ORIGINAL ARTICLE

Stereological Evaluation of Liver Volume inLiving Donor Liver Transplantation Using MDCTvia the Cavalieri MethodCihan Duran,1 Bulent Aydinli,2 Yaman Tokat,3 Yildiray Yuzer,3 Mecit Kantarci,4 Metin Akgun,5

Kamil Yalcin Polat,2 Bunyami Unal,6 Refik Killi,1 and S. Selcuk Atamanalp2

1Department of Radiology, Medical Faculty, Bilim University, Istanbul, Turkey; 2Department of GeneralSurgery, Medical Faculty, Ataturk University, Erzurum, Turkey; 3Department of General Surgery, MedicalFaculty, Bilim University, Istanbul, Turkey; 4Department of Radiology, Medical Faculty, Ataturk University,Erzurum, Turkey; 5Department of Chest Diseases, Medical Faculty, Ataturk University, Erzurum, Turkey;6Department of Histology and Embryology, Medical Faculty, Ataturk University, Erzurum, Turkey

In living donor liver transplantation (LDLT), obtaining the precise volume of the graft is very important to decrease volume-related postoperative complications, especially in cases with suspected small-for size grafts. We used stereology based on theCavalieri method (CM), a new method to measure liver graft volume, and compared the results with those obtained throughintraoperative measurement (IOM) and through multidetector computed tomography (MDCT) measurement. Liver volumesestimated using the 3 methods were well-correlated with each other (r2 � 0.94 and P � 0.001 for IOM and CM; r2 � 0.91 andP � 0.001 for IOM and MDCT, and r2 � 0.95 and P � 0.001 for CM and MDCT); however, they were different from each other(in descending order, 908 � 124 cm3, 861 � 121 cm3, and 777 � 168 cm3 for MDCT, CM, and IOM, respectively). AlthoughMDCT and CM overestimated the volumes, the results of CM were almost similar to those obtained via IOM. In conclusion, ourresults suggest that CM measured the liver graft volume more reliably. Thus, its use, particularly in cases with suspectedsmall-for-size graft, may prove useful. Liver Transpl 13:693-698, 2007. © 2007 AASLD.

Received October 8, 2006; accepted January 21, 2007.

The shortage of cadaveric livers for transplantationcontinues to limit this therapy, but the use of livingdonors and split grafts has helped to solve this prob-lem.1 In living donor liver transplantation (LDLT), anexact preoperative volume calculation of both the graftto be transplanted and the remaining part of the poten-tial donor liver is crucial to avoid severe postoperativecomplications associated with the graft volume and therecipient recovery rate, and to maintain donor safety.1-3

The use of small-for-size grafts (graft-to-recipientweight ratio �1%) has been found to lead to lower graftsurvival. This lower survival rate is caused by enhancedparenchymal cell injury and reduced metabolic andsynthetic capacity.2

Currently, LDLT is planned by multiple imaging ap-proaches using planar reformations of ultrasonogra-

phy, computed tomography (CT), magnetic resonance,and angiographic examinations.4,5 Recently, preopera-tive liver volumetry–based on contrast-enhanced mul-tidetector CT (MDCT) has resulted in significantly im-proved outcomes, compared to the use of2-dimensional CT.6-11 The MDCT images revealed theanatomy of the hepatic vein, hepatic artery, and portalvein, but unfortunately volumetry by MDCT still pro-duces an error ratio of approximately 13%.2 The errormight be due to factors such as the mismatch betweenthe cutting line in the simulation and that in the actualhepatectomy and possible changes in graft volume sec-ondary to the lack of blood pressure on the vascular bedof the graft.2

On the other hand, the Cavalieri principle (CM) ofstereological methodology is well suited to rapid and

Abbreviations: LDLT, living donor liver transplantation; CM, Cavalieri method; IOM, intraoperative measurement; MDCT, multide-tector computed tomography; CT, computed tomography; MHV, middle hepatic vein.Address reprint requests to Bulent Aydinli, M.D., Ataturk University, Medical Faculty, Department of General Surgery, 25070 Erzurum, Turkey.Telephone: 90 442 3166333-2247; FAX: 90 442 3166340; E-mail: bulentaydinli@gmail.com

DOI 10.1002/lt.21132Published online in Wiley InterScience (www.interscience.wiley.com).

LIVER TRANSPLANTATION 13:693-698, 2007

© 2007 American Association for the Study of Liver Diseases.

accurate volumetric evaluation, based on standard CTscans of liver tumors, hepatomegaly, and surgical pro-cedures involving liver transplantation and hepatec-tomy.12

CM with stereological point counting provides unbi-ased volume estimates with predictable precision and ismore efficient than traditional region drawing.13-15 Themethodology is applicable to landmarks clearly visibleon a CT image. It was used in the current protocol tocompute tissue volumes but may also be used in con-junction with segmented images. Analysis is relativelyrapid in the hands of a skilled rater because it elimi-nates the need to outline anatomical regions and eval-uate every slice of the CT image.11

It is necessary to perform the volume measurementcarefully and to obtain a preoperative volume as preciseas possible, especially in a case with suspected small-for-size graft. Our aim was to retrospectively comparethe results of the MDCT and CM measurements withthe results of intraoperative measurement (IOM) per-formed in 36 cases that had undergone right-lobeLDLT. To our best knowledge, this is the first studycomparing these methods.

Study Procedure

A total of 36 healthy donors (21 female and 15 male,with an average age of 43 � 8 yr) for liver transplanta-tion, weighing between 56 and 92 kg, were evaluated ina 2-yr period. Preoperative MDCT images of all the do-nors were obtained, and no liver disease was detected.The right lobe volume of the liver was estimated for allthe donors via MDCT volumetric measurement by usinga 3-phase contrast-enhanced technique and alsothrough CM on the same MDCT images, as describedbelow. Donor operations were performed by an experi-enced general surgeon (Y.Y.). Then, preoperatively, theright lobe of the liver (Segments V, VI, VII, and VIIIbased on the Couinaud classification system) was re-moved and weighed using a digital scale (IOM). Weperformed the weighing procedure before perfusion. Atthat time, 1 cm3 of liver was estimated to be 1 gm. Allthe results were evaluated statistically, and the weightof the donors was considered. Only 1 case was sus-pected of having a small-for-size graft. However, nopostoperative complication was encountered.

Multidetector CT Protocol and VolumeEstimation

MDCT was performed on a 16-detector-row CT scanner(Sensation 16; Siemens Medical Solutions, Erlangen,Germany) by using a 3-phase contrast-enhanced tech-nique. Scans were obtained with 16 � 0.75 mm colli-mation, at 1.0-mm slice thickness. The hepatic venousphase was used for preoperative CT volumetric mea-surement of the donor liver because in this phase, thehepatic veins are determined with maximum contrast.Iodinated contrast medium (iohexol, Omnipaque; Am-ersham Health, Cork, Ireland) of 160 mL was injectedintravenously at 4 mL/second followed by 40 mL of

saline at 2.5 mL/second (Fig. 1). Large vessels such asthe extrahepatic portal vein in the area of the portahepatis and the inferior vena cava, as well as largerfissures, and the teres hepatic ligament, were excludedfrom volumetric marking (Fig. 2). MDCT measurementswere conducted on the middle hepatic vein (MHV) bor-der in only 24 patients in whom the right hepatic veinwas within the graft area, and on the line passing 5 mmlateral to the MHV in 12 patients in whom both the righthepatic vein and the MHV fell within the graft area. Thecases in which the MHV was considered dominant inthe venous drainage of the fifth and eighth segmentswas inclusion criterion for measurement of MHV. All

Figure 1. Well-visualized hepatic veins of the right liver lobeon contrast-enhanced axial CT imaging.

Figure 2. Volume measurement of the right hepatic lobe byMDCT software.

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the CT data, in the original resolution of 512 � 512,were sent from the scanner to a freestanding commer-cially available workstation using In Space Software(Leonardo; Siemens Medical Solutions) for postprocess-ing. Real-time axial scrolling, interactive maximum-in-tensity-projection, and volume-rendered techniqueswere used to evaluate the hepatic parenchyma.

Volume Estimation With CM

The volumes of the right lobe of the liver (Segments V,VI, VII, and VIII based on the Couinaud classificationsystem) were calculated using a software package (Ste-reoInvestigator, version 6.0; Microbrightfield, Colches-ter, VT) that uses a point counting technique based onthe Cavalieri principle.16-21 This method requires sec-tioning the structure into a series of parallel planessuch as histological and CT slices. To avoid bias, thefirst section must be placed at a uniform and randomposition in a constant interval of length (t); i.e., to startthe scanning always at, for example, 1 cm from the righttip of the object will, in general, introduce an unknownamount of bias. Moreover, the series of sections mustencompass the object entirely. The direction of cuttingdoes not affect the objectivity, but will affect the esti-mation precision in general.19 Thus, an unbiased esti-mate of volume can be obtained by multiplying the totalarea of the sectional cut surfaces through the structureon all the sections. A different approach, with 3 sepa-rate stages combined with the CM of modern designstereology, was used to estimate the volume in ourstudy.16-21

First, all CT images were directly projected onto apersonal computer screen. Second, the areas of theright lobe of the liver on serial CT images were markedwith the software. The border of the right lobe of theliver was determined similarly to the methods describedabove for MDCT measurement. Finally, the areas ofinterest on these section images were evaluated with aCavalieri estimator (Fig. 3). A point-counting grid wasused for the area estimation of section profiles (k � 1-20�m intervals depending on the area of the liver seg-ments).

Error Predictions for the Cavalieri Estimation

The amount of section and the point density of thepoint-counting grid were designed to obtain an appro-priate coefficient of error for images of the serial sec-tions. The coefficient of error and coefficient of variationwere estimated according to Gundersen and Jensen’sformula.22

The error prediction for this study was calculatedaccording to the data in Table 1.

Noise � 0.0724 � �b/�a� � �n � �P

Noise is the value of information on the complexity ofthe examined cut surface area of the specimen; b/�a isequivalent to the mean boundary length of the profilesdivided by the square root of their mean area; n is the

section number that is being examined, and �P is thenumber of points hitting the in whole section

VarSRS� �i�1

n

a� � �3x� A � Noise� � 4xB � C�/12

where VarSRS��i�1

n a� indicates the variance of total area

TABLE 1. Sample Data for Predicted Error Estimation

Section

number Pi

A B C

Pi � Pi Pi � Pi1 Pi � Pi2

1 95 9,025 14,440 23,2752 152 23,104 37,240 46,5123 245 60,025 74,970 77,6654 306 93,636 97,002 97,6145 317 100,489 101,123 88,4436 319 101,761 89,001 86,7687 279 77,841 75,888 67,5188 272 73,984 65,824 66,3689 242 58,564 59,048 60,016

10 244 59,536 60,512 56,12011 248 61,504 57,040 50,09612 230 52,900 46,460 41,40013 202 40,804 36,360 31,71414 180 32,400 28,260 24,66015 157 24,649 21,509 15,54316 137 18,769 13,563 11,09717 99 9,801 8,019 5,74218 81 6,561 4,698 2,59219 58 3,364 1,856 75420 32 1,024 41621 13 169Total 3,908 909,910 893,229 853,897

Abbreviations: Pi, point count; Pi1, point count offollowing section; Pi2, point count of section afterfollowing section.

Figure 3. Volume measurement of the right hepatic lobe byCM.

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in the systematic random sampling. These data provideinformation on the sufficient number of sections re-quired to obtain an appropriate variation for sectionsamples. A, B, and C are the total numerical values forthe data.

TotalVar � Noise � VarSRS.

The coefficient of error is the last calculated value.The generally accepted highest limit of coefficient oferror is 5%.17

Statistical Analysis

The means of the estimated liver volumes were com-pared by using the Student’s t-test. Pearson’s correla-tion test was used whether a correlation was presentamong the 3 methods analyzed. All of the statisticalanalyses were performed using SPSS version 13.0 soft-ware for Windows (SPSS Inc., Chicago, IL). All statisti-cal values under 0.05 (P � 0.05) were considered sig-nificant.

RESULTS

The mean volumetric values of the liver estimatedthrough the IOM, CM, and MDCT methods are summa-rized in Table 2 and Figure 4. Although the estimatedliver volumes were well correlated with each other (r2 �0.94 and P � 0.001 for IOM and CM; r2 � 0.91 and P �0.001 for IOM and MDCT; and r2 � 0.95 and P � 0.001for CM and MDCT), estimated mean liver volumes were

different from each other (in descending order, 908 �124 cm3, 861 � 121 cm3, and 777 � 168 cm3 for MDCT,CM, and IOM, respectively).

Both CM and MDCT overestimated the actual volumeof the liver that was also measured with IOM. However,the only statistical difference was determined betweenthe volumes estimated via MDCT and IOM (P � 0.05).Although the liver volumes estimated by CM werehigher than those estimated by IOM, the difference wasnot statistically significant. In both methods, the meanmeasurement time for each patient was calculated as12 � 2 minutes.

DISCUSSION

LDLT was developed to overcome the shortage of suit-ably-sized organs for children and adults with end-stage liver disease. Since impaired liver function afterresection and transplantation is caused by insufficientliver volume, reliable volumetric assessment of hepaticsegments of potential living donors is one of the keyfactors in the preoperative donor evaluation.3

Determination of the right lobe volume is essential toreduce the risk of graft malfunction. It has been esti-mated that the minimum graft volume required to pro-vide sufficient functional hepatocytes to the recipient isapproximately 40% of the standard liver mass, as cal-culated using the body surface area. A large graftmakes implantation more challenging, especially whenperforming the vascular anastomosis and when con-trolling bleeding. Moreover, closure of the abdominalwall may be difficult.23 Small-for-size grafts are proneto dysfunction, not only because of insufficient func-tional hepatic mass but also because the graft andsinusoidal cells may be injured by excessive portal per-fusion.1,2,8,24-26 In addition, many authors reportedthat more than 30% of the donor liver remnant wasessential to ensure donor safety.27

Recently, preoperative liver volumetry based on con-trast-enhanced MDCT has resulted in significantly im-proved outcomes.1,2,6-11 However, volumetry by thisMDCT software produces an error ratio of approxi-mately 13 to 20%.2,6 Some factors thus need to beconsidered in relation to this error. First, a mismatchexists between the cutting line in these simulations andthat in the actual hepatectomy; a 2-cm discrepancycould represent a difference of as much as 200 gm.Second, we need to consider the reduction of the vas-cular bed of the graft. The total liver volume before andafter fluid infusion showed an approximately 33% dif-

TABLE 2. Estimation of Liver Volumes With 3 Different Methods

IOM (cm3) CM (cm3)

Difference of CM

from IOM (%)

MDCT

(cm3)

Difference of MDCT

from IOM (%)

Body weight

(kg)

Mean � SD 777 � 168 861 � 121 13 � 16 908 � 124 20 � 19 75 � 13Range 422-975 670-1,066 2-59 729-1,093 5-73 56-92

Abbreviations: SD, standard deviation.

Figure 4. All volumetric results obtained by 3 different meth-ods. IOM, intraoperative measurement of liver volume; CM,volume of liver with the Cavalieri method; MDCT, volume ofliver with MDCT.

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ference in a porcine model. Third, dehydration from theosmotic pressure of the University of Wisconsin solu-tion could result in a decrease of graft weight by ap-proximately 4%.2,6,28 Because we performed the weigh-ing procedure before perfusion, we considered that ourIOM results were closer to real size than previouslyused ones that explained above due to our approach.

CM is one of the most popular stereological approachessuggested for estimating any interesting volume; it con-sists of a sampling technique to mathematically estimatethe geometric properties of 3-dimensional structureswithout bias, based on 2-dimensional slices of the ob-ject.29 It offers some very important advantages to theresearcher, such as: 1) no prejudice about the structure isrequired; in other words, it is a design-based approach,not a model based approach; 2) with this method, theactual features of the structure, such as section thick-ness, are taken into consideration without disregarding;and 3) the sampling or estimating procedure can be easilymodified to obtain the appropriate coefficient of varia-tion.30 In determining the actual volume of a structure,the validity of the Cavalieri volume estimation method hasbeen shown to be superior to the fluid displacementmethod31 and thus the method has been repeatedly re-ported to be reliable and efficient.30 On the other hand,the Cavalieri principle of stereological methodology is wellsuited to rapid and accurate volumetric evaluation, on thebasis of standard CT scans of liver tumors, hepatomegaly,and surgical procedures involving liver transplantationand hepatectomy.12 We previously reported on the valid-ity of stereology for volume estimation based on magneticresonance and CT image data and demonstrated its usein determining volumes of regional brain lesions, esoph-agus tumor, and hepatic alveolar echinococcosis.32-34

The measurement of graft volume is important inLDLT, especially in cases with suspected small-for-sizegraft. Thus, we compared 2 methods, but only 1 of ourdonors had suspected small-for-size graft.

In this work, we report that liver volume, obtained byCM of right lobe LDLT donors was correlated with theother volumes obtained by the IOM and MDCT meth-ods. However, according to our results CM is the closestmethod to IOM, which gives us real volumetric values.

Our results showed that there was no statistical dif-ference between the results of the measurements usingMDCT and CM; however, the results of the measure-ment using CM were almost similar to those obtainedthrough IOM. Our results obtained by CM were moreaccurate compared with those obtained by MDCT be-cause CM uses a more sensitive point-gridding tech-nique. Furthermore, CM does not necessitate addi-tional CT volume software, and it could easily beapplied on all printed CT images, including 2-dimen-sional images. In addition to these advantages of CM,postoperative quantitative regeneration assessment fol-low-up of the donor liver may be easily performed.

In conclusion, to prevent complications associatedwith volume both in donor and recipient, especially incases with suspected small-for-size graft, which neces-sitate extreme caution, CM may be more suitable inevaluating volume and may be added to MDCT to

achieve the best results in cases with suspected small-for-size grafts.

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