Americn Journl of Nephrology Originl Report: Ptient-Oriented; Trnsltionl Reserch Am J Nephrol 213;38:333 341 Received: July 23, 213 Accepted: August 28, 213 Pulished online: Octoer 5, 213 Novel Approch to Estimte Kidney nd Cyst Volumes Using Mid-Slice Mgnetic Resonnce Imges in Polycystic Kidney Disese Kyongte T. Be Cheng To Jinhong Wng Din Ky Zhiyun Wu Junu T. Be Arlene B. Chpmn c Vicente E. Torres d Jred J. Grnthm e Michl Mrug f Willim M. Bennett g Michel F. Flessner h Doug P. Lndsittel for the Consortium for Rdiologic Imging Studies of Polycystic Kidney Disese (CRISP) Deprtments of Rdiology nd Internl Medicine, University of Pittsurgh School of Medicine, Pittsurgh, P., c Deprtment of Internl Medicine, Emory University School of Medicine, Atlnt, G., d Deprtment of Internl Medicine, Myo College of Medicine, Rochester, Minn., e Deprtment of Internl Medicine, Knss University Medicl Center, Knss City, Kns., f Division of Nephrology, University of Alm, Birminghm, Al., g Legcy Good Smritn Hospitl, Portlnd, Oreg., nd h Ntionl Institute of Dietes nd Digestive nd Kidney Diseses, Ntionl Institutes of Helth, Bethesd, Md., USA Key Words Kidney Polycystic kidney disese Kidney volume Renl cysts Mgnetic resonnce imging Astrct Ojective: To evlute whether kidney nd cyst volumes cn e ccurtely estimted sed on limited re mesurements from mgnetic resonnce (MR) imges of ptients with utosoml dominnt polycystic kidney disese (ADPKD). Mterils nd Methods: MR coronl imges of 178 ADPKD prticipnts from the Consortium for Rdiologic Imging Studies of ADPKD (CRISP) were nlyzed. For ech MR imge slice, we mesured kidney nd renl cyst res using stereology nd region-sed thresholding methods, respectively. The kidney nd cyst oserved volumes were clculted y summing up the re mesurements of ll the slices covering the kidney. To estimte the volume, we selected coronl mid-slice in ech kidney nd multiplied its re y the totl numer of slices ( PANK2 for kidney nd PANC2 for cyst). We then compred the kidney nd cyst volumes predicted from PANK2 nd PANC2, respectively, to the corresponding oserved volumes, using liner regression nlysis. Results: The kidney volume predicted from PANK2 correlted extremely well with the oserved kidney volume (R 2 =.994 for the right kidney nd.991 for the left kidney). The liner regression coefficient multiplier to PANK2 tht est fit the kidney volume ws.637 (95% CI:.629.644) for the right kidney nd.624 (95% CI:.616.633) for the left kidney. The correltion etween the cyst volume predicted from PANC2 nd the oserved cyst volume ws lso very high (R 2 =.984 for the right kidney nd.967 for the left kidney). The lest squres liner regression coefficient for PANC2 ws.637 (95% CI:.624.649) for the right kidney nd.68 (95% CI:.591.625) for the left kidney. Conclusion: Kidney nd cyst volumes cn e closely pproximted y multiplying the product of the mid-slice re mesurement nd the totl numer of slices in the coronl MR imges of ADPKD kidneys y.61.64. This informtion will help sve processing time needed to estimte totl kidney nd cyst volumes of ADPKD kidneys. 213 S. Krger AG, Bsel E-Mil krger@krger.com www.krger.com/jn 213 S. Krger AG, Bsel 25 895/13/384 333$38./ K.T. Be, MD, PhD Deprtment of Rdiology, University of Pittsurgh School of Medicine Presyterin South Tower, Room 395 2 Lothrop St., Pittsurgh, PA 15213 (USA) E-Mil ek @ upmc.edu
Introduction Autosoml dominnt polycystic kidney disese (ADPKD) is progressive disorder tht cuses life-ltering symptoms nd potentilly lethl complictions. The disese egins with reltively few cystic renl tuules; however, these cysts expnd over time. Indeed, the ppernce nd growth of cysts in the kidney, the hllmrks for the dignosis of ADPKD, strongly correlte with the progression of the disese [1]. The Consortium for Rdiologic Imging Studies of Polycystic Kidney Disese (CRISP) ws estlished to crete dtse consisting of mgnetic resonnce imging (MRI) dt, renl functionl prmeters, nd other selected mrkers of disese progression in individuls with ADPKD who re in the erly course of their disese [2]. The CRISP study reveled tht kidney volume mesurements from MRI re more sensitive thn renl function mesures in ssessing yerly progression of the disese, nd tht kidney enlrgement resulting from the expnsion of cysts in ADPKD ptients is ssocited with the decline of renl function [3]. While kidney nd renl cyst volumes re importnt metrics for the ssessment of ADPKD progression, the mesurement of these volumes is not trivil. A numer of techniques re ville to mesure kidney nd renl cyst volumes from CT or MR imges. Some of these techniques rely primrily on mnul opertions (e.g. mnul delinetion of the kidney oundry on ech imge slice over series of slices covering the entire volume of kidneys), while others use more utomted opertions. Although fully utomted segmenttion is fesile for norml kidneys, it is exceedingly chllenging for ADPKD kidneys ecuse of the high vriility in oth the morphology of the ffected kidneys nd the composition of cyst fluid. In ddition, mesurement of the kidney cyst volume presents n even greter chllenge thn mesurement of the whole kidney volume due to the fct tht cysts re often numerous nd vry in size nd imging ppernce [2, 4]. Totl kidney nd cyst volumes re typiclly clculted from set of contiguous CT or MR imges y summing the products of the re mesurements nd the slice thickness. However, mesuring the re of every slice in series of imges is lorious nd time-consuming. If the volume of the kidney or renl cysts cn e ccurtely estimted from the re mesurement of limited numer of slices, we my e le to expedite the mesuring process. Thus, the purpose of the current study is to evlute whether kidney nd cyst volumes cn e ccurtely estimted from limited re mesurements on MR imges in ptients with ADPKD. Mterils nd Methods The study protocol for the CRISP (clinicl trils registrtion: NCT139987, registrtion dte: Dec. 23, 29) hs een previously descried [2, 3, 5] nd ws pproved y the institutionl review ord t ech prticipting clinicl center. Informed consent ws otined from ll sujects who prticipted in the CRISP study. Prticipnts nd MRI CRISP ws lunched in 1999 to cquire prospective, multiyer longitudinl mesurements of renl nd renl cyst volumes in lrge cohort of ADPKD prticipnts. Detiled descriptions of the CRISP study protocol, the clinicl chrcteristics of the cohort, nd the seline chrcteristics hve een pulished previously [2, 3, 5]. The MRI protocol for the CRISP study ws stndrdized nd implemented in 1.5-tesl MRI scnners t four clinicl centers (Myo Clinic, Emory University, University of Knss Medicl Center, nd University of Alm t Birminghm). In ech prticipnt, phsed-rry surfce coil ws positioned with its center over the inferior costl mrgin, estimted s the upper mrgin of the kidney. The field of view ws mintined etween 3 nd 35 cm. The kidneys were imged first posteronterior in the coronl plne using T2-weighted single-shot fst spin-echo sequence with ft sturtion t 3-mm fixed-slice thickness during rethhold(s). After T2-weighted imges were otined, reth-hold coronl, three-dimensionl spoiled grdient interpolted T1- weighted imges without ft sturtion t 3-mm fixed-slice thickness were otined [2]. MR Imge Anlysis MR imges from 178 CRISP II prticipnts otined in yers 27 28 were nlyzed. In the CRISP II protocol, MR imges were cquired without the use of gdolinium contrst ecuse of the potentil ssocition etween nephrogenic systemic firosis nd gdolinium contrst in ptients with impired renl function. The re of the kidney ws mesured t ech slice of the T1-weighted imges without the use of gdolinium, using stereology method tht is sed on counting the numer of intersections of rndomly oriented nd positioned grid over the oject [2, 4]. The re of the kidney in ech imge ws clculted y collecting selected points tht overlid the kidney regions nd then converting the point count to pixel count for the re mesurements [2, 4, 6]. The kidney volume ws then clculted from the set of contiguous imges y summing the products of the re mesurements nd the slice thickness. The totl volume of cysts in ech kidney ws mesured using region-sed thresholding method [2, 5]. Becuse of their wter content, cysts were righter thn the renl prenchym in T2- weighted imges. Therefore, they could e mesured y summing voxels with intensity vlues greter thn those of the ckground renl prenchym. On ech renl MR imge slice, n nlyst selected threshold to visully distinguish the cyst from renl prenchyml regions nd generte inry signl-intensity mp. In the inry mp, cysts tht were righter thn renl prenchym were represented s white regions, wheres the ckground renl prenchym ws designted s lck regions. By summing the pixels of white regions, the cystic re ws mesured in ech slice. Just s with kidney volume, the totl cyst volume ws clculted from ech set of contiguous imges y summing the products of the res mesured nd the slice thickness. 334 Am J Nephrol 213;38:333 341 Be et l.
Dt Anlysis for Kidney nd Cyst Volumes with Mid-Slice Are Mesurements From series of coronl MR imges of the right or left kidney in ech suject, we selected the mid-slice y reviewing nd scrolling the imge set. We defined the mid-slice s the slice whose imge numer corresponded to hlf of the sum of the first slice nd lst slice imge numers in the imge set (if the sum ws odd, the mid-slice corresponded to the neighoring slice, rounding up from the men). The product of the mid-slice kidney re nd the numer of slices covering the kidney ( PANK2 ) ws then computed for ech kidney. Likewise, the product of the mid-slice cyst re nd the numer of slices covering the whole kidney ( PANC2 ) ws lso computed for ech kidney. A liner regression model without constnt ws pplied to PANK2 or PANC2 s the independent vrile, while the corresponding oserved kidney or cyst volume served s the dependent vrile. A multiplier tht est fit the liner regression model ws computed in ech comprison. Dt Anlysis for Kidney nd Cyst Volumes with Three-Slice Are Mesurements In ddition to the mid-slice (i.e. the 2nd qurtile) imge, we lso selected two dditionl slices from ech kidney imge series: the mid-slice of the nterior hlf (the 1st qurtile) nd the mid-slice of the posterior hlf (the 3rd qurtile) of the series. We retrieved the kidney nd cyst re mesurement from these slices nd then multiplied the re y the numer of slices covering the kidney, resulting in dditionl slice re mesurements: PANK1 from the 1st qurtile kidney re; PANK3 from the 3rd qurtile kidney re; PANC1 from the 1st qurtile cyst re, nd PANC3 from the 3rd qurtile cyst re. For the liner regression nlysis, we used two different pproches to comine the three-slice re mesurements (PANK1, PANK2, PANK3) or (PANC1, PANC2, PANC3). For the first pproch, we considered these three products s three independent vriles nd clculted the lest squres regression coefficients for predicting the corresponding oserved volume in liner regression model. As n lterntive pproch, we comined the three products y pplying predetermined fixed weight to ech product to generte sum s n independent vrile: [(8/27) PANK1 + (2/9)PANK2 + (8/27)PANK3]. The weight vlues were determined sed on the ellipsoidl geometry (see Appendix). This comined vrile ws compred ginst the oserved kidney or cyst volume s the dependent vrile in liner regression nlysis. Model fit ws judged y the R 2 vlue, i.e. the proportion of vriility in volume explined y the regression model (or the liner comintion with predetermined coefficients). Dt Anlysis for Kidney Volume for Smll- nd Moderte-Size Kidneys To evlute whether the sme coefficients nd level of prediction pplied to predicting kidney volume for smll- nd modertesize kidneys, the nlyses were rerun for kidneys less thn the medin volume (i.e. 576.2 ml for the right kidney nd less thn 616. ml for the left kidney). Assessment of Vriility in Correltion Coefficients Bootstrp confidence intervls were clculted to quntify the degree of vriility in the R 2 vlues. More specificlly, 1, ootstrp smples were creted y smpling with replcement, nd then the R 2 vlue ws clculted for ech of those 1, dt sets. The 95% confidence intervls were then defined s the R 2 vlues representing the 2.5 nd 97.5 percentiles of the ootstrp distriution. This pproch provides nonprmetric estimte tht does not depend on ny distriutionl ssumptions for the R 2 vlues. All regression models nd ssocited plots were fit with Stt (version 12) nd ootstrp nlyses nd ssocited confidence intervls were clculted with R (version 9.2). R e s u l t s Kidney nd Cyst Volume Estimtion from the Mid-Slice Are Mesurements The kidney volume predicted from PANK2 (the product of the mid-slice re nd the numer of slices) correlted extremely well with the oserved kidney volume mesurements: R 2 =.994 (95% CI:.991,.996) for the right kidney nd.991 (95% CI:.986,.995) for the left kidney. The liner regression lest squres coefficient for PANK2 (to predict kidney volume) ws.637 (95% CI:.629,.644) for the right kidney nd.624 (95% CI:.616,.633) for the left kidney ( fig. 1 ). The regression of PANK2 seemed highly predictive of the kidney volume mesurements cross the entire rnge of kidney sizes, with only few points hving visily higher residuls t higher volumes. Similrly, the cyst volume predicted from PANC2 correlted extremely well with the oserved cyst volume mesurements: R 2 =.984 (95% CI:.973,.994) for the right kidney nd.967 (95% CI:.95,.99) for the left kidney. The lest squres coefficient for PANC2 (to predict cyst volume) ws.637 (95% CI:.624,.649) for the right kidney nd.68 (95% CI:.591,.625) for the left kidney ( fig. 2 ). Two notle outliers in the regression corresponded to one prticipnt with prominent clustered nd exophytic cysts in the mid-slice of reltively smll kidneys ( fig. 3 ) nd the other prticipnt with numerous cysts clustered more centrlly in the mid-slices of lrge right nd left kidneys. Becuse of n overly lrge contriution from these mid-slice cysts, the volume estimtion from the mid-slice cyst re mesurement gretly exceeded the oserved cyst volumes in these kidneys. Kidney nd Cyst Volume Estimtion from the Three-Slice Are Mesurements When the three-slice kidney re mesurements (PANK1, PANK2, PANK3) were used s independent vriles in liner regression to predict the oserved Kidney nd Cyst Volumes in ADPKD Am J Nephrol 213;38:333 341 335
4, 3, 2, 1, 4, 3, 2, 1, Color version ville online 1, 2, 3, 4, 1, 2, 3, 4, Fig. 1. Comprison of the oserved kidney volume mesurements nd the product of the mid-slice re nd the numer of slices for the right ( ) nd left ( ) kidneys. The correltion etween the oserved kidney volume mesurement nd the product of the mid-slice re nd the numer of slices (PANK2) ws R 2 =.994 for the right kidney nd.991 for the left kidney. The liner regression coefficient multiplier to the re product tht est fit the kidney volume ws.637 (95% CI:.629,.644) for the right kidney nd.624 (95% CI:.616,.633) for the left kidney. 3, 2, 1, 4, 3, 2, 1, Color version ville online 1, 2, 3, 1, 2, 3, 4, Fig. 2. Comprison of the oserved cyst volume mesurements nd the product of the mid-slice re nd the numer of slices for the right ( ) nd left ( ) kidneys. The correltion etween the oserved cyst volume mesurement nd the product of the mid-slice re nd the numer of slices (PANC2) ws R 2 =.984 for the right kidney nd.967 for the left kidney. The liner regression coefficient multiplier to the re product tht est fit the cyst volume ws.637 (95% CI:.624,.649) for the right kidney nd.68 (95% CI:.591,.625) for the left kidney. Two pprent outliers re indicted y the rrows. The midslice imges from one of the outliers (white rrow) re shown in figure 3. kidney volume, the correltion ws higher thn tht of PANK2 lone: R 2 =.999 for oth the right (95% CI:.9986,.9993) nd left (95% CI:.9985,.9992) kidneys ( fig. 4 ). The corresponding liner regression coefficients for PANK1, PANK2, nd PANK3 were.319 (95% CI:.297,.34),.171 (95% CI:.137,.25), nd.36 (95% CI:.274,.339), respectively, for the right kidney nd.315 (95% CI:.296,.334),.185 (95% CI:.154,.217), nd.288 (95% CI:.254,.323), respectively, for the left kidney. Using the geometriclly predetermined 336 Am J Nephrol 213;38:333 341 Be et l.
Fig. 3. The mid-slice imges of the right ( ) nd left ( ) kidneys from the outlier indicted in figure 2 y the white rrow. Becuse of n overly lrge contriution from lrge clustered nd exophytic cysts in the mid-slices, the cyst volumes (right 1,28. ml, left 1,67.3 ml) predicted from the product of the mid-slice cyst re mesurement (right 36. cm 2, left 45. cm 2 ) nd the numer of slices (right 44, left 37) gretly exceeded the oserved cyst volumes (right 362. ml, left 378.6 ml) tht were mesured y summing ll the slices covering the whole kidney. The multiplier to the cyst re product used to predict the volume ws.637 for the right kidney nd.68 for the left kidney. 4, 3, 2, 1, 4, 3, 2, 1, Color version ville online 1, 2, 3, 4, 1, 2, 3, 4, Fig. 4. Comprison of the oserved kidney volume mesurements nd the product of the three-slice re nd the numer of slices for the right ( ) nd left ( ) kidneys. The correltion etween the oserved kidney volume mesurement nd PANK1, PANK2, nd PANK3 s three independent vriles in liner comintion ws extremely strong: R 2 =.999 for oth the right (95% CI:.9986,.9993) nd left (95% CI:.9985,.9992) kidneys. coefficients for PANK1, PANK2, nd PANK3 led to slightly etter correltions with oserved volumes thn the mid-slice, with R 2 vlues of.996 (95% CI:.994,.997) for the right kidney nd.995 (95% CI:.993,.996) for the left kidney. The three-slice cyst re mesurements (PANC1, PANC2, PANC3) were then entered s independent vriles in liner regression, which yielded n R 2 vlue of.992 (95% CI:.979,.999) for the right kidney nd.989 (95% CI:.979,.998) for the left kidney ( fig. 5 ). The corresponding liner regression lest squres coefficients for PANC1, PANC2, nd PANC3 were.27 (95% CI:.226,.314),.246 (95% CI:.185,.37), nd.246 (95% CI:.185,.38), respectively, for the right kidney nd.34 (95% CI:.252,.355),.43 (95% CI:.17,.12), nd.47 (95% CI:.49,.531), respectively, for the left kidney. Using the three-slice re mesurements (PANC1, PANC2, PANC3) with the geometriclly predetermined coefficients led to similr correltions with the oserved cyst volumes, with R 2 =.983 (95% CI:.946,.997) for the right kidney nd.963 (95% CI:.92,.994) for the left kidney. Kidney nd Cyst Volumes in ADPKD Am J Nephrol 213;38:333 341 337
3, 2, 1, 4, 3, 2, 1, Color version ville online 1, 2, 3, 1, 2, 3, 4, Fig. 5. Comprison of the oserved cyst volume mesurements nd the product of the three-slice re nd the numer of slices for the right ( ) nd left ( ) kidneys. The correltion etween the oserved cyst volume mesurement nd PANC1, PANC2, nd PANC3 s three independent vriles in liner comintion ws extremely strong: R 2 =.992 (95% CI:.979,.999) for the right kidney nd.989 (95% CI:.979,.998) for the left kidney. Kidney Volume Estimtion for Smll- nd Moderte-Size Kidneys R 2 vlues for smll- nd moderte-size kidneys were highly comprle to those for lrger kidneys for prediction sed on the mid-slice nd ll three slices (with differences of.3% or less), with lrger ut still very minor differences in the ellipsoid R 2 vlues (1.8 3.1%). The liner regression coefficients for the mid-slice of smll- nd moderte-size kidneys were lso very similr to those of lrger kidneys (with multiplier of.61 s compred to.62.64). The coefficients using regression of three slices yielded moderte differences in the multipliers (with differences of.52.119); however, this ws not unexpected since the three products (of the re times the numer of slices) were nerly colliner (with pirwise correltions etween.88 nd.97), nd thus likely to e unstle in terms of individul coefficients. D i s c u s s i o n The CRISP study demonstrted tht we could relily mesure totl kidney nd cyst volumes from MRI, supporting the use of these indices for monitoring disese progression nd trgeted therpeutic trils in ptients with ADPKD [2, 3]. For instnce, in recent clinicl tril [7], nnul MRI mesurements were used to quntify kidney volume. This tril demonstrted tht the rte of increse in totl kidney volume ws slowed with use of tolvptn. There re numer of imging techniques nd mesurement methods to quntify totl kidney volume nd kidney cyst volume [2, 4, 8, 9]. In ultrsonogrphy (US) imging, kidney volume is commonly estimted from the mximum length (L), width (W), nd depth (D) of the kidney, using the formul for n ellipsoid (πlwd/6) [8]. Length nd width re mesured from longitudinl imges cquired in plnes rnging from sgittl to coronl, wheres depth is otined from trnsverse imges of the mid-kidney cquired in the plne perpendiculr to the longitudinl plne. This US method, sed on 3 liner xil mesurements, is limited for ccurtely estimting kidney volume, prticulrly in ADPKD kidneys tht re irregulrly shped nd frequently too lrge to ccurtely mesure the three xil dimensions. Of the three xil mesurements of the kidney, the depth (i.e. distnce from the lterl edge to the centrl hilum on the coronl plne) is often more difficult to determine thn the other two. Even with MR mesurements of kidney volume nd re, we must crefully exclude hilr structures (vessel, collecting systems) in the mid-slice. Furthermore, some exophytic cysts my deform the renl contour, resulting in inccurte xil mesurements. Although renl volume sed on the ellipsoid formul is simple to use, it ws shown to e less ccurte nd precise thn tht of MR- 338 Am J Nephrol 213;38:333 341 Be et l.
sed mesurement in ADPKD [8]. Compred to kidney volume, cyst volume is even more chllenging to mesure from US imging ecuse of the limited imging resolution nd the difficulty in identifying the numerous cysts within the kidney. In computed tomogrphy (CT) nd MR imging, kidney nd cyst volumes re typiclly computed y mesuring the re of ech slice of contiguous imges covering the entire volume nd then summing the products of the re mesurements nd the slice thickness. Mesuring the volume y summing the re of every slice in series of imges (typiclly 2 4 slices per ech ADPKD kidney t 3-mm slice thickness) is lorious nd timeconsuming. By limiting the numer of re mesurements (e.g. only one mid-slice) from set, we cn gretly improve the efficiency of mesuring kidney or kidney cyst volumes. Our study reveled extremely strong correltions etween the oserved volume nd the product of the midslice re nd the numer of slices for oth the renl nd cyst volumes of the right nd left kidneys. The correltions for the kidney volume (R 2 =.994 for the right kidney nd.991 for the left kidney) were greter thn those for the cyst volume (R 2 =.984 for the right kidney nd.967 for the left kidney). The correltions for the right kidney were minimlly greter thn tht for the left kidney. The correltions for the kidney volume for smll- nd moderte-size kidneys were very similr to those of lrger kidneys. These extrordinry high correltions nd regression nlysis results indicted tht we cn ccurtely predict the kidney nd cyst volumes from limited re mesurements on MR imges in ptients with ADPKD. Since the coefficients nd R 2 vlues were determined using the sme dt, findings my e more optimistic thn would e chieved in nother dt set; results should therefore e vlidted in future studies. The liner regression coefficients multiplied y the product of the mid-slice re nd the numer of slices to est fit the oserved volume were.637 nd.624 for the kidney volumes (the right nd left kidney, respectively) nd.637 nd.68 for the cyst volume (the right nd left kidney, respectively). The significnce of these numers reflects the geometry of kidney. Assuming tht the kidney hs n ellipsoid shpe, the volume corresponds to πabc/6, where A, B, nd C represent the dimeters in three xes. The mid cross-section of the ellipsoid long xis C is n ellipse with its re corresponding to πab/4. Since the numer of slices corresponds to C, the mid-slice re times the numer of slices equls πabc/4. Thus, multiplier to this product tht would result in the ellipsoid volume of πabc/6 is 2/3 or.67. This vlue is close to the liner regression coefficients,.61.64, which we empiriclly estimted. This theoreticl nd empiricl consistency supports the possiility tht we my e le to pproximte kidney or cyst volume from the mid-slice re mesurement nd numer of slices y pplying our empiriclly derived multipliers. When we used the three-slice re mesurements s three independent vriles for predicting the corresponding oserved volumes, the correltions were even higher thn those with the mid-slice lone. However, given the lredy extremely high correltions with the mid-slice re mesurement, this incrementl improvement with two dditionl re mesurements my not e significntly contriutory in prctice. In ddition, the empiricl liner regression coefficients for the three-slice re mesurements were vrile. Thus, we cnnot predetermine multiplier for ech of the threeslice re mesurements to provide the est volume estimte. When three-slice re mesurements were comined y multiplying predetermined liner coefficients sed on the ellipsoidl geometry, the correltions for predicting the oserved kidney volumes were higher thn those for the mid-slice only, ut slightly lower thn those for the three-slice independent vrile fitting. Although the three methods were sttisticlly different (with nonoverlpping CI), the R 2 vlues were within out 1% of ech other cross ll three methods for predicting oserved kidney volume. On the other hnd, for the cyst volume prediction, the correltions for the threeslice re mesurements with predetermined liner coefficients were slightly lower thn those for the other two methods (mid-slice only or three-slice independent vrile fitting). Nevertheless, ll three methods for predicting oserved cyst volume produced overlpping confidence intervls, thus reflecting lck of sttisticl differences. Our method for estimting kidney volume from the mid-slice re mesurement nd the numer of slices my e pplicle directly to CT nd possily to US imging. The trnsxil CT imges cn e reformtted in the coronl plne to mesure the mid-slice re. The kidney or cyst volume cn e estimted from the midslice re mesurement on CT nd the numer of slices. For US imging, the cross-sectionl re of the kidney cn e mesured from the mid-slice imge in the coronl plne. The width (the nteroposterior dimension) of the kidney, corresponding to the numer of Kidney nd Cyst Volumes in ADPKD Am J Nephrol 213;38:333 341 339
slices in MR imging, cn e mesured perpendiculr to the coronl mid-slice. The kidney volume cn then e predicted using the mid-slice re nd width mesurements. The proposed volume mesurement method for CT or US imging my require vlidtion in future studies. Our study demonstrted tht kidney nd cyst volumes cn e pproximted from the mid-slice re mesurement nd the numer of slices. This pproch is fr more efficient thn mesuring re in every slice of MR imging set to derive kidney or cyst volume. However, when precise volumetric mesurement is needed, e.g. to determine sutle chnges in volumetric follow-up, mesurement nd nlysis of every slice my still e required. In some cses, regionl morphologicl vritions in ADPKD my cuse lrge error in the estimtion of volumes with the use of limited set of imges (e.g. outliers in fig. 2 ). The estimtion of renl cyst volume is likely more chllenging thn tht of kidney volume ecuse of higher locl vritions ( fig. 3 ). The mid-slice imges from the two outliers in our study cses presented with fr lrger nd exophytic thn other cysts distriuted in the remining kidney. When using this technique, nlysts should tke into considertion the possiility tht this pttern of cystic dominnce towrd the mid-slice my led to n overestimtion of the cystic volume. In prctice, the trde-off in the volume mesurement etween the mid-slice pproximtion nd mesurement from every slice should e determined y lncing the required degree of precision versus mesurement efficiency in ech ppliction. In conclusion, kidney nd cyst volumes cn e closely pproximted y multiplying.61.64 with the product of the mid-slice re mesurement nd the totl numer of slices in the coronl MR imges of ADPKD kidneys. A further expnsion of the volume prediction y including re mesurements from two dditionl slices ws not prticulrly contriutory. Appliction of the proposed mid-slice technique will decrese the mount of processing time needed to estimte the totl kidney nd cyst volumes of ptients with ADPKD. We elieve tht our proposed method is sufficiently precise nd therefore useful for clinicl reserch tht relies on kidney or cyst volume mesurement s n imging iomrker, unless study requires highly precise volumetric mesurement to determine sutle volumetric chnges in short follow-up period. Nevertheless, precision threshold determining the mid-slice pproximtion versus every-slice volume mesurement should e investigted in future study. Acknowledgements The CRISP study is supported y coopertive greements from the Ntionl Institute of Dietes nd Digestive nd Kidney Diseses of the Ntionl Institutes of Helth (DK56943, DK56956, DK56957, DK56961), y the Ntionl Center for Reserch Resources Generl Clinicl Reserch Centers t ech institution (RR39, Emory University; RR585, Myo College of Medicine; RR2394, Knss University Medicl Center; RR32, University of Alm t Birminghm), nd the Ntionl Center for Reserch Resources Clinicl nd Trnsltionl Science Awrds t ech institution (RR258, Emory; RR2415, Myo College of Medicine; RR33179, Knss University Medicl Center; RR25777 nd UL1TR165, University of Alm t Birminghm; RR24153 nd UL1TR5, University of Pittsurgh School of Medicine). The investigtors re indeted to the rdiologists, rdiology technologists, imging engineers, nd study coordintors in CRISP. Disclosure Sttement K.T.B., A.B.C., nd J.J.G. re consultnts to Otsuk Corportion, nd V.E.T. received reserch support from Otsuk Corportion. M.M. is consultnt to Otsuk Corportion nd Alexion Phrmceuticls. A p p e n d i x For n ellipsoid with its three principl xes of length A, B, nd C, the volume corresponds to πabc/6. When the ellipsoid is sliced long xis C, the numer of slices in the MRI set is equivlent to length C. At the midpoint of the xis (i.e. t C/2), the cross-section of the ellipsoid is n ellipse with its re corresponding to πab/4. At the 1st qurtile (C/4) or 3rd qurtile (3C/4) long xis C, the cross-section of the ellipsoid is lso n ellipse, ut with n re smller thn tht of C/2, i.e. 75% of the midpoint ellipse: [(3/4) πab/4]. We considered the three-slice re mesurements in the MR imge set of ech kidney s corresponding to the ellipsoidl crosssections t the 1st qurtile (t C/4), mid-slice (t C/2), nd 3rd qurtile (t 3C/4) long xis C. We need to pply n pproprite weighting vlue to ech of the three re mesurements to chieve their lnced contriutions to estimte the ellipsoid volume. Using the proportionlity determined from the forementioned ellipsoidl cross-sections, the comined contriutions from the three re mesurements cn e expressed s follows: comined re (Are c ) = [(4/9) of the 1st qurtile re + (1/3) of the mid re + (4/9) of the 3rd qurtile re]. This comined re (Are c ) equls πab/4 for n ellipsoid with its three principl xes of length A, B, nd C. The kidney volume is estimted y multiplying the numer of slices (length C of the ellipsoid) nd 2/3: Volume = Are c C (2/3) = [(8/27)PANK1 + (2/9)PANK2 + (8/27)PANK3]. 34 Am J Nephrol 213;38:333 341 Be et l.
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