Measuring stone volume three-dimensional software reconstruction or an ellipsoid algebra formula?
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1 Measuring stone volume three-dimensional software reconstruction or an ellipsoid algebra formula? William Finch, Richard Johnston*, Nadeem Shaida, Andrew Winterbottom and Oliver Wiseman* Department of Urology, Norfolk and Norwich University Hospitals NHS Foundation Trust, Norfolk, and Departments of *Urology and Radiology, Addenbrooke's Hospital, Cambridge, UK Objectives To determine the optimal method for assessing stone volume, and thus stone burden, by comparing the accuracy of scalene, oblate, and prolate ellipsoid volume equations with three-dimensional (3D)-reconstructed stone volume. Kidney stone volume may be helpful in predicting treatment outcome for renal stones. While the precise measurement of stone volume by 3D reconstruction can be accomplished using modern computer tomography (CT) scanning software, this technique is not available in all hospitals or with routine acute colic scanning protocols. Therefore, maximum diameters as measured by either X-ray or CT are used in the calculation of stone volume based on a scalene ellipsoid formula, as recommended by the European Association of Urology. Methods In all, stones with both X-ray and CT (1 2-mm slices) were reviewed. Complete and partial staghorn stones were excluded. Stone volume was calculated using software designed to measure tissue density of a certain range within a specified region of interest. Correlation coefficients among all measured outcomes were compared. Stone volumes were analysed to determine the average shape of the stones. Results The maximum stone diameter on X-ray was 3 25 mm and on CT was 3 36 mm, with a reasonable correlation (r =.77). Smaller stones (<9 mm) trended towards prolate ellipsoids ( rugby-ball shaped), stones of 9 15 mm towards oblate ellipsoids (disc shaped), and stones >15 mm towards scalene ellipsoids. There was no difference in stone shape by location within the kidney. Conclusions As the average shape of renal stones changes with diameter, no single equation for estimating stone volume can be recommended. As the maximum diameter increases, calculated stone volume becomes less accurate, suggesting that larger stones have more asymmetric shapes. We recommend that research looking at stone clearance rates should use 3D-reconstructed stone volumes when available, followed by prolate, oblate, or scalene ellipsoid formulas depending on the maximum stone diameter. Keywords kidney, urolithiasis, stone volume, CT, X-ray, algebra Introduction Stone burden has traditionally been assessed by measuring the maximum stone length or stone surface area on plain X-ray, IVU, or non-contrast-enhanced CT (NCCT) [1,2]. As kidney stones are irregular three-dimensional (3D) structures that often have complex geometric shapes, two-dimensional (2D) measurements may inaccurately predict stone volume and thus not reflect total stone burden [3,4]. Accurate pretreatment stone measurements are of significant clinical importance because stone volume is an independent predictor of successful treatment after extracorporeal shockwave lithotripsy (ESWL) of upper urinary tract calculi [5,6]. In addition, stone volume has also been suggested as a predictor of successful outcomes after flexible ureterorenoscopy [7]. Stone volume can be estimated using an ellipsoid formula, as recommended by the European Association of Urology, (stone volume =π*l*w*d*.167), where length (l), width (w), and depth (d) are stone diameter measured in three axes [8]. This is the general equation for a scalene ellipsoid in which the lengths of all three axes are unequal (a > b > c). However, BJU Int 214; 113: wileyonlinelibrary.com BJU International 213 BJU International doi:.1111/bju Published by John Wiley & Sons Ltd.
2 Measuring stone volume ellipsoids can have two axes of equal length and be oblate (disk-like) in shape (a = b > c) or prolate ( rugby ball ) in shape (a = b < c). Transformations of the scalene equation are available that more accurately reflect the volume of oblate (equatorial diameter as the major axis) and prolate (polar diameter as the major axis) spheroid shapes. To the best of our knowledge, no study has compared the use of scalene, oblate, and prolate ellipsoid volume equations to measure kidney stone volume. While the precise measurement of stone volume by 3D reconstruction can be accomplished using modern CT scanning software [9,], this technique is not available in all hospitals or with routine acute colic scanning protocols. Therefore, we sought to determine the optimal method for assessing stone volume, and thus stone burden, by comparing the accuracy of scalene, oblate, and prolate ellipsoid volume equations with 3D-reconstructed stone volume and the degree of correlation between plain X-ray and CT for measuring stone diameter. Materials and Methods We reviewed renal stones that had both plain film X-ray and CT scans performed. All stones were scanned by CT using a slice thickness of 2 mm. All renal stones were confined to one region of the kidney and staghorn, partial staghorn, and ureteric stones were excluded. Stone composition was not evaluated. Plain film X-rays and CTs were assessed by both a urologist and radiologist. Maximal diameter and perpendicular diameter were recorded and, in the case of CTs, a third diameter was calculated from the number of CT slices involved. The maximal and minimal diameters on plain X-rays were also recorded. Angular eccentricity was measured using PACS software. All examinations were performed using either a Siemens Somatom Sensation 64-slice or a Siemens Definition Flash 128-slice CT scanner (Siemens Medical, Forchheim, Germany). Images were acquired using a standard protocol involving an initial unenhanced examination with on table review by the radiologist followed by a delayed phase examination when necessary. Only the unenhanced images were used for analysis. Stone volume measurements were performed using a dedicated volume measurement software package on a Siemens Syngo CT workstation (Siemens Medical, Forchheim, Germany). Regions of interest were drawn around each calculus. Tissue with a Hounsfield unit (HU) attenuation outside of the range of 2 HU was excluded to prevent a falsely elevated volume measurement from any soft tissue density material around the calculus. Each set of images was subsequently reviewed again to ensure that the measured volume corresponded to the calculus. Pearson correlation coefficients were calculated to compare all measured values against the gold standard of 3Dreconstructed volume. In addition, estimated volume and surface area were calculated using the formula π/6*a*b*c* for a scalene spheroid, π/6*a*a*c* for an oblate spheroid, and π/6*a*b*b* for a prolate spheroid where a is the equatorial diameter, b is the polar diameter, and c is the third measurable diameter. A linear least squares model was generated to estimate the best fit curve to assess whether renal stones trended towards oblate, prolate, or scalene shapes. Results The maximum time difference between the performance of plain film X-ray and CT was 6 h. In all, 11 stones were not visible on plain film X-ray and were presumably urate in composition. Of the stones measured, 49 were located in the renal pelvis, 22 in the lower pole, 18 in the upper pole and 11 in the interpolar region. On plain film X-ray, the median (range) diameter was.5 (3 25) mm. By CT, the median (range) diameter was (3 36) mm. The diameter measurements from the two different imaging methods showed a reasonable correlation (r =.77). Plain film X-ray consistently underestimated diameter compared with CT, with a relatively constant ratio of.9 ±.5 (95% CI). The median (range) stone volume on 3D reconstruction was 78 ( ) mm 3. Reconstructed volumes were compared with volumes determined using three different spheroid formulas, including prolate, oblate, and scalene. Smaller stones (<9 mm in diameter) trended towards prolate, stones of 9 15 mm in diameter trended towards oblate, and stones >15 mm in diameter trended towards scalene. Discussion Information on stone burden is essential for the appropriate planning of treatments to remove stones from the urinary tract. The need to describe a stone in terms of size and shape has become particularly important as non-invasive or minimally invasive treatments have replaced open surgery. In addition, to assess the efficacy and indications of different treatment methods, it is important to have an accurate assessment of stone burden. The most common way in which to express the size of stones is to give the maximum diameter of the stone in any measurable axis. Maximum stone diameter has been shown to correlate well with arithmetically derived stone surface area for plain abdominal radiographs of the kidneys, ureters and bladder. The exceptions to this are stones with a pronounced irregular shape and staghorn calculi. These deviate from standard ellipsoid geometry and therefore other methods for assessing stone burden are necessary [11]. The limitation with maximum stone length and measured surface area is that they are 2D measurements of stone burden and provide no volumetric information. As the total volume of BJU International 213 BJU International 611
3 Finch et al. Table 1 Correlation between CT 3D volume and estimated volume using three different spheroid equations. Stone diameter, mm Calculated mean volume in mm 3 (range) 3D volume Scalene r Oblate r Prolate r All 78 ( ) 1 18 ( ) ( ) ( ) ( ) 133 ( ) ( ) ( ) (145 9) 612 ( ) ( ) ( ).75 > ( ) 194 ( ) ( ) ( ).7 r is the correlation to 3D-reconstructed volume. a cylinder is twice the volume of a sphere of the same diameter and height, the shape and depth of a stone have important implications for stone volume and thus stone burden. This was clearly outlined by Bandi et al. [6] with their example of the volume of a stone measuring 15 mm and mm in the third axis is a third less than a stone measuring 15 mm in the third axis (15 μl vs 225 μl). These differences may be even more pronounced for larger, irregularly shaped stones. Stone location was analysed to identify any trends in stone shape for a specific stone location. Anecdotally, some people may expect stone shape to depend on the location within the kidney, but there is currently no published evidence to support this. Analysing the present data set, stones of <9mm clearly show no shape differences by location within the kidney. As the size of stones increases the stone shape becomes more random but no clear differences in stone shape by location were identified. Stone volume, as measured by NCCT, is the strongest predictor of stone-free status after ESWL [5,6] and is more significant on logistic regression analysis than body mass index, skin to stone distance, peak and mean stone density, and axial stone diameter [6]. NCCT has become the imaging technique of choice for investigating and managing patients with stone disease. NCCT provides a rapid assessment of stone size, shape, number, and location, with maximum axial diameter most commonly used to assess stone burden. It also allows for the maximum diameter to be measured in three planes for a stone. Modern CT scanning software can create a 3D reconstruction using the acquired images. Stone volume calculated using 3D reconstruction is extremely accurate, with a bias (mean difference) of 2%, precision (standard deviation) of 2% [] and is highly reproducible (inter-observer correlation of r >.97). However, this process requires specialised scanning protocols and software and so may not be available as part of a standard acute colic scanning protocol. Using diameter measurements obtained by NCCT, we calculated stone volume using scalene, oblate, and prolate ellipsoid formulas as shown in Table 1. While European Guidelines recommend the use of a scalene ellipsoid formula to estimate stone volume [8], we found that for most stones the scalene formula is the least accurate. The present results suggest that the average shape of stones changes with increasing maximum diameter (Fig. 1). Specifically, smaller stones (<9 mm maximum diameter) trended towards prolate ellipsoids whereas stones of 9 15 mm trended towards oblate ellipsoids. Only stones of >15 mm trended towards scalene ellipsoids. In addition, while maximum stone diameters obtained by X-ray and NCCT were fairly well correlated (r =.77) as shown in Table 2, caution should be used when estimating stone volume using diameters obtained by X-ray, as they consistently underestimated stone volume with a relatively constant ratio of.9 ±.5 (95% CI). There are significant shortcomings for any method of stone volume assessment short of 3D reconstruction. The orientation of stones does not conveniently correspond to axial body scanning, making the measurement of maximum diameters relatively artificial. Also, it is likely that most stones are asymmetrical and therefore their volume cannot be captured using a simple algebraic formula. For the present study, we used data that would typically be available from a CT scan to determine the most accurate method for modelling stone volume in a practical day-to-day setting. We are aware that the differences in volume measurement outlined in the present study are largely academic, but they do have important practical and clinical relevance. There can be no doubt that the gold standard of stone burden analysis is 3D reconstruction. It is very important that future urolithiasis studies use 3D-reconstructed stone volume as a marker of stone burden when reporting research outcomes. This will enable the meaningful comparisons of outcomes for various urolithiasis treatment methods and techniques in the future. On a clinical level, the accurate measurement of stone volume may alter the treatment method a clinician offers a patient and may have an effect on the patient outcome. In conclusion, the best way to measure stone burden is by 3D-reconstructed stone volume. The maximum diameter on CT or plain film X-ray gives useful information but can both over- and under-estimate stone volume and thus stone burden. Following published guidelines regarding the use of a scalene ellipsoid formula as a surrogate measure of stone 612 BJU International 213 BJU International
4 Measuring stone volume Fig. 1 (A) A linear least squares model for surface area showed good correlation to the expected prolate average curve for stones in the range 3 to 9 mm and good correlation to the oblate average curve for stones with a range of 9 to 15 mm. Stones of >15 mm had poor correlation to both curves and should be considered scalene. (B) A linear least squares model for surface area showed good correlation to the expected prolate average curve for stones in the range 3 to 9 mm and good correlation to the oblate average curve for stones with a range of 9 to 15 mm. Stones of >15 mm had poor correlation to both curves and should be considered scalene. A Log Norm Surface Area Prolate Sphere Oblate Individual stone Surface Area B Polar Diameter, mm Favours Prolate Favours Oblate Stone Volume Perfect Sphere Diameter Equatorial Diameter, mm Table 2 Correlation between maximum stone diameter obtained by X-ray and CT. n Median (range) largest diameter, mm Median (range) 3D volume, mm 3 Plain film X-ray 89.5 (3 25) N/A.77 CT (3 36) 78 ( ) burden consistently over estimates stone volume, particularly for stones with diameters of <15 mm. Stones with a maximum diameter of <9 mm are more accurately represented as prolate spheroids, while stones with maximum diameters between 9 and 15 mm are predominately oblate in shape. Special transformation equations to calculate a prolate spheroid or oblate spheroid volume should be used in these cases to reduce inaccuracies in calculated stone volume. In addition, we call for the Urological literature to use 3D-reconstructed stone volume as a marker of stone burden when reporting research outcomes to facilitate the easier comparisons of outcomes for various urolithiasis treatment methods and techniques. Conflict of Interest W.F. received reimbursement from Boston Scientific, Pfizer, Astellas, SEP, European School of Urology for attending training courses and conferences as part of SpR Urology Training, all outside the submitted work. O.W. received reimbursement for training courses run in conjunction with r Boston Scientific, Olympus, Storz, for attending meetings and performing live surgery, all outside the submitted work. O.W. is a director of Uroscreen Ltd. No other conflicts to declare. References 1 Shine S. Urinary calculus: IVU vs. CT renal stone? A critically appraised topic. Abdom Imaging 28; 33: Worster A, Preyra I, Weaver B, Haines T. The accuracy of noncontrast helical computed tomography versus intravenous pyelography in the diagnosis of suspected acute urolithiasis: a meta-analysis. Ann Emerg Med 22; 4: Tiselius HG, Andersson A. Stone burden in an average Swedish population of stone formers requiring active stone removal: how can the stone size be estimated in the clinical routine? Eur Urol 23; 4: Ackermann D, Griffith DP, Dunthorn M, Newman RC, Finlayson B. Calculation of stone volume and urinary stone staging with computer assistance. J Endourol 1989; 3: Yoshida S, Hayashi T, Morozumi M, Osada H, Honda N, Yamada T. Three-dimensional assessment of urinary stone on non-contrast helical computed tomography as the predictor of stonestreet formation after extracorporeal shock wave lithotripsy for stones smaller than 2 mm. Int J Urol 27; 14: Bandi G, Meiners RJ, Pickhardt PJ, Nakada SY. Stone measurement by volumetric three-dimensional computed tomography for predicting the outcome after extracorporeal shock wave lithotripsy. BJU Int 29; 3: Al-Qahtani SM, Gil-Deiz-de-Medina S, Traxer O. Predictors of clinical outcomes of flexible ureterorenoscopy with holmium laser for renal stone greater than 2 cm. Adv Urol 212; 212: TiseliusHG,AlkenP,BuckCetal.European Association of Urology 28 Guidelines on Urolithiasis. Available at: BJU International 213 BJU International 613
5 Finch et al. fileadmin/user_upload/guidelines/urolithiasis.pdf. Accessed 17 June Hubert J, Blum A, Cormier L, Claudon M, Regent D, Mangin P. Three-dimensional CT-scan reconstruction of renal calculi. A new tool for mapping-out staghorn calculi and follow-up of radiolucent stones. Eur Urol 1997; 31: Demehri S, Kalra MK, Rybicki FJ et al. Quantification of urinary stone volume: attenuation threshold-based CT method a technical note. Radiology 211; 258: Blandy JP, Marshall VR. Size of renal calculi, recurrence rate and follow-up. BrJUrol1976; 48: Correspondence: William Finch, Department of Urology, Norfolk and Norwich University Hospitals NHS Foundation Trust, Colney Lane, Norwich, Norfolk NR4 7UY, UK. wjgfinch@doctors.org.uk Abbreviations: (3)(2)D, (three)(two)-dimensional; ESWL, extracorporeal shockwave lithotripsy; NCCT, non-contrast-enhanced CT. 614 BJU International 213 BJU International
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