- Email: [email protected]
Investigation on a small FoV gamma camera based on LaBr3:Ce continuous crystal
Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205 www.elsevier.com/locate/npbps
Investigation on a small FoV gamma camera based on LaBr3 :Ce continuous crystal R. Pania∗ , R. Pellegrinia , P. Bennatib , M. N. Cintic , F. Vittorinic , R. Scaf`ed , S. Lo Meoe , F. L. Navarriae , G. Moschinif , V. Orsolini Cencellig , F. De Notaristefanig a
INFN Rome and Experimental Medicine Dpt. Sapienza University of Rome, Rome (Italy).
b
INFN Rome and EDEMOM PhD School of Microelectronics, University of Rome III, Rome (Italy).
c
INFN Rome and Physics Dpt. Sapienza University of Rome, Rome (Italy).
d e f
INFN and ENEA, Casaccia, Rome (Italy).
INFN Bologna and Physics Dpt. Alma Mater Studiorum - University of Bologna, Bologna (Italy)
INFN - LNL and Physics Dpt. University of Padua, Padua (Italy).
g
INFN Department of Engineering Electronic ”Roma III” University of Rome, Rome (Italy).
Recently scintillating crystals with high light yield coupled to photodetectors with high quantum efficiency have been opening a new way to make gamma cameras with superior performances based on continuous crystals. In this work we propose the analysis of a gamma camera based on a continuous LaBr3 :Ce crystal coupled to a multi-anodes photomultiplier tube (MA-PMT). In particular we take into account four detector configurations, different in crystal thicknesses and assembling. We utilize a new position algorithm to reduce the position non linearity affecting intrinsic spatial resolution of small FoV gamma cameras when standard Anger algorithm is applied. The experimental data are obtained scanning the detectors with 0.4 mm collimated 99m Tc source, at 1.5 mm step. An improvement in position linearity and spatial resolution of about a factor two is obtained with the new algorithm. The best values in terms of spatial resolution were 0.90 mm, 0.95 mm and 1.80 mm for integral assembled, 4.0 mm thick and 10 mm thick LaBr3 :Ce crystal respectively.
1. Introduction Single Photon Emission techniques may be the best choice when sub-millimeter spatial resolution is required. Over the last years scintillation crystal arrays have been developed with very small pixel size (about 1.0 mm pitch size for NaI:Tl and CsI:Tl crystal respectively) with the intrinsic spatial resolution limited by pixel size. Many researchers have utilized continuous crystal of different scintillation materials to make gamma cameras with small Field of View (FoV), obtaining spatial resolution worse than scintilla∗ Corresponding
Author: [email protected] “Sapienza” University of Rome Viale Regina Elena 272 00161, Rome Italy (telephone and fax: +390649918277)
0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.10.067
tion array [1]-[2]. Continuous LaBr3 :Ce crystal, with an excellent energy resolution and high light yield, could be the best candidate to obtain a gamma imaging detector with sub-millimeter spatial resolution. LaBr3 :Ce scintillation crystal has very similar absorption radiation properties than NaI:Tl and a light yield almost twice with better energy resolution response. Recently Pani et al.[3] have measured spatial resolution values less than 1.0 mm with a 49 mm × 49 mm LaBr3 :Ce continuous crystal, 5.0 mm thickness corresponding to a detection efficiency of about 80% at 140keV. To better understand the capabilities in gamma ray imaging of this scintillation crystal, in this work a more complete study of four continuous LaBr3 :Ce crystals is presented.
R. Pani et al. / Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205
2. Equipment and Method 2.1. Experimental set up and measurements In this study we take into account three continuous LaBr3 :Ce scintillation crystals with same detection area of 51 mm × 51 mm. Two of them have a 3.0 mm glass window and the same 4.0 mm thickness, chosen to minimize the distance between photocathode and photon interaction point and to obtain a detection efficiency of about 70% at 140 keV. They differ for the treatment of the front surface: the first one is grounded with black coating and the second one is polished with white coating. The third one has 10 mm thickness with 3.0 mm glass window and the front surface is polished with white coating. The 10 mm thickness is chosen to have the highest detection efficiency at 140 keV (95%) and eventually to investigate the response at higher photon energies. A fourth crystal is taken into account with 49 × 49 mm2 detection area, 5.0 mm thickness, integral assembled to a Multi Anode -Photomultiplier (MAPMT), and the same front surface treatment as previous one. This assembling allows to remove the additional glass window reducing the overall optical guide thickness to 1.5 mm. In this configuration we expect narrowest light distribution and an 80% efficiency at 140 keV photon energy. To avoid light reflections and consequent light PSF distortions, all crystals have a black light absorber at the edges. In Table 1 the characteristics of all scintillation crystals are summarized.
Table 1 LaBr3 :Ce crystals configurations Thick Windows Edge Surface 4 mm 3 mm Black Ground 4 mm 3 mm White Polished 10 mm 3 mm White Polished 5 mm no White Polished
Eff 70% 70% 95% 80%
All scintillation crystals are coupled to a Hamamatsu H8500 flat panel MA-PMT. This PMT has an external size of 52 mm × 52 mm × 14.7 mm,
203
the photocathode is bialkali and 12 stages metal channel dynode are used as electron multiplier. An array of 8×8 anodes (64 channels - 6 mm pitch) is used for position determination. The PMT gain is about 3 ×106 at - 1000V. It is characterized by an anode dark current of 1 nA, a glass window thickness of 1.5 mm and finally by anode gain variation range of about 45:100. An individual anode electronic read out was used, READ system, developed at Southampton University [4], in which the charge on each anode is individually read out and digitized. The READ system, 64 independent channels, is based on four HX2 chip. The serial output from the HX2 board is subsequently red by a 1.5 MHz National Instruments DAQ 6110E Analogue to Digital Converter (ADC) mounted in host PC. On all LaBr3 :Ce crystals we perform a scanning by a 0.4 mm collimated 99m Tc source, at 1.5 mm step. The spatial resolution is calculated applying a new algorithm for position determination, shortly described in the next paragraph, and presented in [5]. 2.2. New Centroid Algorithm for position determination The classical algorithm, proposed by Anger in 1958 [6], applied on the 8×8 charge distribution of MA-PMT anode plane, permits to calculate the event position (XC and YC) as the weighted centroid of the charge distribution. The Intrinsic Spatial resolution (ISR) can be expressed by the formula [5]: F W HMP SF image (1) ISR = L where L is the position linearity, representing the angular coefficient of position linearity curve at each measured point and F W HMP SF image is relative to the Point Spread Function of the image, assumed to have a two dimensional Gaussian shape. Equation 1 suggests that ISR is improved if F W HMP SF is reduced, obtainable by reducing the thickness of the crystal and/or the light guide. Linearity also influences intrinsic spatial resolution since ISR is minimized by L =1 (best linearity). A new algorithm is proposed [5] to improve position determination, operating on the light PSF. The new procedure, applied on the collected two dimensional charge distributions
204
R. Pani et al. / Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205
on MA-PMT anodic array, consists of applying a threshold, to remove the charge (light) background, and of a squaring, that produces a narrowing of the measured charge distribution. The centroid algorithm is modified by the following: XC =
k 2 j (nj − t) · xj k 2 j (nj − t)
(2)
3. Results and discussion First of all we show the effect of the new position algorithm on detector FoV. In Fig.1 the images from a 57 Co flood field irradiation of the integral assembly detector are shown. The image on the left is obtained applying the standard algorithm, while on the right the effect of the position linearity correction on the image is clearly visible. In Figure 1 (lower) are shown the image profiles obtained by scanning half FoV of the integral assembly detector with a 0.4 mm 99m Tc collimated source . We can estimate a FoV of 19 mm and 38 mm with standard and new algorithm respectively. Taking into account the equation 1, the intrinsic spatial resolution of the detector is depending on FWHM of PSFimage and position linearity. So we characterize the imaging performances of all detectors, quantifying these two parameters. A scanning of the overall detectors with 99m Tc collimated source is utilized to evaluate the position linearity, reported in Table II, column two.
Table 2 Position Linearity and FWHM of PSFimage Crystal Thick
4 mm 4 mm 10 mm 5 mm
L
mm mm
(Anger Logic) 0.78 0.65 0.42 0.51
P SF F W HM (Anger Logic) 1.5 mm 1.7 mm 4.5 mm 1.9 mm
P SF F W HM (L=1) 0.95 1.10 1.90 0.90
mm mm mm mm
Figure 1. Integral assembly detector. Upper: Im-
age of a flood field irradiation with 57 Co free source. Images were obtained with the standard position algorithm (left) and the new algorithm (right). Lower: Image profiles obtained by scanning half FoV of detector with a 0.4 mm 99m Tc collimated source.
Since L represents the angular coefficient of position linearity curve, a good linearity is considered if it is not just costant but also close to 1. The poor linearity response of 10 mm thickness detector confirms the worsening of position linearity coefficient with the detector thicknesses.The best value is obtained for the all black detector (0.78), demonstrating that the black painting reduces position distortion produced by light reflections and truncation of light distribution at the edges. Finally, we evaluate the intrinsic spatial resolution, by subtracting the collimator contribution, as summarized in Table II, column four. The most impressive result is obtained with 10 mm thickness LaBr3 :Ce crystal (1.9 mm) although the charge distribution spread is always truncated on the MAPMT anode plane. The integral assembly detector shows the best value of 0.9 mm. To evaluate the improvement obtained with the new algorithm, these results have to be compared with ones obtained applying the standard
R. Pani et al. / Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205
algorithm, reported in Table II, column three. During all measurements energy resolution values are recorded,obtaining the best value for 4.0 and 5.0 mm thickness with white coating, but in any case never better than 8.5 - 9.0%. These values result worst with respect to ones obtained coupling the same crystals to a standard PMT [5]. We can conclude that MA-PMT suffers of a poor number of photoelectrons as produced from photocathode and transmitted from first dynode. It could be an additional source for limiting spatial resolution values. Sanchez et al [2] presented the results obtained with a small camera based on CsI(Na) continuous crystals. In particular the two proposed crystals had the same surface treatment of our two LaBr crystals with 4 mm thick: one with white entrance/black edge and the other one all black painted. Sanchez et al. made a similar scanning of the crystal surface with a collimated 99m Tc source performing a study of spatial resolution as a function of position. In Fig.2 the literature values are compared with our measured ones.
205
CsI(Na) is clearly visible. The response of two CsI(Na) crystals results very discontinuous when the source position is moving away from the crystal center. The response of the white/black lanthanum crystal results reasonably uniform, with a worsening of about 20% in peripheral zone. The best result is obtained with all black crystal, having a uniformity of response up to 22 mm to the crystal center, and an average value of l.1 mm. It is worth that position linearity coefficients reported by Sachez et al. are about 0.69 and 0.78 for CsI(Na) with white entrance/black edge and black entrance/black edge respectively, demostrating that the spatial resolution results could be further improved. 4. Conclusion We investigated the potentiality of LaBr3 :Ce scintillation crystal to improve Intrinsic Spatial Resolution when assembled in continuous configuration on a small FoV Gamma Camera. Four different configurations of gamma camera were studied in term of crystal thickness and surface treatment. A new centroid algorithm is utilized to improve intrinsic spatial resolution by correcting the position non-linearity arising when continuous crystals are utilized in small FoV gamma camera. Spatial resolution results are the best obtained until now with small FoV gamma cameras of comparable size and crystal thickness. REFERENCES
Figure 2. Comparison of spatial resolution values obtained by LaBr3 :Ce and CsI(Na) crystals with the same surface treatment
The points at 0 mm and at 25 mm position correspond to the center and the edge of the crystal respectively. The improving in spatial resolution performance of the lanthanum crystal respect to
1. M.N. Cinti et al., IEEE Transactions On Nuclear Science, Vol. 54, No. 3, June 2007. 2. F. Sanchez et al., Med.Phys., Vol.31, June 2004. 3. R. Pani et al., Nuclear Instruments and Methods in Physics Research A, Vol. 567, Issue: 1, pp 294-297 (2006). 4. A. J. Bird et al., Nucl. Instrum. Methods A348, 668-672 (1994). 5. R.Pani et al., Nuclear Science Symposium Conference Record, 2008 NSS-IEEE, Page(s):1763 - 1771. 6. Anger H. O., Rev. Sci. Instrum. 29, 27-33, 1958.
Investigation on a small FoV gamma camera based on LaBr3 :Ce continuous crystal R. Pania∗ , R. Pellegrinia , P. Bennatib , M. N. Cintic , F. Vittorinic , R. Scaf`ed , S. Lo Meoe , F. L. Navarriae , G. Moschinif , V. Orsolini Cencellig , F. De Notaristefanig a
INFN Rome and Experimental Medicine Dpt. Sapienza University of Rome, Rome (Italy).
b
INFN Rome and EDEMOM PhD School of Microelectronics, University of Rome III, Rome (Italy).
c
INFN Rome and Physics Dpt. Sapienza University of Rome, Rome (Italy).
d e f
INFN and ENEA, Casaccia, Rome (Italy).
INFN Bologna and Physics Dpt. Alma Mater Studiorum - University of Bologna, Bologna (Italy)
INFN - LNL and Physics Dpt. University of Padua, Padua (Italy).
g
INFN Department of Engineering Electronic ”Roma III” University of Rome, Rome (Italy).
Recently scintillating crystals with high light yield coupled to photodetectors with high quantum efficiency have been opening a new way to make gamma cameras with superior performances based on continuous crystals. In this work we propose the analysis of a gamma camera based on a continuous LaBr3 :Ce crystal coupled to a multi-anodes photomultiplier tube (MA-PMT). In particular we take into account four detector configurations, different in crystal thicknesses and assembling. We utilize a new position algorithm to reduce the position non linearity affecting intrinsic spatial resolution of small FoV gamma cameras when standard Anger algorithm is applied. The experimental data are obtained scanning the detectors with 0.4 mm collimated 99m Tc source, at 1.5 mm step. An improvement in position linearity and spatial resolution of about a factor two is obtained with the new algorithm. The best values in terms of spatial resolution were 0.90 mm, 0.95 mm and 1.80 mm for integral assembled, 4.0 mm thick and 10 mm thick LaBr3 :Ce crystal respectively.
1. Introduction Single Photon Emission techniques may be the best choice when sub-millimeter spatial resolution is required. Over the last years scintillation crystal arrays have been developed with very small pixel size (about 1.0 mm pitch size for NaI:Tl and CsI:Tl crystal respectively) with the intrinsic spatial resolution limited by pixel size. Many researchers have utilized continuous crystal of different scintillation materials to make gamma cameras with small Field of View (FoV), obtaining spatial resolution worse than scintilla∗ Corresponding
Author: [email protected] “Sapienza” University of Rome Viale Regina Elena 272 00161, Rome Italy (telephone and fax: +390649918277)
0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.10.067
tion array [1]-[2]. Continuous LaBr3 :Ce crystal, with an excellent energy resolution and high light yield, could be the best candidate to obtain a gamma imaging detector with sub-millimeter spatial resolution. LaBr3 :Ce scintillation crystal has very similar absorption radiation properties than NaI:Tl and a light yield almost twice with better energy resolution response. Recently Pani et al.[3] have measured spatial resolution values less than 1.0 mm with a 49 mm × 49 mm LaBr3 :Ce continuous crystal, 5.0 mm thickness corresponding to a detection efficiency of about 80% at 140keV. To better understand the capabilities in gamma ray imaging of this scintillation crystal, in this work a more complete study of four continuous LaBr3 :Ce crystals is presented.
R. Pani et al. / Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205
2. Equipment and Method 2.1. Experimental set up and measurements In this study we take into account three continuous LaBr3 :Ce scintillation crystals with same detection area of 51 mm × 51 mm. Two of them have a 3.0 mm glass window and the same 4.0 mm thickness, chosen to minimize the distance between photocathode and photon interaction point and to obtain a detection efficiency of about 70% at 140 keV. They differ for the treatment of the front surface: the first one is grounded with black coating and the second one is polished with white coating. The third one has 10 mm thickness with 3.0 mm glass window and the front surface is polished with white coating. The 10 mm thickness is chosen to have the highest detection efficiency at 140 keV (95%) and eventually to investigate the response at higher photon energies. A fourth crystal is taken into account with 49 × 49 mm2 detection area, 5.0 mm thickness, integral assembled to a Multi Anode -Photomultiplier (MAPMT), and the same front surface treatment as previous one. This assembling allows to remove the additional glass window reducing the overall optical guide thickness to 1.5 mm. In this configuration we expect narrowest light distribution and an 80% efficiency at 140 keV photon energy. To avoid light reflections and consequent light PSF distortions, all crystals have a black light absorber at the edges. In Table 1 the characteristics of all scintillation crystals are summarized.
Table 1 LaBr3 :Ce crystals configurations Thick Windows Edge Surface 4 mm 3 mm Black Ground 4 mm 3 mm White Polished 10 mm 3 mm White Polished 5 mm no White Polished
Eff 70% 70% 95% 80%
All scintillation crystals are coupled to a Hamamatsu H8500 flat panel MA-PMT. This PMT has an external size of 52 mm × 52 mm × 14.7 mm,
203
the photocathode is bialkali and 12 stages metal channel dynode are used as electron multiplier. An array of 8×8 anodes (64 channels - 6 mm pitch) is used for position determination. The PMT gain is about 3 ×106 at - 1000V. It is characterized by an anode dark current of 1 nA, a glass window thickness of 1.5 mm and finally by anode gain variation range of about 45:100. An individual anode electronic read out was used, READ system, developed at Southampton University [4], in which the charge on each anode is individually read out and digitized. The READ system, 64 independent channels, is based on four HX2 chip. The serial output from the HX2 board is subsequently red by a 1.5 MHz National Instruments DAQ 6110E Analogue to Digital Converter (ADC) mounted in host PC. On all LaBr3 :Ce crystals we perform a scanning by a 0.4 mm collimated 99m Tc source, at 1.5 mm step. The spatial resolution is calculated applying a new algorithm for position determination, shortly described in the next paragraph, and presented in [5]. 2.2. New Centroid Algorithm for position determination The classical algorithm, proposed by Anger in 1958 [6], applied on the 8×8 charge distribution of MA-PMT anode plane, permits to calculate the event position (XC and YC) as the weighted centroid of the charge distribution. The Intrinsic Spatial resolution (ISR) can be expressed by the formula [5]: F W HMP SF image (1) ISR = L where L is the position linearity, representing the angular coefficient of position linearity curve at each measured point and F W HMP SF image is relative to the Point Spread Function of the image, assumed to have a two dimensional Gaussian shape. Equation 1 suggests that ISR is improved if F W HMP SF is reduced, obtainable by reducing the thickness of the crystal and/or the light guide. Linearity also influences intrinsic spatial resolution since ISR is minimized by L =1 (best linearity). A new algorithm is proposed [5] to improve position determination, operating on the light PSF. The new procedure, applied on the collected two dimensional charge distributions
204
R. Pani et al. / Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205
on MA-PMT anodic array, consists of applying a threshold, to remove the charge (light) background, and of a squaring, that produces a narrowing of the measured charge distribution. The centroid algorithm is modified by the following: XC =
k 2 j (nj − t) · xj k 2 j (nj − t)
(2)
3. Results and discussion First of all we show the effect of the new position algorithm on detector FoV. In Fig.1 the images from a 57 Co flood field irradiation of the integral assembly detector are shown. The image on the left is obtained applying the standard algorithm, while on the right the effect of the position linearity correction on the image is clearly visible. In Figure 1 (lower) are shown the image profiles obtained by scanning half FoV of the integral assembly detector with a 0.4 mm 99m Tc collimated source . We can estimate a FoV of 19 mm and 38 mm with standard and new algorithm respectively. Taking into account the equation 1, the intrinsic spatial resolution of the detector is depending on FWHM of PSFimage and position linearity. So we characterize the imaging performances of all detectors, quantifying these two parameters. A scanning of the overall detectors with 99m Tc collimated source is utilized to evaluate the position linearity, reported in Table II, column two.
Table 2 Position Linearity and FWHM of PSFimage Crystal Thick
4 mm 4 mm 10 mm 5 mm
L
mm mm
(Anger Logic) 0.78 0.65 0.42 0.51
P SF F W HM (Anger Logic) 1.5 mm 1.7 mm 4.5 mm 1.9 mm
P SF F W HM (L=1) 0.95 1.10 1.90 0.90
mm mm mm mm
Figure 1. Integral assembly detector. Upper: Im-
age of a flood field irradiation with 57 Co free source. Images were obtained with the standard position algorithm (left) and the new algorithm (right). Lower: Image profiles obtained by scanning half FoV of detector with a 0.4 mm 99m Tc collimated source.
Since L represents the angular coefficient of position linearity curve, a good linearity is considered if it is not just costant but also close to 1. The poor linearity response of 10 mm thickness detector confirms the worsening of position linearity coefficient with the detector thicknesses.The best value is obtained for the all black detector (0.78), demonstrating that the black painting reduces position distortion produced by light reflections and truncation of light distribution at the edges. Finally, we evaluate the intrinsic spatial resolution, by subtracting the collimator contribution, as summarized in Table II, column four. The most impressive result is obtained with 10 mm thickness LaBr3 :Ce crystal (1.9 mm) although the charge distribution spread is always truncated on the MAPMT anode plane. The integral assembly detector shows the best value of 0.9 mm. To evaluate the improvement obtained with the new algorithm, these results have to be compared with ones obtained applying the standard
R. Pani et al. / Nuclear Physics B (Proc. Suppl.) 197 (2009) 202–205
algorithm, reported in Table II, column three. During all measurements energy resolution values are recorded,obtaining the best value for 4.0 and 5.0 mm thickness with white coating, but in any case never better than 8.5 - 9.0%. These values result worst with respect to ones obtained coupling the same crystals to a standard PMT [5]. We can conclude that MA-PMT suffers of a poor number of photoelectrons as produced from photocathode and transmitted from first dynode. It could be an additional source for limiting spatial resolution values. Sanchez et al [2] presented the results obtained with a small camera based on CsI(Na) continuous crystals. In particular the two proposed crystals had the same surface treatment of our two LaBr crystals with 4 mm thick: one with white entrance/black edge and the other one all black painted. Sanchez et al. made a similar scanning of the crystal surface with a collimated 99m Tc source performing a study of spatial resolution as a function of position. In Fig.2 the literature values are compared with our measured ones.
205
CsI(Na) is clearly visible. The response of two CsI(Na) crystals results very discontinuous when the source position is moving away from the crystal center. The response of the white/black lanthanum crystal results reasonably uniform, with a worsening of about 20% in peripheral zone. The best result is obtained with all black crystal, having a uniformity of response up to 22 mm to the crystal center, and an average value of l.1 mm. It is worth that position linearity coefficients reported by Sachez et al. are about 0.69 and 0.78 for CsI(Na) with white entrance/black edge and black entrance/black edge respectively, demostrating that the spatial resolution results could be further improved. 4. Conclusion We investigated the potentiality of LaBr3 :Ce scintillation crystal to improve Intrinsic Spatial Resolution when assembled in continuous configuration on a small FoV Gamma Camera. Four different configurations of gamma camera were studied in term of crystal thickness and surface treatment. A new centroid algorithm is utilized to improve intrinsic spatial resolution by correcting the position non-linearity arising when continuous crystals are utilized in small FoV gamma camera. Spatial resolution results are the best obtained until now with small FoV gamma cameras of comparable size and crystal thickness. REFERENCES
Figure 2. Comparison of spatial resolution values obtained by LaBr3 :Ce and CsI(Na) crystals with the same surface treatment
The points at 0 mm and at 25 mm position correspond to the center and the edge of the crystal respectively. The improving in spatial resolution performance of the lanthanum crystal respect to
1. M.N. Cinti et al., IEEE Transactions On Nuclear Science, Vol. 54, No. 3, June 2007. 2. F. Sanchez et al., Med.Phys., Vol.31, June 2004. 3. R. Pani et al., Nuclear Instruments and Methods in Physics Research A, Vol. 567, Issue: 1, pp 294-297 (2006). 4. A. J. Bird et al., Nucl. Instrum. Methods A348, 668-672 (1994). 5. R.Pani et al., Nuclear Science Symposium Conference Record, 2008 NSS-IEEE, Page(s):1763 - 1771. 6. Anger H. O., Rev. Sci. Instrum. 29, 27-33, 1958.