increasing the number of divisions (NOD), and consequently the total SM's time was increased. An important issue is the tradeoff between the NODs and computational time. For this purpose, a Monte Carlo simulated Jaszczak phantom study was performed by the Monte Carlo N-Particle transport code version 5 (MCNP5) in which the tomographic images of resolution and contrast phantoms were reconstructed by maximum likelihood expectation maximization (MLEM) algorithm, and the influence of NODs variations was investigated. The results show that the lowest and best quality have been obtained at the NODs of 0 and 8, respectively and in the optimum case, the SM's total time at NOD of 8 was 925 s, which was much lower than those of the conventional Monte Carlo simulations and experimental test.

Introducing a novel coefficient on mixed-nanoparticles material: relationship between the theoretical and experimental densities.

Nanoparticles (NPs) indicating a unique potential in bioradiation and nuclear reactor shielding are employed in many fields due to their particular specifications leading improving the mechanical properties as well as pore structure of the concrete-shield. The aim was to introduce a novel coefficient ( ξ ), namely the experimental to theoretical density ratio for mixed-NPs material at various nanoparticles percent concentrations ( ω n a n o ) based on pure mathematical aspects along with the some suitable physical purposes by Monte Carlo method. The change in the mixture density to the change in ω n a n o is always proportional to the ω n a n o value. The density will become maximum at the ω n a n o ∗ in which the physical, morphological and chemical features of NPs along with the amounts of voids in the material have a key role over estimating porosity percentage. The NPs' separation probability as born-cascaded-pairs towards very small radii may be formulated as ξ - ξ - 1 + ω n a n o ∗ + k ' ' | ω n a n o - ω n a n o ∗ | = k ' where k ' and k ' ' are constant values. In conclusion, the theoretical results may be experimentally used in future work for different applications such as designing shield at a nuclear facility.

Estimation of microvascular capillary physical parameters using MRI assuming a pseudo liquid drop as model of fluid exchange on the cellular level.

AIM: One of the most important microvasculatures' geometrical variables is number of pores per capillary length that can be evaluated using MRI. The transportation of blood from inner to outer parts of the capillary is studied by the pores and the relationship among capillary wall thickness, size and the number of pores is examined. BACKGROUND: Characterization of capillary space may obtain much valuable information on the performance of tissues as well as the angiogenesis. METHODS: To estimate the number of pores, a new pseudo-liquid drop model along with appropriate quantitative physiological purposes has been investigated toward indicating a package of data on the capillary space. This model has utilized the MRI perfusion, diffusion and relaxivity parameters such as cerebral blood volume (CBV), apparent diffusion coefficient (ADC), ΔR 2 and Δ R 2 * values. To verify the model, a special protocol was designed and tested on various regions of eight male Wistar rats. RESULTS: The maximum number of pores per capillary length in the various conditions such as recovery, core, normal-recovery, and normal-core were found to be 183 ± 146, 176 ± 160, 275 ± 166, and 283 ± 143, respectively. This ratio in the normal regions was more than that of the damaged ones. The number of pores increased with increasing mean radius of the capillary and decreasing the thickness of the wall in the capillary space. CONCLUSION: Determination of the number of capillary pore may most likely help to evaluate angiogenesis in the tissues and treatment planning of abnormal ones.

Determination of Gamma Camera's Calibration Factors for Quantitation of Diagnostic Radionuclides in Simultaneous Scattering and Attenuation Correction.

OBJECTIVE: The characterization of cancerous tissue and bone metastasis can be distinguished by accurate assessment of accumulated uptake and activity from different radioisotopes. The various parameters and phenomena such as calibration factor, Compton scattering, attenuation and penetration intrinsicallyinfluence calibration equation, and the qualification of images as well. METHODS: The camera calibration factor (CF) translates reconstructed count map into absolute activity map, which is determined by both planar and tomographic scans using different phantom geometries. In this study, the CF for radionuclides of Tc-99m and Sm-153 in soft tissue and bone was simulated by the Monte Carlo method, and experimental results were obtained in equivalent tissue and bone phantoms. It may be employed for the simultaneous correction of the scattering and attenuation rays interacted with the camera, leading to corrected counts. Also, the target depth (d) may be estimated by a combination of scattering and photoelectric functions, which we have published before. RESULTS: The calibrated equations for soft tissue phantom for the radionuclides were obtained by RTc = - 10d+ 300 and RSm = -8d + 100, and the relative errors between the simulated and experimental results were 4.5% and 3.1%, respectively. The equations for bone phantom were RTc = -30d + 300 and RSm = - 10d + 100, and the relative errors were 5.4% and 5.6%. The R and d are in terms of cpm/mCi and cm. Besides, the collimators' impact was evaluated on the camera response, and the relevant equations were obtained by the Monte Carlo method. The calibrated equations as a function of various radiation angles on the center of camera's cells without using collimator indicated that both sources have the same quadratic coefficient by -2E-08 and same vertical width from the origin by 8E-05. CONCLUSION: The presented procedure may help determine the absorbed dose in the target and likewise optimize treatment planning.

Evaluation of tomographic image quality of extended and conventional parallel hole collimators using maximum likelihood expectation maximization algorithm by Monte Carlo simulations.

OBJECTIVE: One of the major problems associated with parallel hole collimators (PCs) is the trade-off between their resolution and sensitivity. To solve this problem, a novel PC - namely, extended parallel hole collimator (EPC) - was proposed, in which particular trapezoidal denticles were increased upon septa on the side of the detector. MATERIALS AND METHODS: In this study, an EPC was designed and its performance was compared with that of two PCs, PC35 and PC41, with a hole size of 1.5 mm and hole lengths of 35 and 41 mm, respectively. The Monte Carlo method was used to calculate the important parameters such as resolution, sensitivity, scattering, and penetration ratio. A Jaszczak phantom was also simulated to evaluate the resolution and contrast of tomographic images, which were produced by the EPC6, PC35, and PC41 using the Monte Carlo N-particle version 5 code, and tomographic images were reconstructed by using maximum likelihood expectation maximization algorithm. RESULTS: Sensitivity of the EPC6 was increased by 20.3% in comparison with that of the PC41 at the identical spatial resolution and full-width at tenth of maximum here. Moreover, the penetration and scattering ratio of the EPC6 was 1.2% less than that of the PC41. The simulated phantom images show that the EPC6 increases contrast-resolution and contrast-to-noise ratio compared with those of PC41 and PC35. CONCLUSION: When compared with PC41 and PC35, EPC6 improved trade-off between resolution and sensitivity, reduced penetrating and scattering ratios, and produced images with higher quality. EPC6 can be used to increase detectability of more details in nuclear medicine images.

Design and performance evaluation of a new high energy parallel hole collimator for radioiodine planar imaging by gamma cameras: Monte Carlo simulation study.

OBJECTIVE: In addition to the trade-off between resolution and sensitivity which is a common problem among all types of parallel hole collimators (PCs), obtained images by high energy PCs (HEPCs) suffer from hole-pattern artifact (HPA) due to further septa thickness. In this study, a new design on the collimator has been proposed to improve the trade-off between resolution and sensitivity and to eliminate the HPA. METHODS: A novel PC, namely high energy extended PC (HEEPC), is proposed and is compared to HEPCs. In the new PC, trapezoidal denticles were added upon the septa in the detector side. The performance of the HEEPCs were evaluated and compared to that of HEPCs using a Monte Carlo-N-particle version5 (MCNP5) simulation. The point spread functions (PSF) of HEPCs and HEEPCs were obtained as well as the various parameters such as resolution, sensitivity, scattering, and penetration ratios, and the HPA of the collimators was assessed. Furthermore, a Picker phantom study was performed to examine the effects of the collimators on the quality of planar images. RESULTS: It was found that the HEEPCD with an identical resolution to that of HEPCC increased sensitivity by 34.7%, and it improved the trade-off between resolution and sensitivity as well as to eliminate the HPA. In the picker phantom study, the HEEPCD indicated the hot and cold lesions with the higher contrast, lower noise, and higher contrast to noise ratio (CNR). CONCLUSION: Since the HEEPCs modify the shaping of PSFs, they are able to improve the trade-off between the resolution and sensitivity; consequently, planar images can be achieved with higher contrast resolutions. Furthermore, because the HEEPCS reduce the HPA and produce images with a higher CNR, compared to HEPCs, the obtained images by HEEPCs have a higher quality, which can help physicians to provide better diagnosis.

Estimation of the Number of Compartments Associated With the Apparent Diffusion Coefficient in MRI: The Theoretical and Experimental Investigations.

OBJECTIVE: The goal of the present study was to estimate the number of compartments and the mean apparent diffusion coefficient (ADC) value with the use of the DWI signal curve. MATERIALS AND METHODS: A useful new mathematic model that includes internal correlation among subcompartments with a distinct number of compartments was proposed. The DWI signal was simulated to estimate the approximate association between the number of subcompartments and the molecular density, with density corresponding to the ratio of the ADC values of the compartments, as determined using the Monte Carlo method. RESULTS: Various factors, such as energy depletion, temperature, intracellular water accumulation, changes in the tortuosity of the extracellular diffusion paths, and changes in cell membrane permeability, have all been implicated as factors contributing to changes in the ADC of water (ADCw); therefore, one may consider them as pseudocompartments in the new model proposed in this study. The lower the coefficient is, the lower the contribution of the compartment to the net signal will be. The results of the simulation indicate that when the number of compartments increases, the signal will become significantly lower, because the gradient factor (i.e., the b value) will increase. In other words, the signal curve is approximately linear at all b values when the number of compartments in which the tissues have been severely damaged is low; however, when the number of compartments is high, the curve will become constant at high b values, and the perfusion parameters will prevail on the diffusion parameters at low b values. Therefore, normal tissues will be investigated when the number of compartments and the ADC values are high and the b values are low, whereas damaged tissues will be evaluated when the number of compartments and the ADC values are low and the b values are high. CONCLUSION: The present study investigates damaged tissues at high b values for which the effect of eddy currents will also be compensated. These b values will probably be used in functional MRI.

Evaluation of Compton attenuation and photoelectric absorption coefficients by convolution of scattering and primary functions and counts ratio on energy spectra.

PURPOSE: Estimation of Compton attenuation and the photoelectric absorption coefficients were explored at various depths. METHODS: A new method was proposed for estimating the depth based on the convolution of two exponential functions, namely convolution of scattering and primary functions (CSPF), which the convolved result will conform to the photopeak region of energy spectrum with the variable energy-window widths (EWWs) and a theory on the scattering cross-section. The triple energy-windows (TEW) and extended triple energy-windows scatter correction (ETEW) methods were used to estimate the scattered and primary photons according to the energy spectra at various depths due to a better performance than the other methods in nuclear medicine. For this purpose, the energy spectra were employed, and a distinct phantom along with a technetium-99 m source was simulated by Monte Carlo method. RESULTS: The simulated results indicate that the EWW, used to calculate the scattered and primary counts in terms of the integral operators on the functions, was proportional to the depth as an exponential function. The depth will be calculated by the combination of either TEW or ETEW and proposed method resulting in the distinct energy-window. The EWWs for primary photons were in good agreement with those of scattered photons at the same as depths. The average errors between these windows for both methods TEW, and ETEW were 7.25% and 6.03% at different depths, respectively. The EWW value for functions of scattered and primary photons was reduced by increasing the depth in the CSPF method. CONCLUSIONS: This coefficient may be an index for the scattering cross-section.

Evaluation of various energy windows at different radionuclides for scatter and attenuation correction in nuclear medicine.

OBJECTIVE: Improving signal to noise ratio (SNR) and qualified images by the various methods is very important for detecting the abnormalities at the body organs. Scatter and attenuation of photons by the organs lead to errors in radiopharmaceutical estimation as well as degradation of images. The choice of suitable energy window and the radionuclide have a key role in nuclear medicine which appearing the lowest scatter fraction as well as having a nearly constant linear attenuation coefficient as a function of phantom thickness. METHODS: The energy windows of symmetrical window (SW), asymmetric window (ASW), high window (WH) and low window (WL) using Tc-99m and Sm-153 radionuclide with solid water slab phantom (RW3) and Teflon bone phantoms have been compared, and Matlab software and Monte Carlo N-Particle (MCNP4C) code were modified to simulate these methods and obtaining the amounts of FWHM and full width at tenth maximum (FWTM) using line spread functions (LSFs). The experimental data were obtained from the Orbiter Scintron gamma camera. RESULTS: Based on the results of the simulation as well as experimental work, the performance of WH and ASW display of the results, lowest scatter fraction as well as constant linear attenuation coefficient as a function of phantom thickness. WH and ASW were optimal windows in nuclear medicine imaging for Tc-99m in RW3 phantom and Sm-153 in Teflon bone phantom. Attenuation correction was done for WH and ASW optimal windows and for these radionuclides using filtered back projection algorithm. Results of simulation and experimental show that very good agreement between the set of experimental with simulation as well as theoretical values with simulation data were obtained which was nominally less than 7.07 % for Tc-99m and less than 8.00 % for Sm-153. Corrected counts were not affected by the thickness of scattering material. The Simulated results of Line Spread Function (LSF) for Sm-153 and Tc-99m in phantom based on four windows and TEW method were indicated that the FWHM and FWTM values were approximately the same in TEW method and WH and ASW, but the sensitivity at the optimal window was more than that of the other one. CONCLUSIONS: The suitable determination of energy window width on the energy spectra can be useful in optimal design to improve efficiency and contrast. It is found that the WH is preferred to the ASW and the ASW is preferred to the SW.

Modulation transfer function assessment in parallel beam and fan beam collimators with square and cylindrical holes.

OBJECTIVE: This study investigates modulation transfer function (MTF) in parallel beam (PB) and fan beam (FB) collimators using the Monte Carlo method with full width at half maximum (FWHM), square and circular-shaped holes, and scatter and penetration (S + P) components. METHODS: A regulation similar to the lead-to-air ratio was used for both collimators to estimate output data. The hole pattern was designed to compare FB by PB parameters. The radioactive source in air and in a water phantom placed in front of the collimators was simulated using MCNP5 code. RESULTS: The test results indicated that the square holes in PB (PBs) had better FWHM than did the cylindrical (PBc) holes. In contrast, the cylindrical holes in the FB (FBc) had better FWHM than the square holes. In general, the resolution of FBc was better than that of the PBc in air and scatter mediums. The S + P decreased for all collimators as the distance from the source to the collimator surface (z) increased. The FBc had a lower S + P than FBs, but PBc had a higher S + P than PBs. Of the FB and PB collimators with the identical hole shapes, PBs had a smaller S + P than FBs, and FBc had a smaller S + P than PBc. The MTF value for the FB was greater than for the PB and had increased spatial frequency; the FBc had higher MTF than the FBs and PB collimators. CONCLUSIONS: Estimating the FB using PB parameters and diverse hole shapes may be useful in collimator design to improve the resolution and efficiency of SPECT images.

Evaluation of collimators' response: round and hexagonal holes in parallel and fan beam.

With regard to the different requirements, various collimators are widely employed within nuclear medicine systems in order to evaluate the metabolism of organs as well as improve the contrast of images and better diagnosis. In this study, Fan Beam (FB) and Parallel Beam (PB) collimators in the shapes of round and hexagonal holes have been investigated and compared based on the Geometric Efficiency (G), Geometric Resolution (R(c)), Total Resolution (R(t)), FWHM and Scatter and Penetration (S + P) components using the Monte Carlo simulation. Calculations demonstrated that the G was improved with the increase in the distance between point source and collimator face (z). In contrast, the G was reduced with an increase in the angle of slant hole. In the FB collimator, the R(c) and R(t) were increased when the increase in the hole angle and/or the distance. The simulated results indicated in both collimators with the increase in z, a) the FWHM was increased as well as the peak of the PSF curve was decreased, and b) the S + P amounts decreased, but in the distinct z, the FWHM of the FB collimator is better than that of the PB collimator. It is shown that the results were in agreement with the ADAC company data. Also, Benchmark for measuring ADAC company demonstrated the calculated and simulated amounts of the R(c) and R(t) with round and hexagonal holes shapes had maximum and minimum average relative differences equal to -7.6% for PB and 1% for FB, respectively.

Estimation of fan beam and parallel beam parameters in a wire mesh design.

UNLABELLED: Special collimators used in imaging systems play an important part in obtaining qualified images to improve diagnosis in medicine. METHODS: The primary aim of this study was to compare resolution between fan beam and parallel beam collimators using Monte Carlo simulation in the shape of cubic holes. Also, parameters such as geometric efficiency, geometric resolution, scatter, penetration, and full width at half maximum were studied to compare their special characteristics. RESULTS: The simulation results demonstrated that the geometry efficiency of a fan beam collimator increased as the angle of the slant hole increased, and the geometric resolution decreased as the angle of the slant hole increased, at a distinct distance from a monoenergetic source of γ-rays. In contrast, at a distinct angle, geometric resolution increased as the distance between the source and the collimator surface increased. For both collimators, scatter and penetration decreased as the distance increased. These results were in agreement with ADAC company data. Finally, fan beam collimators were found to have better resolution than parallel beam collimators with a cubic hole shape in a wire mesh design. CONCLUSION: Estimation of the fan beam by parallel beam parameters as cubic holes can be suitable in collimator design to improve resolution and efficiency.