Home About us Editorial board Search Ahead of print Current issue Archives Submit article Instructions Subscribe Contacts Login 
Home Print this page Email this page Small font size Default font size Increase font size Users Online: 362

 Table of Contents 
Year : 2022  |  Volume : 45  |  Issue : 3  |  Page : 131-137  

Optimization of FLUKA detector model for HPGe array

1 Health Physics Division, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India
2 Health Physics Division, Bhabha Atomic Research Centre; Homi Bhabha National Institute, Mumbai, Maharashtra, India

Date of Submission29-Nov-2022
Date of Decision23-Dec-2022
Date of Acceptance11-Jan-2023
Date of Web Publication18-May-2023

Correspondence Address:
C S Charubala
Health Physics Division, Bhabha Atomic Research Centre, Mumbai, 400 085, Maharashtra
Login to access the Email id

Source of Support: None, Conflict of Interest: None

DOI: 10.4103/rpe.rpe_35_22

Rights and Permissions

Monte Carlo codes, such as FLUKA, are widely used to optimize calibration of spectrometric systems. HPGe detector array (HDA) for lung monitoring was modeled in FLUKA code using available information about their geometry and optimized for efficiency using 241Am point source at smaller distances (<10 cm) as in case of in-vivo monitoring scenarios. Thickness of dead layer (DL) on the top and lateral detector surfaces for low energy counting was determined by considering the experimental and simulated efficiency for various energies. Using trial and error method, optimized DL thickness was found out to be 2.5 μm on top surface and 1.8 mm on lateral surfaces for each HPGe detector in the array. For the optimized model, it was found that the simulated and experimental efficiency and the simulated and experimental spectra were in reasonable agreement. Optimization of the HDA was an important benchmarking step to reduce the simulation errors before they are implemented in complex numerical problems using computational phantoms.

Keywords: Dead layer, FLUKA, gamma spectrometry, HPGe detector array

How to cite this article:
Charubala C S, Santhanakrishnan V, Ganesh G, Kulkarni M S. Optimization of FLUKA detector model for HPGe array. Radiat Prot Environ 2022;45:131-7

How to cite this URL:
Charubala C S, Santhanakrishnan V, Ganesh G, Kulkarni M S. Optimization of FLUKA detector model for HPGe array. Radiat Prot Environ [serial online] 2022 [cited 2023 Jun 2];45:131-7. Available from: https://www.rpe.org.in/text.asp?2022/45/3/131/377233

  Introduction Top

Direct detection of gamma-emitting radionuclides in the human body has been conventionally carried out by organ monitoring and whole body counting techniques using gamma spectrometry systems[1],[2] In-vivo monitoring of lungs for radiation workers is generally carried out using HPGe detector array (HDA) or Phoswich-based detection system within the steel room to reduce the background in the low energy region.[3] The calibration of the detection system is carried out by Lawrence Livermore National Laboratory[4] or Japan Atomic Energy Research Institute[5] physical phantoms. Although the efficiency of detector systems is evaluated using physical phantoms for the purpose of practical applications, it is appreciable to perform numerical calibration for solving more specific problems. The availability of ICRP computational phantoms[6],[7],[8] along with various Monte Carlo codes has made it possible to numerically calibrate the in vivo detection systems[9],[10] However, in order to compare the numerical calculations using voxel phantom with other physical calibration methods, the detection systems themselves should be validated.[11],[12]

Previous research shows that the operation of HPGe detectors over several years can lead to the change in dead layer (DL) thickness on the detector surface.[13] DL is usually a thin layer of detector material which is not useful for the detection purpose but attenuates the radiation.[14] In a previous study, the relative deviation (RD) in efficiency between experiment and simulations for 59.5 keV using nominal detector parameters of p-type Ge spectrometers was reported to be 159% which was further reduced to 13% using an optimized model.[15] Several other studies also shows the importance of incorporating the DL thickness in the Monte Carlo model for the accurate description of the system.[15],[16],[17] Various methods were conventionally implemented in simulations to determine the DL thickness of HPGe systems.[15],[18],[19]

In the current study, the n-type detectors in HDA are expected to have nominal DL thicknesses of a few micrometers on its top surface considering its applicability in low energy photons counting. The lateral DL of HDA may act as a controlling element for active volume whose effect becomes prominent at higher energies.[17] Simulations were performed using FLUKA Monte Carlo Code to determine top and lateral DL thicknesses and the HDA system was optimized for its use in low energy organ counting scenarios.

  Materials and Methods Top

HPGe detector array system in steel room

The HDA system for lung counting is housed inside the steel room of internal dimension 2500 mm × 2000 mm × 2000 mm. The room is shielded by 200 mm low background mild steel with graded lining of 3 mm Pb + 2 mm Cd + 1 mm3 from all sides. HDA consists of an array of three large area Canbera make n-type HPGe detectors (Model No: EGMP3 × 60-20-R). The dimension of each detector is 60 mm dia, 20 mm thickness and 1.1 mm carbon entrance window. The three detectors are arranged in triangular geometry and mounted in copper casing which is connected to a liquid nitrogen Dewar. The geometric model of HDA system based on manufacturer specifications is shown in [Figure 1]. Each detector output is connected to separate Multi Channel Analyzer cards and integrated to generate the summed spectrum using the acquisition and analysis software Interwinner 7.0. The geometry HDA was incorporated in FLUKA code to evaluate the spectrum and counting efficiency (CE).
Figure 1: Geometric description of HPGe detector array system based on specifications

Click here to view

Experimental measurements

The experimental efficiency of HDA was determined using 241Am source from Areva (AM241EGSA10) with active area diameter of 3 mm, holder diameter of 25 mm and activity of 4.2 kBq. The measurement uncertainty of 241Am source quoted by the manufacturer is 3.5%. The experimental efficiency of the detection system was obtained by placing the 241Am source under HDA in such a way that the centre of the source coincides with the center of the triangle formed by the three HPGe detectors [Figure 2]a. The counting measurements were repeated for at least two trials and CE can be calculated for each trial using the Equation; (1)
Figure 2: Irradiation Geometry for HPGe detector array: (a) Experiment (b) Simulation

Click here to view

where G is the sum of gross counts from three HPGe detectors acquired in T seconds, B is the background counts in T seconds and A is the decay corrected activity of the source. The experimental spectra after summation of outputs from individual detectors were generated by Interwinner 7.0.

FLUKA simulations

FLUKA is a general purpose Monte Carlo code[20],[21],[22] used for particle transport simulations and it can be integrated with FLAIR,[23] an advanced user friendly graphical interface for input creation and geometry visualization. For the purpose of simulations, 241Am source of 3 mm diameter encapsulated in Perspex emitting the energies and yields as given in [Table 1][24] was incorporated using the user written source routine in FLUKA. The source was located under the HDA system in simulations as per the measurement geometry considered in experiments [Figure 2]b. It may be noted that the Source to Detector Distance (SDD) in FLUKA code varies along the Y-axis of the coordinate system. The input file for FLUKA simulations was generated using a combination of relevant cards in FLAIR. The geometry of the detectors can be created by forming regions based on the available detector specifications and assigning the corresponding materials to these regions. The detector spectra was simulated using DETECT card for scoring energy deposition in terms of counts/photon. The simulations were run for 20 × 106 histories so that the relative error falls below 2% for all values considered in the study.
Table 1: Yields of various gamma energies used for simulating 241Am point source

Click here to view

To compare the simulation with experimental results, output of DETECT card must be treated for Gaussian energy broadening, gamma abundance, experimental source activity and counting time. Gaussian broadening was performed using a user routine, userou.f, provided by FLUKA (https://fluka.cern) so that the output of DETECT card gives Gaussian smeared values. This user routine requires to be supplied with the regression coefficients (A, B and C) of the Full Width at Half Maximum (FWHM) function,[25],[26] characteristic of the detector as given by Equation (2).

Hence to determine the FWHM function, a series of experimental measurements were performed. 152Eu disc source (25 mm diameter, 6 mm thickness) was used to obtain FWHM values of the summed spectra for a range of gamma energies (E). The FWHM function was obtained in the form of Equation (2) by regression method.

The Gaussian smeared output of DETECT card was also corrected for abundance of respective gamma energies[24] [Table 1]. The counts registered in the region of interest in the output were summed to obtain the CE for simulated detector response. Since DETECT card output gives counts per incident photon for energy intervals, it was further multiplied by experimental source activity and counting time so that the experiments and simulation spectra can be compared.

Optimization of detector model and dead layer thickness

For the HDA system used in this study, the initial DL thickness at the time of manufacturing is unknown. Iteration method was implemented to determine the top and lateral thickness of DL for HDA system. If Dtop is the top DL thickness, and Dlat is lateral DL thickness of HDA, it is assumed that the DL thickness is uniform on each surface and all the three detectors have same Dtop and Dlat. This assumption is based on the fact that all the three detectors were identically manufactured and operated in unison under same conditions at all times. Various DL thicknesses starting from nominal values were assumed on the detector surfaces of HDA for carrying out simulations. It may be noted that increased thickness of DL also means a reduced active volume for the detection system.

Although the current work look for optimization of HDA system for the detection of most useful 59.5 keV gamma energy, the system was also used in wound monitoring scenarios where lower energies of 241Am was also proven to be useful.[27] counting time was set in such a way that the peak area counts are ~ 104. Any effect of coincidence summing at close measurement geometry was not considered in this study. Using FLUKA simulations, a combination of most suitable values of DL thicknesses (Dtop and Dlat) which leads to the least deviation from experimental efficiencies was estimated for the optimization purpose, considering 241Am energies.

  Results and Discussion Top

Verification of measurement geometry

The measurement geometry for HDA simulations was verified by plotting the source particles superimposed on the X-Z plane of the array of detectors. The source particle intensity (in arbitrary units) in XZ plane is plotted in [Figure 3] which is as expected from the low energy photons of 241Am source used in experiments according to the measurement geometry in [Figure 2].
Figure 3: Source particle intensity in measurement geometry for HPGe detector array

Click here to view

Full width at half maximum function

FWHM values of summed spectra (as obtained by Interwinner 7.0 software) for various energies of 152Eu were used to derive FWHM function in terms of energies by the method of regression [Figure 4].
Figure 4: Plot of FWHM variation with energy for HPGe detector array. FWHM: Full width at half maximum

Click here to view

The regression coefficients in Equation (3), after converting to the units of GeV, are incorporated in FLUKA simulations to generate Gaussian smeared spectra.

Dead layer thickness estimation

A uniform DL formation was assumed in all the three detectors in HDA as the detectors are similar and always used together under same measurement conditions. In the simulations, CEs for all the energies in 241Am spectra was estimated for various combinations of surface DLs, i.e., (Dtop, Dlat). In this iterative method, Dtop was varied without Dlat to deduce effect of top DL on CE. Similarly, in another set of trials, Dlat was varied without Dtop in picture. The variations in CE with respect to lateral and top DL thicknesses are shown in [Figure 5]. It is found that 10 μm difference in Dlat leads to almost no difference in CE for all the energies considered. A change of 100 μm in Dlat leads to ~0.3% difference in CEs of all energies and a change in 1000 μm leads to ~4% difference in CEs. Meanwhile, for a change in Dtop by 2 μm, CE reduces by 15% for 13.9 keV, 8% for 17.8 keV, 6% for 20.8 keV, 3% for 26.3 keV and 0.3% for 59.5 keV. Thus, the numerical experiments on effects of changing surface DL thicknesses on efficiency gave results as expected theoretically. It was found that CE reduces slower with the lateral thickness of DL and faster with the top DL. This also indicates that the change in active volume due to lateral DL leads to a smaller change in CE for a range of lower energy photons, but change in top DL presents attenuation that reduces with increasing energy.
Figure 5: Variation in counting efficiency with (a)lateral and (b) top DL thickness values

Click here to view

Taking all these results to consideration, it may be deduced that a few micrometers of thickness for Dtop and a few millimeters of thickness for Dlat for each detector in HDA could make an optimized model. The CEs corresponding to various combinations of DL thickness values used in iterations are summarized in [Table 2]. RD for simulated results with experiment for each (Dtop, Dlat) pair was estimated for all energies [Table 3]. The values of ratio (R) given in [Table 4] are derived as the ratio of counts in lower energy peaks to that in 59.5 keV peak. Hence, if 59.5 keV has R = 1, the relative counts in the lower energy peaks can give an idea about similarity between the experimental and simulated spectra. It was found that the greatest similarity between experiment and simulations (i.e., minimum RD for 59.5 keV, but all lower energies also have reasonably low RDs and closest match of R with the experiment) corresponds to Dtop = 2.5 μm and Dlat = 1.8 mm. Although (2.5 μm, 2 mm) also gives results of less RD and closer R for all energies in general, the former combination was chosen since our aim was to optimize the system for the most useful energy, 59.5 keV, firstly. However, secondarily, since lower energies are considered while using HDA as a wound monitor, the reasonably lower RD and closer R for those energies were also taken into consideration in the optimization process.
Table 2: Counting efficiencies obtained from simulations for various dead layer thicknesses and experimnt for SDD=5 cm

Click here to view

Click here to view
Table 4: Ratio for various energies corresponding to (Dtop, Dlat) (Dtop in μm and Dlat in mm) and experiment

Click here to view

Introducing a DL combination of (2.5 μm, 1.8 mm) in HDA leads to the reduction of active volume from 169.56 cm3 (3 × 56.52 cm3) to 149.80 cm3 (3 × 49.93 cm3). A comparison picture of CE variation corresponding to three scenarios, i.e., without any DL, with optimized DL and experiment is shown in [Figure 6]. It can be seen that the optimized model exhibits more similarity with the experimental CEs.
Figure 6: Variation CE with energy without dead layer, with optimized model and experiment. CE: counting efficiency

Click here to view

The experiment and simulated detector spectrum for 241Am corresponding to the optimized model and (Source to Detector Distance) SDD = 5 cm is shown in [Figure 7]. The comparison of both the spectra shows a slight channel shift due to energy calibration. Although, CE of 59.5 keV is greatly matching between experiment and simulations, the peak is not replicated exactly but reasonably matching. This is due to Gaussian smearing in simulations not precisely replicating the experimental peak broadening effects. However, since the counts under the peak area matches between experiment and simulations, the model can be regarded as valid for practical calibration purposes.
Figure 7: Experimental and simulated spectra for HPGe detector array for SDD = 5 cm

Click here to view

Verification of optimized model

The optimized model of HDA was used in simulations to determine CEs at two different SDDs, i.e., SDD = 6 cm and SDD = 10 cm for all the energies of 241Am. The results obtained from simulations and experiments are listed in [Table 5]. It can be seen from [Table 5] that the experiment and simulated CEs differ by 1% for SDD = 6 cm and 4% for SDD = 10 cm for 59.5 keV gamma energy. For all the other energies variations lie between 2% (for 20.8 keV) and 6% (26.3 keV) for SDD = 6 cm and 5% (for 26.3 ekV) and 9% (for 17.8 keV) for SDD = 10 cm. The results of the verification exercise show that HDA system can be regarded as an optimized model for low energy counting at shorter distances since the simulated results are in concordance with experiments with deviations <10%.
Table 5: Counting efficiencies at two different SDDs from experiment and simulations

Click here to view

Uncertainty evaluation

A brief evaluation of possible uncertainty components associated with the experiments was performed. It may be noted that Type A uncertainties associated with statistical fluctuations are ~1% for all measurements since the data acquisition time was chosen such that peak area counts are ~104. Type B uncertainties associated with the systematic errors of the measurements include uncertainty in the preparation of calibration sources, positional errors, changes in measurement conditions, errors in data acquisition, and spectrum analysis, etc.[28] When the measurements are compared with FLUKA results, the simulation uncertainties such as differences in material composition of detector parts,[29] detector dimensions and FWHM function incorporated in the code may also be considered.

It was found from the current study that the efficiency reduces significantly with top DL thickness for lower energies. With the absence of DL thickness in the simulations, the discrepancy with experimental measurements was as high as 29% for 13.8 keV. In case of HDA system, the measurement geometry was achieved by manual adjustment of the source so that it faces the center of the triangle formed by the centers of three HPGe detectors. The source to detector distance was set using a measuring scale of least count 1 mm and adjusting the source base, which is subjected to parallax errors. A set of FLUKA simulations was performed for various coordinates to estimate positional errors corresponding to 5 mm displacement along X (Δx), Y (Δy) and Z (Δz) axes for SDD = 5 cm and CEs obtained are tabulated in [Table 6]. The results show that the deviations are highest along Y-axis with 7% for 59.5 keV, 4% for 13.9 keV and 6% for all other energies. The displacement along X and Z axes leads to negligible change in CEs for HDA.
Table 6: Counting efficiencies for source displacement of 0.5 mm along x, y and z axes

Click here to view

  Conclusions Top

In the current study, top and lateral DL thicknesses were determined for the HDA system by trial and error method. The simulated values of CE were compared with the experimental results for various energies of 241Am point source. A very good correlation of experimental and simulated efficiencies was obtained at top DL thickness of 2.5 μm and lateral DL thickness between 1.8 and 2 mm. For an optimized model, 1.8 mm lateral thickness was chosen as it gives the closest match with experimental efficiency for 59.5 keV emissions, which is used for in-vivo detection of 241Am. The optimized model was verified at different SDDs and the difference in CEs between optimized FLUKA model and experiments was found to be <10% for all energies of 241Am. It was also observed that 5 mm displacement of source from the detector causes 4%–7% change in efficiency for HDA system for various energies of 241Am for SDD = 5 cm, while the same displacement along the plane of detectors caused negligible difference in terms of efficiency. The optimized of FLUKA detector model for HDA may be used in advanced numerical problems related to in vivo monitoring, making use of voxel or mesh phantoms.


We thank all the staff members of health physics laboratory for their help related to this work.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

  References Top

Griffith R, et al. Direct determination of the body content of radionuclides: Abstract. J ICRU 2003;3:9-9. [doi: 10.1093/jicru/3.1.9].  Back to cited text no. 1
International Atomic Energy Agency. Direct Methods for Measuring Radionuclides in the Human Body. Vienna: International Atomic Energy Agency; 1996.  Back to cited text no. 2
International Atomic Energy Agency. Occupational Radiation Protection, General Safety Guides. Vienna: International Atomic Energy Agency; 2018.  Back to cited text no. 3
Griffith RV, Anderson AL, Dean PN, Fisher JC, Sundbeck CW. Tissue-equivalent Torso Phantom for Calibration of Transuranic-nuclide Counting Facilities. United States; 1986.  Back to cited text no. 4
Shirotani T. Realistic torso phantom for calibration of in-vivo transuranic-nuclide counting facilities. J Nucl Sci Technol 1988;25:875-883. [doi: 10.1080/18811248.1988.9735941].  Back to cited text no. 5
Bolch WE, Eckerman K, Endo A, Hunt JG, Jokisch DW, Kim CH, et al. ICRP publication 143: Paediatric reference computational phantoms. Ann ICRP 2020;49:5-297.  Back to cited text no. 6
ICRP. Adult reference computational phantoms ICRP. In: Annals of the ICRP. Vol. 110. 2009.  Back to cited text no. 7
Kim CH, Yeom YS, Petoussi-Henss N, Zankl M, Bolch WE, Lee C, et al. ICRP publication 145: Adult mesh-type reference computational phantoms. Ann ICRP 2020;49:13-201.  Back to cited text no. 8
de Carlan L, Roch P, Blanchardon E, Franck D. Application of voxel phantoms in whole-body counting for the validation of calibration phantoms and the assessment of uncertainties. Radiat Prot Dosimetry 2007;125:477-82.  Back to cited text no. 9
Takahashi M, Kinase S, Kramer R. Evaluation of counting efficiencies of a whole-body counter using Monte Carlo simulation with voxel phantoms. Radiat Prot Dosimetry 2011;144:407-10.  Back to cited text no. 10
Conti CC, Salinas IC, Zylberberg H. A detailed procedure to simulate an HPGe detector with MCNP5. Prog Nucl Energy 2013;66:35-40. [doi: 10.1016/j.pnucene. 2013.03.003].  Back to cited text no. 11
Hegenbart L, Marzocchi O, Breustedt B, Urban M. Validation of a Monte Carlo efficiency calibration procedure for a partial body counter system with a voxel model of the LLNL torso phantom. Radiat Prot Dosimetry 2009;133:158-64.  Back to cited text no. 12
Huy NQ, Binh DQ, An VX. Study on the increase of inactive germanium layer in a high-purity germanium detector after a long time operation applying MCNP code. Nucl Instrum Methods Phys Res A 2007;573:384-388. [doi: 10.1016/j.nima. 2006.12.048].  Back to cited text no. 13
Knoll, Glenn F. Radiation detection and measurement / Glenn F. Knoll Wiley New York 1989  Back to cited text no. 14
Budjás D, Heisel M, Maneschg W, Simgen H. Optimisation of the MC-model of a p-type Ge-spectrometer for the purpose of efficiency determination. Appl Radiat Isot 2009;67:706-10.  Back to cited text no. 15
Chuong HD, Thanh TT, Ngoc Trang le T, Nguyen VH, Tao CV. Estimating thickness of the inner dead-layer of n-type HPGe detector. Appl Radiat Isot 2016;116:174-7.  Back to cited text no. 16
Ródenas J, Pascual A, Zarza I, Serradell V, Ortiz J, Ballesteros L. Analysis of the influence of germanium dead layer on detector calibration simulation for environmental radioactive samples using the Monte Carlo method. Nucl Instrum Methods Phys Res A 2003;496:390-399. [doi: 10.1016/S0168-9002(02)01748-5].  Back to cited text no. 17
Elanique A, Marzocchi O, Leone D, Hegenbart L, Breustedt B, Oufni L. Dead layer thickness characterization of an HPGe detector by measurements and Monte Carlo simulations. Appl Radiat Isot 2012;70:538-42.  Back to cited text no. 18
Loan TT, Ba VN, Thy TH, Hong HT, Huy NQ. Determination of the dead-layer thickness for both p- and n-type HPGe detectors using the two-line method. J Radioanal Nucl Chem 2018;315:95-101. [doi: 10.1007/s10967-017-5637-8].  Back to cited text no. 19
Ahdida C, Bozzato D, Calzolari D, Cerutti F, Charitonidis N, Cimmino A, et al. New Capabilities of the FLUKA Multi-Purpose Code, Frontiers in Physics 2022;9:788253.  Back to cited text no. 20
Battistoni G, Boehlen T, Cerutti F, Chin PW, Esposito LS, Fassò A, et al. Overview of the FLUKA code, Annals of Nuclear Energy 2015;82: 10-8.  Back to cited text no. 21
Available from: https://fluka.cern. [last accessed on 2022 Nov 20]  Back to cited text no. 22
Vlachoudis V, FLAIR: A Powerful But User Friendly Graphical Interface For FLUKA, Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs: New York; 2009. p. 790-800.  Back to cited text no. 23
International Atomic Energy Agency. Update of X Ray and Gamma Ray Decay Data Standards for Detector Calibration and Other Applications. Vol. 2. Vienna: International Atomic Energy Agency; 2007.  Back to cited text no. 24
Eftekhari Zadeh E, Feghhi SA, Bayat E, Roshani GH. Gaussian Energy Broadening Function of an HPGe Detector in the Range of 40 keV to 1.46 MeV. J Exp Phys 2014;2014:1–4. [doi: 10.1155/2014/623683].  Back to cited text no. 25
Metwally WA, Gardner RP, Sood A. Gaussian broadening of MCNP pulse height spectra. Transactions of the American Nuclear Society 2004;91:789-790.  Back to cited text no. 26
Nadar MY, Patni HK, Akar DK, Mishra L, Singh IS, Rao DD, et al. Monte Carlo simulation of embedded 241Am activity in injured palm. Radiat Prot Dosimetry 2013;154:148-56.  Back to cited text no. 27
Schlagbauer M, Hrnecek E, Rollet S, Fischer H, Brandl A, Kindl P. Uncertainty budget for a whole body counter in the scan geometry and computer simulation of the calibration phantoms. Radiat Prot Dosimetry 2007;125:149-52.  Back to cited text no. 28
Vrba T. Crucial parameters for proper simulation of the detector used in in vivo measurements. Radiat Prot Dosimetry 2016;170:359-363. [doi: 10.1093/rpd/ncv448].  Back to cited text no. 29


  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]

  [Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]


Similar in PUBMED
   Search Pubmed for
   Search in Google Scholar for
 Related articles
Access Statistics
Email Alert *
Add to My List *
* Registration required (free)

  In this article
Materials and Me...
Results and Disc...
Article Figures
Article Tables

 Article Access Statistics
    PDF Downloaded36    
    Comments [Add]    

Recommend this journal