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Optimal Section Spacing in Single-Detector Helical CT¹

¹ From the Department of Diagnostic Radiology, Yale University School of Medicine, 333 Cedar St, 2-332 SP, New Haven, CT 06520 (J.A.B.); the Department of Radiology, University of Iowa, Iowa City (G.W.); and the Mallinckrodt Institute of Radiology, St Louis, Mo (E.G.M.). Received February 1, 1999; revision requested April 5; revision received May 5; accepted August 30. Address reprint requests to J.A.B. (e-mail: james.brink@yale.edu).

	Abstract

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
To define the section spacing that maximizes longitudinal resolution without needless section overlap, the optimal percentage of overlap was computed theoretically and expressed as a constant relative to the effective section thickness. For imaging applications that require maximal longitudinal resolution, single-detector helical computed tomographic images should be reconstructed with at least 60% overlap relative to the effective section thickness.

Index terms: Computed tomography (CT), image processing • Computed tomography (CT), image quality • Computed tomography (CT), physics • Computed tomography (CT), spiral technology

	Introduction

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
On a single helical computed tomographic (CT) scan, the number of reconstructed sections is limitless such that hundreds of overlapping transverse images may be reconstructed with a small section increment. Urban et al (1) reported a 10% increase in liver lesion detection when images were reconstructed with 50% overlap. However, if 50% overlap is valuable, what about higher degrees of overlap such as 80% or 90%? Even subtle excess in section overlap can lead to substantial costs associated with the time to reconstruct the images and the resources needed to store the images.

For three-dimensional imaging applications, investigators (2) conclude empirically that images should be reconstructed with at least 50% overlap. On the basis of qualitative assessment of three-dimensional rendering in a CT colonographic application, we previously reported that transverse images should be reconstructed with at least 60% overlap (relative to the effective section thickness [EST]) (3). These results are difficult to compare with previous theoretic estimates for section spacing that were made with the Nyquist sampling criterion. Specifically, Wang and Vannier (4) report the section spacing that satisfies the Nyquist sampling criterion is the number of reconstructed sections per collimation as a function of pitch (Table 1). However, most radiologists find it difficult to remember or use such a complex relationship when they specify helical CT protocols.

	Materials and Methods

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
We applied the previously defined theoretic relationship between optimal section spacing (expressed as the number of sections per collimation) and pitch to the standard descriptor of the EST as measured by Polacin et al (5), full width at half maximum (FWHM) of the section sensitivity profile. Polacin et al report that the EST is unchanged at a pitch of 1.0 relative to conventional scanning and is increased by 30% at a pitch of 2.0. They also found a linear relationship at intermediate pitches between 1.0 and 2.0. Thus, we computed the percentage of overlap relative to the collimation and the percentage of overlap relative to EST on the basis of the relationship between the number of sections per collimation and pitch described by Wang and Vannier (4) (Table 1).

We next approached this problem from a theoretic standpoint whereby the section sensitivity profile was presumed to be Gaussian, and the EST was estimated from the collimation and table increment (Appendix). Theoretic estimates of the FWHM, full width at 10th maximum, and full width at 10th area of the section sensitivity profile for helical CT with 5.0-mm collimation and pitch of 2.0 were compared with similar empiric measures from Polacin et al (5), and the percentage of error was calculated. Mathematic analysis was carried further, and the optimal percentage of overlap was expressed as a constant relative to the EST.

	Results

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
The percentage of overlap relative to the collimation and the percentage of overlap relative to EST for pitch settings between 1.0 and 2.0 are illustrated in Table 2 for 5.0- and 3.0-mm collimations on the basis of the relationship between the number of sections per collimation and pitch described by Wang and Vannier (4) (Table 1). The optimal percentage of overlap expressed relative to the collimation ranged from 63% to 49% for pitch values ranging from 1.0 to 2.0. However, the optimal percentage of overlap expressed relative to the EST ranged from 63% to 61% for pitch values ranging from 1.0 to 2.0, independent of collimation.

	Discussion

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
With helical CT, the EST is inherently broadened. Thus, with consideration of EST alone, helical CT with full-scan interpolation resulted in worsened longitudinal resolution relative to conventional scanning (6). Advances in the interpolation algorithms used to estimate data for transverse image reconstruction minimized this effect such that, for a pitch of 1.0, no appreciable increase in EST (FWHM) was seen with helical CT (5). With this benefit, investigators began increasing pitch as the pitch-related increase in EST was less prohibitive with half-scan than with full-scan interpolation algorithms. This loss of resolution owing to broadening of the section sensitive profile is compensated by the ability to reconstruct images retrospectively with a high degree of overlap. With overlapping image reconstruction, the longitudinal resolution that may be achieved with helical CT approaches a theoretic maximum (7). The section spacing required to maximize longitudinal resolution without needless section overlap was the topic of this investigation.

The optimal section spacing may be loosely expressed as reconstruction of two to three sections per collimation. Although the difference between two and three sections per collimation may not be apparent in routine clinical applications, specialized applications may reveal differences in the conspicuity of small structures and the magnitude of artifacts present on three-dimensional renderings. In addition, there is a large difference between two and three sections per collimation in terms of the processing time required to reconstruct these sections and the physical memory required to store these images for three-dimensional rendering. Thus, we wished to reconstruct sections with the least amount of overlap required to achieve maximum longitudinal resolution without needless section overlap and to develop a simple but precise means of describing the optimal section spacing.

In specifying protocols for helical CT examinations, radiologists commonly recall the relationship between EST and pitch described by Polacin et al (5). With half-scan interpolation, remembering that the EST (FWHM) is unchanged with a pitch of 1.0 and increases linearly by 30% with a pitch of 2.0 (compared with conventional scanning), computation of the EST is simple. Thus, radiologists easily recall that 5.0-mm collimation with a pitch of 2.0 results in an EST of 6.5 mm. Similarly, 3.0-mm collimation with a pitch of 2.0 results in an EST of 3.9 mm.

What is not so easily remembered is the reconstruction interval necessary to achieve maximal longitudinal resolution as expressed in Table 1. On the basis of our previous empiric determination (3) and the theoretic predictions of this study, radiologists can now remember that images should be reconstructed with at least 60% overlap relative to the EST. Thus, for 5.0-mm collimation and a pitch of 2.0, the EST (FWHM) is increased by 30% (6.5 mm), and images should be reconstructed with a reconstruction interval of 2.5 mm. This results in a percentage of overlap of 62% relative to the EST: [(6.5 - 2.5)/6.5] x 100. Table 4 lists some commonly employed helical CT techniques which satisfy this criterion. Given the predictable increase in EST with single-detector helical CT with use of half-scan interpolation, the optimal percentage of overlap relative to the collimation may be expressed as decreasing from approximately 60% to 50% as pitch is increased from 1.0 to 2.0 (Table 2), thus obviating recall of the specific increase in EST for such scanners.

Thus, specification of scanning protocols for single-detector helical CT can be simplified by remembering two facts. First, the EST is broadened by 30% with an increase of pitch from 1.0 to 2.0. Second, to maximize longitudinal resolution without needless section overlap, images should be reconstructed with 60% overlap relative to the EST.

	Appendix

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
Number of Reconstructed Sections per Collimation
It has been shown that the SD of the section sensitivity profile can be computed as follows (4):

The area from -3 SDs to +3 SDs under a normal (Gaussian) probability density function curve is 99.7% of the total area. As a result, in statistical practice, any event outside of this range is typically considered unlikely (less than a chance of 0.3%). Because the section sensitivity profile is very similar to a Gaussian function in shape, its Fourier transform is also Gaussian-like. For these reasons, we chose the cutoff frequency to be 3 SDs.

Hence, the longitudinal sampling step , which is the reconstruction interval between adjacent transverse sections, can be obtained by meeting the Nyquist sampling requirement:

EST(p)
The EST is a figure of merit used to measure the width of the section sensitivity profile, which is a function of the pitch p. The popular ESTs include the FWHM, the full width at 10th maximum (FWTM), and the full width at 10th area (FWTA). The following formula can be used to compute EST(p):

Number of Reconstructed Sections per EST
The percentage of overlap (EST) can be expressed as

Thus, these theoretic predictions indicate that sections should be reconstructed with at least 63% overlap relative to the EST.

	Footnotes

 
Abbreviations: EST = effective section thickness FWHM = full width at half maximum

Author contributions: Guarantors of integrity of entire study, J.A.B., E.G.M., G.W.; study concepts, J.A.B., E.G.M., G.W.; study design, J.A.B., G.W.; definition of intellectual content, J.A.B., E.G.M., G.W.; literature research, J.A.B., E.G.M.; data analysis, J.A.B., G.W.; statistical analysis, J.A.B., G.W.; manuscript preparation, J.A.B.; manuscript editing and review, J.A.B., E.G.M., G.W.

	References

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 

1. Urban BA, Fishman EK, Kuhlman JE, Kawashima A, Hennessey JG, Siegelman SS. Detection of focal hepatic lesions with spiral CT: comparison of 4- and 8-mm interscan spacing. AJR Am J Roentgenol 1993; 160:783-785.[Abstract/Free Full Text]
2. Brink JA. Technical aspects of helical (spiral) CT. Radiol Clin North Am 1995; 33:825-841.[Medline]
3. McFarland EG, Brink JA, Loh J, et al. Visualization of colorectal polyps with spiral CT colography: evaluation of processing parameters with perspective volume rendering. Radiology 1997; 205:701-707.[Abstract/Free Full Text]
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7. Wang G, Vannier MW. Longitudinal resolution in volumetric x-ray computerized tomography: analytical comparison between conventional and helical computerized tomography. Med Phys 1994; 21:429-433.[Medline]
8. Fox SH, Tanenbaum LN, Ackelsberg S, He HD, Hsieh J, Hu H. Future directions in CT technology. Neuroimaging Clin N Am 1998; 8:497-513.[Medline]
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