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Assessment of the optimum section thickness for the estimation of liver volume using magnetic resonance images: A stereological gold standard study
European Journal of Radiology 57 (2006) 96–101
Assessment of the optimum section thickness for the estimation of liver volume using magnetic resonance images: A stereological gold standard study Bunyamin Sahin a,∗ , Hayati Ergur b a
Department of Anatomy, Medical School, Ondokuz Mayis University, 55139 Samsun, Turkey b Akademi Radiological Diagnosis Center, 55030 Samsun, Turkey Received 26 April 2005; received in revised form 1 July 2005; accepted 14 July 2005
Abstract Estimation of liver volume using magnetic resonance (MR) images has been described previously. We have, however, not found a gold standard study, which analyzes the effect of section thickness on the estimation of liver volume. In the present study, five normal cadaveric livers were scanned in the horizontal plane using a 1.5 T MR machine (Signa 1.5T SYS#GEMSOW General Electronic, Wisconsin, USA). Consecutive sections at a thickness of 10, 7.5, 5 and 2.5 mm were used to estimate the total volume of the livers by means of the Cavalieri principle. The point counting and planimetry were used for the volume estimates. With a view to evaluating the accuracy of two techniques, all the estimations were done by the same observer. The estimated volumes concur with the actual volume of the livers obtained by the fluid displacement technique (p > 0.05). However, the section thickness has an over- or under-projection effect on the estimated volume. The obtained volume estimation results were analyzed to reveal the deviation principles of the estimates based on the section thickness. The most suitable section thickness for the liver volume estimation was assessed to be 4–5 mm. There were no significant differences between the estimation results of two methods (p > 0.05). The point-counting technique did, however, take less time than planimetry for estimating liver volume from MR images. Results also showed that the effect of section thickness on volume estimates using the two approaches could not be omitted and the values obtained could be calibrated using the proposed regression formula presented in this study. © 2005 Elsevier Ireland Ltd. All rights reserved. Keywords: Cavalieri principle; Liver; Magnetic resonance; Section thickness; Volume estimation
1. Introduction The volume of organs or structures can be obtained using the Cavalieri principle of stereological approaches [1,2]. The requirement for the application of this method is an entire set of two-dimensional slices through the object, provided they are parallel, separated by a known distance and begin randomly within the object, criteria that are met by standard magnetic resonance (MR) imaging techniques [3,4]. Planimetry and point-counting are two methods for estimating volume based on the Cavalieri principle. Planimetry ∗ Corresponding author. Present address: Department of Anatomy, Medical School, Ondokuz Mayis University, 55139 Samsun, Turkey. Tel.: +90 362 312 1919x2262; fax: +90 362 457 6041. E-mail address: [email protected] (B. Sahin).
0720-048X/$ – see front matter © 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.ejrad.2005.07.006
which involves manually tracing the boundaries of objects of interest on images of sections is the most commonly used technique for estimation of volume. The sum of the measured areas of sections obtained by planimetry is multiplied by the section thickness and the volume of the structure is estimated. The point-counting method consists of overlying each selected section with a regular grid of test points, which is randomly positioned. After each superimposition, the number of test points hitting the structure of interest on the sections is counted, and the volume of the structure is estimated by multiplying section thickness, total number of points and the representing area per point in the grid [4,5]. Some of the studies providing volume estimates of liver using MR images have used the planimetric technique [6–9] and three-dimensional MR images [10]. However, the efficiency of the point-counting approaches for volume estima-
B. Sahin, H. Ergur / European Journal of Radiology 57 (2006) 96–101
tion has recently been demonstrated. In addition, the pointcounting method is simple, inexpensive and produces results similar to other techniques [11,12]. It is well known that physical examination of the liver does not provide accurate information regarding the volume of the organ [13]. MR imaging is, however, considered to be a powerful modality for the detection and characterization of liver pathology [14]. In all these cases, accurate measurement of the liver volume is important for treatment planning and can be obtained using non-invasive cross-sectional imaging. Routine abdominal MR imaging is widely used to evaluate volume changes of liver. Many studies have proposed different approaches to estimating liver volume using MR images [4,12]. Little attention has, however, been paid in these studies to the effects of section thickness on the accuracy of the estimated liver volume. In this gold standard study, we aimed to compare the accuracy and the reliability of planimetry and point-counting methods and the effects of section thickness on the accuracy of liver volume estimates based on MR imaging. We also proposed an easy way to calibrate over/under-estimation effects of liver volume on routine MR images. 2. Material and method The MR imaging of five livers obtained from formaldehyde fixed human cadavers in different sizes were performed using a 1.5 T MR machine (Signa 1.5T SYS#GEMSOW, General Electronic, Wisconsin, USA). The scanning was performed with the following parameters: spin-echo axial, repetition time (TR): 210, echo time (TE): 3.5 and field of view (FOV): 23.4 cm × 29.7 cm. Each liver was scanned in horizontal plane and the slice thicknesses were 10, 7.5, 5 and 2.5 mm at intervals of 0, 2.5, 5 and 7.5 mm, respectively. Liver volume was estimated using the Cavalieri principle as a combination of a point-counting method of stereological approaches and the planimetry technique. The same sections were used for both volume estimation methods. 2.1. Point-counting method The MR images of a section series at four different thicknesses (10, 7.5, 5 and 2.5 mm) were used to estimate liver volume. These images were printed on films in square frames measuring 8 cm × 8 cm. A square grid test system with d = 0.5 cm between test points (Fig. 1A) was used to estimate the sectioned surface area of the slices. To estimate liver volume, the modified formula used for volume estimations of radiological images was applied [15,16]: SU × d 2 V =t× × P (1) SL where ‘t’ is the section thickness (including interval) of consecutive sections, ‘SU’ the scale unit of the printed film, ‘d’
97
the distance between the test points of the grid, ‘SL’ the measured length of the scale printed on the film and ‘ P’ is the total number of points hitting the sectioned cut surface areas of liver. The films were placed on a light bow and a transparent square grid test system was superimposed, randomly covering the entire image frame. The points hitting the liver sectioned surface area were counted for each section and the volume of the entire liver was estimated using the 1st formula. The coefficient of error (CE) of the point-counting method was calculated using the formula described in previous studies [4,17]. 2.2. Planimetry method The same observer who carried out the stereological volume estimates performed the liver volume estimates using planimetry. Liver boundaries were manually traced on each MR image using the computer’s mouse. Three-dimensional postprocessing software (Functool Version 2.5.36a, General Electronic, Wisconsin, USA) automatically calculated the number of pixels enclosed by the traced liver contours on each section and provided the cross-sectional area of the liver on a slice-by-slice basis (Fig. 1B). The sum of the above areas multiplied by the section thickness (including the interval or space) provided the total liver volume. The CE of planimetric volume estimations was calculated using the following formula described in previous studies [12,18]. m −1 CE =
Ai
i=1
1 × × 12
m
3
i=1
A2i
+
m−2 i=1
Ai ×Ai+2 −4
m−1 i=1
1/2 Ai × Ai+1
(2)
This formula allows to the researcher to evaluate the area changes and the measured cut surface areas in the consecutive section series. The mean time for the volume estimations was also provided. Calculation of liver volume, CE of estimates and other related data were obtained as a spreadsheet using Microsoft Excel. After initial setup and preparation of the formula, the point counts, the section cut surface area and other data were entered for each scan and the final data were obtained automatically. The actual liver volumes were measured using fluid displacement technique. For this purpose, the neighboring soft tissues, vessels, gall bladder and bile ducts were removed and isolated livers were immersed in an aquarium filled with tap water at room temperature; the volume of overflowing water was measured as the actual liver volume. Mann–Whitney U-test was performed to compare the percentage deviation of the estimated volumes from the actual volumes for each section thickness. The percentage devi-
98
B. Sahin, H. Ergur / European Journal of Radiology 57 (2006) 96–101
Fig. 1. Estimation of liver volume using point-counting and planimetry methods. (A) A point-counting grid that consists of crosses superimposed on MR image and (B) delineation of the contour of liver for planimetry.
ation of the estimated volumes obtained by two different approaches, namely point-counting and planimetry, were also compared using the same statistical test to check the accuracy and the superiority of the methods. The estimated volumes according to different section thicknesses were compared with the actual liver volume and a regression formula proposed for calibrating the effects of section thickness on the estimated volume using both methods. A “p”-value lower than 0.05 was accepted as being statistically different.
3. Results The volume values obtained by means of the water displacement technique were used as the gold standard data of the present study. The Cavalieri estimations of liver volumes using the point-counting method and planimetry technique for horizontal plane sections and the actual liver volumes obtained by the water displacement technique are summarized in Tables 1 and 2. The mean of estimated volumes obtained from the 10, 7.5, 5 and 2.5 mm section thickness series did not differ statistically significantly from the actual volumes using the point-counting method (p = 0.095, 0.095, 0.310 and 0.310, respectively) or the planimetry method (p = 0.095, 0.095, 0.548 and 0.095, respectively). Analysis of liver volume estimates using the Cavalieri principle showed that the section thickness has an over/under projection effect on the obtained section scan images (Table 3). While three section thicknesses – 10,
Table 1 The Cavalieri estimation results of liver volume using point-counting method for four section thicknesses Liver no.
Section thicknesses (mm)
Actual
10
7.5
5
2.5
1 2 3 4 5
1006 1027 976 1003 1669
978 1008 958 945 1569
932 955 923 929 1539
898 922 888 892 1506
914 937 904 921 1530
Table 2 The Cavalieri estimation results of liver volume using planimetry method for four section thicknesses Liver no.
1 2 3 4 5
Section thicknesses (mm)
Actual
10
7.5
5
2.5
989 1024 958 980 1657
955 963 944 943 1592
916 941 915 925 1537
901 898 873 887 1495
914 937 904 921 1530
Table 3 The percentage deviation (%) of the estimated values from the actual volumes of five livers for both methods and their means Section thicknesses (mm)
Point counting Planimetry Mean Max–min
10
7.5
5
2.5
9.1 7.6 8.4 10.1–6
5.2 3.6 4.4 7.6–2.8
1.5 0.5 1 2.1–0.2
−2 −3 −2.5 −4.1 to −1.5
B. Sahin, H. Ergur / European Journal of Radiology 57 (2006) 96–101
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Fig. 2. A graph showing the relation between the section thickness and the percentage deviation from the actual volume for both volume estimation approaches (mean ± S.D.).
7.5 and 5 mm – have an over-projection effect, 2.5 mm has an under-projection effect producing sections of a different size than the actual projections. The percentage deviations obtained using point-counting and planimetry methods did not show statistically significant differences (p > 0.05). Comparing the mean estimated volumes according to both volume estimation approaches and the actual liver volumes revealed a systematic deviation from actual volume, the degree depending on section thickness. Hence, the obtained volume resulted in an over- or under-estimation of the actual volume. The estimated mean volumes for the two methods were 8.4, 4.4 and 1% larger than the actual volumes for the 10, 7.5 and 5 mm section thickness series, respectively. The estimated mean volumes for both methods were 2.5% lower than the actual volumes for the 2.5 mm section thickness series. Finally, four simple formulae consisting of the multiplication of the raw volume value by the deviation value as a percentage were proposed to calibrate the raw volume values for each section thickness. For this purpose, the raw volume values should be multiplied by 1.084, 1.044, 1.010 and 0.975 for 10, 7.5, 5 and 2.5 mm section thickness, respectively. The percentage deviations of estimated volumes from the actual liver volumes according to four different section thicknesses were evaluated by means of regression analysis (Fig. 2). The following regression formulas were proposed to obtain the percentage deviation according to every section thickness for the point-counting and planimetry approaches, respectively. Anyone can calculate the percentage deviation of estimated volume from the actual volume by entering the section thickness in the 3rd and 4th formulas. Deviation percentage for point counting = −5.77 + 1.48 × section thickness
(3)
Deviation percentage for planimetry = −6.55 + 1.4 × section thickness
(4)
where −5.77, −6.55, 1.48 and 1.4 are constants and the section thickness must be entered in mm.
A linear relationship was found between section thicknesses and estimated liver volumes. The regression curve showing the relation between the section thickness and the percentage deviation from the actual volume, showed that sections with a thickness of 4–5 mm are the most appropriate for liver volume estimates without requiring any calibration. The mean CEs for the liver volume estimates derived from the technique of point-counting and planimetry were 1.4 and 1.1%, respectively. The point-counting time per liver varied between 7:00 and 4:05 min with a mean of 5:37 min. The application time of planimetry per liver varied between 9:54 and 6:00 min with a mean of 7:22 min.
4. Discussion Exact liver volume is required to be able to assess changes in its volume over time as an indicator of therapeutic effectiveness, evaluation of the liver in cirrhosis, monitoring the organ before and after transplantation and other surgical applications [8,19,20]. The assessment of changes in volume over time is an indicator of liver regeneration after major liver resection for tumors and as a means of following up segmental transplantation [6,7,9,21]. The liver volume measurement must, therefore, be quantitative and reproducible and this can only be achieved using imaging techniques [13]. Magnetic resonance imaging of the liver provides superior soft tissue contrast compared to CT, and is performed using non-ionizing radiation [14]. Recent studies have defined more useful and refined techniques for the estimation of liver volume on MR images [4,12]. We are, however, only aware of one gold standard study examining the accuracy of volume estimation of liver using MR images [4]. Moreover, there is one stereological study in the literature, which specifically addresses the effects of section thickness on volume estimation of lesions in multiple sclerosis using MR sections [22]. These authors reported that reducing the section thickness from 5 to 3 mm increased derived lesion volumes. We have not, however, found a study, which addresses the effect of
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section thickness on the precision of liver volume estimation using MR images. According to our knowledge, there is no study addressing the effects of slice thickness on the obtained section surface area. A possible explanation may be recommended as follow: the thicker slices can create blurring of the liver-air interface, and therefore cause the section area to become larger than its actual size. The presented MR imaging study was showed controversial findings than the previous study that examines the effects of section thickness on the estimated liver volume using CT scanning [23]. While the thicker sections produce under-estimation of volumes in CT scans, they produce overestimation in MR imaging. Reduction in section thickness from 10 to 1 mm on CT scan images revealed an increase of the estimated values of liver volume. Controversially, reduction in section thickness produced decrease of the estimated liver volume in MR imaging. There was also a linear relationship between section thickness and estimated liver volumes for MR imaging, however, it was not the case for CT scanning [23]. In the present study, we used five livers obtained from cadavers. The liver volumes were estimated on MR images taken in the horizontal plane at four different section thicknesses to investigate the effect of section thickness on the accuracy of volume estimation. Our results showed that the section thickness dramatically affects the accuracy of liver volume estimation. Reduction of section thickness from 10 to 2.5 mm on MR images decreased the estimated value of liver volume. There was also a linear relationship between section thickness and estimated liver volumes. The “p”-values for the section thickness of 10, 7.5, 5 and 2.5 mm for planimetry estimations were p = 0.095, 0.095, 0.548 and 0.095, respectively, and for the point-counting method they were p = 0.095, 0.095, 0.310 and 0.310, respectively. According to these statistical data, the volume estimation results from sections of thickness 10 to 2.5 mm did not differ significantly from the actual liver volume, if one regards a “p”-value lower than 0.05 to be statistically significant. A statistical evaluation with p = 0.095 may not, however, be within the acceptable range for the clinical measurements. Moreover, the volume estimation values using sections of 10 and 7.5 mm produced a deviation from the actual volumes of up to 10.1%. Estimations using sections of 2.5 mm also produced values up to 3.1% smaller than the actual volumes. Hence, using the sections of certain thicknesses may result in an over- or underestimation of the liver volume. However, the regression curve showing the relation between the section thickness and the percentage deviation from the actual volume indicated that the section thicknesses of 4–5 mm are the most appropriate for liver volume estimates without requiring any calibration. The researcher on the whole could not standardize the section thickness of the routine MR imaging process. It is, however, almost impossible to make a quantitative evaluation without taking into account the effects of section thickness
on the MR images since major differences are found between the estimated value and the actual volume of the liver. In the light of these facts, we have provided a regression formula that can be used to calibrate the effects of section thickness on liver volume estimation. Good agreement was found between results obtained with the point-counting and planimetry techniques, the former being 30% times faster. While the point-counting approach takes less time, planimetry provides more accurate results. As the point-counting method can, be applied to any sets of printed MR images, this approach allows one to perform retrospective and prospective studies, and the MR machines and their PC accessories do not have to be engaged. Moreover, the procedure of manually tracing liver boundaries in all MR sections using planimetry is tedious, requiring experience. The segmentation of the liver volume is not a prerequisite for applying the point-counting technique in a series of MR sections. Determination of the area of the parenchyma on each section is performed using the simple and fast process of point counting. Therefore, the point-counting technique allows the minimization of user interaction as reported by Mazonakis et al. [12]. It is known that non-contiguous slices are not to perform in clinical routine MR imaging. Therefore, we did not aim to offer a new protocol for the sectioning and spacing in MR imaging. Applying the protocol used in this study, we accomplished to sample the same intervals and we took sections in different thicknesses (i.e. 10, 7.5, 5 and 2.5 mm) from the same intervals. Using this approach we were able to analyze only the effects of section thickness on the volume estimation. In the present study, we not only assessed the optimum section thickness for the estimation of liver volume, but also proposed a regression formula that allows the calibration of volume estimates on section thicknesses, which are not optimum. Using the regression formula presented in this study, liver volume can be estimated on any complete set of MR images, where the plane-scan distance and magnification factor is known, something which is already available in MR images. One might conclude from our results that liver volume derived from 10, 7.5 and 2.5 mm sections is different from actual liver volume. Estimated liver volumes should, however, be calibrated to obtain realistic liver volume. Finally, sections of thicknesses 4–5 mm are the most suitable sets for estimation of liver volume using MR imaging.
References [1] Roberts N, Cruz-Orive LM, Reid NMK, Brodie DA, Bourne M, Edwards RHT. Unbiased estimation of human body composition by the Cavalieri method using magnetic resonance imaging. J Microsc 1992;171:239–53. [2] Cruz-Orive LM. Stereology of single objects. J Microsc 1997;186: 93–107.
B. Sahin, H. Ergur / European Journal of Radiology 57 (2006) 96–101 [3] Roberts N, Puddephat MJ, McNulty V. The benefit of stereology for quantitative radiology. Br J Radiol 2000;73:679–97. [4] Sahin B, Emirzeoglu M, Uzun A, et al. Unbiased estimation of the liver volume by the Cavalieri principle using magnetic resonance images. Eur J Radiol 2003;47:164–70. [5] Gong QY, Tan LT, Romaniuk CS, Jones B, Brunt JN, Roberts N. Determination of tumour regression rates during radiotherapy for cervical carcinoma by serial MRI: comparison of two measurement techniques and examination of intraobserver and interobserver variability. Br J Radiol 1999;72:62–72. [6] Mazonakis M, Damilakis J, Mantatzis M, et al. Stereology versus planimetry to estimate the volume of malignant liver lesions on MR imaging. Magn Reson Imaging 2004;227:1011–6. [7] Cheng YF, Chen CL, Huang TL, et al. Single imaging modality evaluation of living donors in liver transplantation: magnetic resonance imaging. Transplantation 2001;72:1527–33. [8] Chan YL, Li CK, Chik KW, Law MY, Howard R. Liver volume in thalassaemia major: relationship with body weight, serum ferritin, and liver function. Pediatr Radiol 2005;35:165–8. [9] Kamel IR, Kruskal JB, Warmbrand G, Goldberg SN, Pomfret EA, Raptopoulos V. Accuracy of volumetric measurements after virtual right hepatectomy in potential donors undergoing living adult liver transplantation. AJR Am J Roentgenol 2001;176:483–7. [10] McNeal GR, Maynard WH, Branch RA, et al. Liver volume measurements and three-dimensional display from MR images. Radiology 1988;169:851–4. [11] Cotter D, Miszkiel K, Al-Sarraj S, et al. The assessment of postmortem brain volume; a comparison of stereological and planimetric methodologies. Neuroradiology 1999;41:493–6. [12] Mazonakis M, Damilakis J, Maris T, Prassopoulos P, Gourtsoyiannis N. Comparison of two volumetric techniques for estimating liver volume using magnetic resonance imaging. J Magn Reson Imaging 2002;15:557–63.
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[13] Zoli M, Magalotti D, Grimaldi M, Gueli C, Marchesini G, Pisi E. Physical examination of the liver: is it still worth it? Am J Gastroenterol 1995;90:1428–32. [14] Laing AD, Gibson RN. MRI of the liver. J Magn Reson Imaging 1998;8:337–45. [15] Akbas H, Sahin B, Eroglu L, et al. Estimation of the breast prosthesis volume by the Cavalieri principle using magnetic resonance images. Aesth Plast Surg 2004;28:275–80. [16] Bilgic S, Sahin B, Sonmez OF, et al. A new approach for the estimation of intervertebral disc volume using the Cavalieri principle and computed tomography images. Clin Neurol Neurosurg 2005;107:282–8. [17] Sahin B, Aslan H, Unal B, et al. Brain volumes of the lamb, rat and bird do not show hemispheric asymmetry: a stereological study. Image Anal Stereol 2001;20:9–13. [18] Sahin B, Alper T, Kokcu A, Malatyalioglu E, Kosif R. Estimation of the amniotic fluid volume using the Cavalieri method on ultrasound images. Int J Gynecol Obst 2003;82:25–30. [19] Chen YS, Cheng YF, De Villa VH, et al. Evaluation of living liver donors. Transplantation 2003;75:S16–9. [20] Caldwell SH, de Lange EE, Gaffey MJ, et al. Accuracy and significance of pretransplant liver volume measured by magnetic resonance imaging. Liver Transpl Surg 1996;2:438–42. [21] Hermoye L, Laamari-Azjal I, Cao Z, et al. Liver segmentation in living liver transplant donors: comparison of semiautomatic and manual methods. Radiology 2005;234:171–8. [22] Molyneux PD, Tubridy N, Parker GJ, et al. The effect of section thickness on MR lesion detection and quantification in multiple sclerosis. AJNR Am J Neuroradiol 1998;19:1715–20. [23] Emirzeoglu M, Sahin B, Selcuk MB, Kaplan S. The effects of section thickness on the estimation of live volume by the Cavalieri principle using computed tomograhpy images. Euro J Radiol 2005;56: 391–7.
Assessment of the optimum section thickness for the estimation of liver volume using magnetic resonance images: A stereological gold standard study Bunyamin Sahin a,∗ , Hayati Ergur b a
Department of Anatomy, Medical School, Ondokuz Mayis University, 55139 Samsun, Turkey b Akademi Radiological Diagnosis Center, 55030 Samsun, Turkey Received 26 April 2005; received in revised form 1 July 2005; accepted 14 July 2005
Abstract Estimation of liver volume using magnetic resonance (MR) images has been described previously. We have, however, not found a gold standard study, which analyzes the effect of section thickness on the estimation of liver volume. In the present study, five normal cadaveric livers were scanned in the horizontal plane using a 1.5 T MR machine (Signa 1.5T SYS#GEMSOW General Electronic, Wisconsin, USA). Consecutive sections at a thickness of 10, 7.5, 5 and 2.5 mm were used to estimate the total volume of the livers by means of the Cavalieri principle. The point counting and planimetry were used for the volume estimates. With a view to evaluating the accuracy of two techniques, all the estimations were done by the same observer. The estimated volumes concur with the actual volume of the livers obtained by the fluid displacement technique (p > 0.05). However, the section thickness has an over- or under-projection effect on the estimated volume. The obtained volume estimation results were analyzed to reveal the deviation principles of the estimates based on the section thickness. The most suitable section thickness for the liver volume estimation was assessed to be 4–5 mm. There were no significant differences between the estimation results of two methods (p > 0.05). The point-counting technique did, however, take less time than planimetry for estimating liver volume from MR images. Results also showed that the effect of section thickness on volume estimates using the two approaches could not be omitted and the values obtained could be calibrated using the proposed regression formula presented in this study. © 2005 Elsevier Ireland Ltd. All rights reserved. Keywords: Cavalieri principle; Liver; Magnetic resonance; Section thickness; Volume estimation
1. Introduction The volume of organs or structures can be obtained using the Cavalieri principle of stereological approaches [1,2]. The requirement for the application of this method is an entire set of two-dimensional slices through the object, provided they are parallel, separated by a known distance and begin randomly within the object, criteria that are met by standard magnetic resonance (MR) imaging techniques [3,4]. Planimetry and point-counting are two methods for estimating volume based on the Cavalieri principle. Planimetry ∗ Corresponding author. Present address: Department of Anatomy, Medical School, Ondokuz Mayis University, 55139 Samsun, Turkey. Tel.: +90 362 312 1919x2262; fax: +90 362 457 6041. E-mail address: [email protected] (B. Sahin).
0720-048X/$ – see front matter © 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.ejrad.2005.07.006
which involves manually tracing the boundaries of objects of interest on images of sections is the most commonly used technique for estimation of volume. The sum of the measured areas of sections obtained by planimetry is multiplied by the section thickness and the volume of the structure is estimated. The point-counting method consists of overlying each selected section with a regular grid of test points, which is randomly positioned. After each superimposition, the number of test points hitting the structure of interest on the sections is counted, and the volume of the structure is estimated by multiplying section thickness, total number of points and the representing area per point in the grid [4,5]. Some of the studies providing volume estimates of liver using MR images have used the planimetric technique [6–9] and three-dimensional MR images [10]. However, the efficiency of the point-counting approaches for volume estima-
B. Sahin, H. Ergur / European Journal of Radiology 57 (2006) 96–101
tion has recently been demonstrated. In addition, the pointcounting method is simple, inexpensive and produces results similar to other techniques [11,12]. It is well known that physical examination of the liver does not provide accurate information regarding the volume of the organ [13]. MR imaging is, however, considered to be a powerful modality for the detection and characterization of liver pathology [14]. In all these cases, accurate measurement of the liver volume is important for treatment planning and can be obtained using non-invasive cross-sectional imaging. Routine abdominal MR imaging is widely used to evaluate volume changes of liver. Many studies have proposed different approaches to estimating liver volume using MR images [4,12]. Little attention has, however, been paid in these studies to the effects of section thickness on the accuracy of the estimated liver volume. In this gold standard study, we aimed to compare the accuracy and the reliability of planimetry and point-counting methods and the effects of section thickness on the accuracy of liver volume estimates based on MR imaging. We also proposed an easy way to calibrate over/under-estimation effects of liver volume on routine MR images. 2. Material and method The MR imaging of five livers obtained from formaldehyde fixed human cadavers in different sizes were performed using a 1.5 T MR machine (Signa 1.5T SYS#GEMSOW, General Electronic, Wisconsin, USA). The scanning was performed with the following parameters: spin-echo axial, repetition time (TR): 210, echo time (TE): 3.5 and field of view (FOV): 23.4 cm × 29.7 cm. Each liver was scanned in horizontal plane and the slice thicknesses were 10, 7.5, 5 and 2.5 mm at intervals of 0, 2.5, 5 and 7.5 mm, respectively. Liver volume was estimated using the Cavalieri principle as a combination of a point-counting method of stereological approaches and the planimetry technique. The same sections were used for both volume estimation methods. 2.1. Point-counting method The MR images of a section series at four different thicknesses (10, 7.5, 5 and 2.5 mm) were used to estimate liver volume. These images were printed on films in square frames measuring 8 cm × 8 cm. A square grid test system with d = 0.5 cm between test points (Fig. 1A) was used to estimate the sectioned surface area of the slices. To estimate liver volume, the modified formula used for volume estimations of radiological images was applied [15,16]: SU × d 2 V =t× × P (1) SL where ‘t’ is the section thickness (including interval) of consecutive sections, ‘SU’ the scale unit of the printed film, ‘d’
97
the distance between the test points of the grid, ‘SL’ the measured length of the scale printed on the film and ‘ P’ is the total number of points hitting the sectioned cut surface areas of liver. The films were placed on a light bow and a transparent square grid test system was superimposed, randomly covering the entire image frame. The points hitting the liver sectioned surface area were counted for each section and the volume of the entire liver was estimated using the 1st formula. The coefficient of error (CE) of the point-counting method was calculated using the formula described in previous studies [4,17]. 2.2. Planimetry method The same observer who carried out the stereological volume estimates performed the liver volume estimates using planimetry. Liver boundaries were manually traced on each MR image using the computer’s mouse. Three-dimensional postprocessing software (Functool Version 2.5.36a, General Electronic, Wisconsin, USA) automatically calculated the number of pixels enclosed by the traced liver contours on each section and provided the cross-sectional area of the liver on a slice-by-slice basis (Fig. 1B). The sum of the above areas multiplied by the section thickness (including the interval or space) provided the total liver volume. The CE of planimetric volume estimations was calculated using the following formula described in previous studies [12,18]. m −1 CE =
Ai
i=1
1 × × 12
m
3
i=1
A2i
+
m−2 i=1
Ai ×Ai+2 −4
m−1 i=1
1/2 Ai × Ai+1
(2)
This formula allows to the researcher to evaluate the area changes and the measured cut surface areas in the consecutive section series. The mean time for the volume estimations was also provided. Calculation of liver volume, CE of estimates and other related data were obtained as a spreadsheet using Microsoft Excel. After initial setup and preparation of the formula, the point counts, the section cut surface area and other data were entered for each scan and the final data were obtained automatically. The actual liver volumes were measured using fluid displacement technique. For this purpose, the neighboring soft tissues, vessels, gall bladder and bile ducts were removed and isolated livers were immersed in an aquarium filled with tap water at room temperature; the volume of overflowing water was measured as the actual liver volume. Mann–Whitney U-test was performed to compare the percentage deviation of the estimated volumes from the actual volumes for each section thickness. The percentage devi-
98
B. Sahin, H. Ergur / European Journal of Radiology 57 (2006) 96–101
Fig. 1. Estimation of liver volume using point-counting and planimetry methods. (A) A point-counting grid that consists of crosses superimposed on MR image and (B) delineation of the contour of liver for planimetry.
ation of the estimated volumes obtained by two different approaches, namely point-counting and planimetry, were also compared using the same statistical test to check the accuracy and the superiority of the methods. The estimated volumes according to different section thicknesses were compared with the actual liver volume and a regression formula proposed for calibrating the effects of section thickness on the estimated volume using both methods. A “p”-value lower than 0.05 was accepted as being statistically different.
3. Results The volume values obtained by means of the water displacement technique were used as the gold standard data of the present study. The Cavalieri estimations of liver volumes using the point-counting method and planimetry technique for horizontal plane sections and the actual liver volumes obtained by the water displacement technique are summarized in Tables 1 and 2. The mean of estimated volumes obtained from the 10, 7.5, 5 and 2.5 mm section thickness series did not differ statistically significantly from the actual volumes using the point-counting method (p = 0.095, 0.095, 0.310 and 0.310, respectively) or the planimetry method (p = 0.095, 0.095, 0.548 and 0.095, respectively). Analysis of liver volume estimates using the Cavalieri principle showed that the section thickness has an over/under projection effect on the obtained section scan images (Table 3). While three section thicknesses – 10,
Table 1 The Cavalieri estimation results of liver volume using point-counting method for four section thicknesses Liver no.
Section thicknesses (mm)
Actual
10
7.5
5
2.5
1 2 3 4 5
1006 1027 976 1003 1669
978 1008 958 945 1569
932 955 923 929 1539
898 922 888 892 1506
914 937 904 921 1530
Table 2 The Cavalieri estimation results of liver volume using planimetry method for four section thicknesses Liver no.
1 2 3 4 5
Section thicknesses (mm)
Actual
10
7.5
5
2.5
989 1024 958 980 1657
955 963 944 943 1592
916 941 915 925 1537
901 898 873 887 1495
914 937 904 921 1530
Table 3 The percentage deviation (%) of the estimated values from the actual volumes of five livers for both methods and their means Section thicknesses (mm)
Point counting Planimetry Mean Max–min
10
7.5
5
2.5
9.1 7.6 8.4 10.1–6
5.2 3.6 4.4 7.6–2.8
1.5 0.5 1 2.1–0.2
−2 −3 −2.5 −4.1 to −1.5
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Fig. 2. A graph showing the relation between the section thickness and the percentage deviation from the actual volume for both volume estimation approaches (mean ± S.D.).
7.5 and 5 mm – have an over-projection effect, 2.5 mm has an under-projection effect producing sections of a different size than the actual projections. The percentage deviations obtained using point-counting and planimetry methods did not show statistically significant differences (p > 0.05). Comparing the mean estimated volumes according to both volume estimation approaches and the actual liver volumes revealed a systematic deviation from actual volume, the degree depending on section thickness. Hence, the obtained volume resulted in an over- or under-estimation of the actual volume. The estimated mean volumes for the two methods were 8.4, 4.4 and 1% larger than the actual volumes for the 10, 7.5 and 5 mm section thickness series, respectively. The estimated mean volumes for both methods were 2.5% lower than the actual volumes for the 2.5 mm section thickness series. Finally, four simple formulae consisting of the multiplication of the raw volume value by the deviation value as a percentage were proposed to calibrate the raw volume values for each section thickness. For this purpose, the raw volume values should be multiplied by 1.084, 1.044, 1.010 and 0.975 for 10, 7.5, 5 and 2.5 mm section thickness, respectively. The percentage deviations of estimated volumes from the actual liver volumes according to four different section thicknesses were evaluated by means of regression analysis (Fig. 2). The following regression formulas were proposed to obtain the percentage deviation according to every section thickness for the point-counting and planimetry approaches, respectively. Anyone can calculate the percentage deviation of estimated volume from the actual volume by entering the section thickness in the 3rd and 4th formulas. Deviation percentage for point counting = −5.77 + 1.48 × section thickness
(3)
Deviation percentage for planimetry = −6.55 + 1.4 × section thickness
(4)
where −5.77, −6.55, 1.48 and 1.4 are constants and the section thickness must be entered in mm.
A linear relationship was found between section thicknesses and estimated liver volumes. The regression curve showing the relation between the section thickness and the percentage deviation from the actual volume, showed that sections with a thickness of 4–5 mm are the most appropriate for liver volume estimates without requiring any calibration. The mean CEs for the liver volume estimates derived from the technique of point-counting and planimetry were 1.4 and 1.1%, respectively. The point-counting time per liver varied between 7:00 and 4:05 min with a mean of 5:37 min. The application time of planimetry per liver varied between 9:54 and 6:00 min with a mean of 7:22 min.
4. Discussion Exact liver volume is required to be able to assess changes in its volume over time as an indicator of therapeutic effectiveness, evaluation of the liver in cirrhosis, monitoring the organ before and after transplantation and other surgical applications [8,19,20]. The assessment of changes in volume over time is an indicator of liver regeneration after major liver resection for tumors and as a means of following up segmental transplantation [6,7,9,21]. The liver volume measurement must, therefore, be quantitative and reproducible and this can only be achieved using imaging techniques [13]. Magnetic resonance imaging of the liver provides superior soft tissue contrast compared to CT, and is performed using non-ionizing radiation [14]. Recent studies have defined more useful and refined techniques for the estimation of liver volume on MR images [4,12]. We are, however, only aware of one gold standard study examining the accuracy of volume estimation of liver using MR images [4]. Moreover, there is one stereological study in the literature, which specifically addresses the effects of section thickness on volume estimation of lesions in multiple sclerosis using MR sections [22]. These authors reported that reducing the section thickness from 5 to 3 mm increased derived lesion volumes. We have not, however, found a study, which addresses the effect of
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section thickness on the precision of liver volume estimation using MR images. According to our knowledge, there is no study addressing the effects of slice thickness on the obtained section surface area. A possible explanation may be recommended as follow: the thicker slices can create blurring of the liver-air interface, and therefore cause the section area to become larger than its actual size. The presented MR imaging study was showed controversial findings than the previous study that examines the effects of section thickness on the estimated liver volume using CT scanning [23]. While the thicker sections produce under-estimation of volumes in CT scans, they produce overestimation in MR imaging. Reduction in section thickness from 10 to 1 mm on CT scan images revealed an increase of the estimated values of liver volume. Controversially, reduction in section thickness produced decrease of the estimated liver volume in MR imaging. There was also a linear relationship between section thickness and estimated liver volumes for MR imaging, however, it was not the case for CT scanning [23]. In the present study, we used five livers obtained from cadavers. The liver volumes were estimated on MR images taken in the horizontal plane at four different section thicknesses to investigate the effect of section thickness on the accuracy of volume estimation. Our results showed that the section thickness dramatically affects the accuracy of liver volume estimation. Reduction of section thickness from 10 to 2.5 mm on MR images decreased the estimated value of liver volume. There was also a linear relationship between section thickness and estimated liver volumes. The “p”-values for the section thickness of 10, 7.5, 5 and 2.5 mm for planimetry estimations were p = 0.095, 0.095, 0.548 and 0.095, respectively, and for the point-counting method they were p = 0.095, 0.095, 0.310 and 0.310, respectively. According to these statistical data, the volume estimation results from sections of thickness 10 to 2.5 mm did not differ significantly from the actual liver volume, if one regards a “p”-value lower than 0.05 to be statistically significant. A statistical evaluation with p = 0.095 may not, however, be within the acceptable range for the clinical measurements. Moreover, the volume estimation values using sections of 10 and 7.5 mm produced a deviation from the actual volumes of up to 10.1%. Estimations using sections of 2.5 mm also produced values up to 3.1% smaller than the actual volumes. Hence, using the sections of certain thicknesses may result in an over- or underestimation of the liver volume. However, the regression curve showing the relation between the section thickness and the percentage deviation from the actual volume indicated that the section thicknesses of 4–5 mm are the most appropriate for liver volume estimates without requiring any calibration. The researcher on the whole could not standardize the section thickness of the routine MR imaging process. It is, however, almost impossible to make a quantitative evaluation without taking into account the effects of section thickness
on the MR images since major differences are found between the estimated value and the actual volume of the liver. In the light of these facts, we have provided a regression formula that can be used to calibrate the effects of section thickness on liver volume estimation. Good agreement was found between results obtained with the point-counting and planimetry techniques, the former being 30% times faster. While the point-counting approach takes less time, planimetry provides more accurate results. As the point-counting method can, be applied to any sets of printed MR images, this approach allows one to perform retrospective and prospective studies, and the MR machines and their PC accessories do not have to be engaged. Moreover, the procedure of manually tracing liver boundaries in all MR sections using planimetry is tedious, requiring experience. The segmentation of the liver volume is not a prerequisite for applying the point-counting technique in a series of MR sections. Determination of the area of the parenchyma on each section is performed using the simple and fast process of point counting. Therefore, the point-counting technique allows the minimization of user interaction as reported by Mazonakis et al. [12]. It is known that non-contiguous slices are not to perform in clinical routine MR imaging. Therefore, we did not aim to offer a new protocol for the sectioning and spacing in MR imaging. Applying the protocol used in this study, we accomplished to sample the same intervals and we took sections in different thicknesses (i.e. 10, 7.5, 5 and 2.5 mm) from the same intervals. Using this approach we were able to analyze only the effects of section thickness on the volume estimation. In the present study, we not only assessed the optimum section thickness for the estimation of liver volume, but also proposed a regression formula that allows the calibration of volume estimates on section thicknesses, which are not optimum. Using the regression formula presented in this study, liver volume can be estimated on any complete set of MR images, where the plane-scan distance and magnification factor is known, something which is already available in MR images. One might conclude from our results that liver volume derived from 10, 7.5 and 2.5 mm sections is different from actual liver volume. Estimated liver volumes should, however, be calibrated to obtain realistic liver volume. Finally, sections of thicknesses 4–5 mm are the most suitable sets for estimation of liver volume using MR imaging.
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