A new method for calculating the volume of ... - CSIRO Publishing

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Animal Production Science, 2009, 49, 1035–1042

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A new method for calculating the volume of primary tissue types in live sheep using computed tomography scanning C. L. Alston A,C, K. L. Mengersen A and G. E. Gardner B A

School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld 4001, Australia. B School of Veterinary and Biomedical Sciences, Murdoch University, 90 South Street, Murdoch, WA 6150, Australia. C Corresponding author. Email: [email protected]

Abstract. Interest in the use of computed tomography (CT) scanning in animal experimentation has increased markedly over the last decade due to the benefits of studying tissue in live subjects over time. In these experiments, the non-carcass components of the scan are removed from the collected data, allowing scientists to study the carcass of a live animal without the need to slaughter the individual. However, there is not yet a consensus regarding the most appropriate manner in which to convert the CT numbers into a meaningful estimate of area, volume or proportion of tissue present in a carcass at the time of scanning. In this paper we use a Bayesian mixture model to estimate the area of each of three tissue types of interest, fat, muscle and bone present in individual CT scan slices. We then use the Cavalieri principle to estimate the volume and proportion of the carcass attributable to each of these tissues. The approach is validated by analysis of experimental sheep carcasses. Additional keywords: Bayesian mixture model, Cavalieri method, trapezoidal rule.

Introduction The use of computed tomography (CT) scanning in animal experimentation has expanded and developed since the early 1990s in several countries including Australia, New Zealand, Norway and the United Kingdom (Thompson and Kinghorn 1992). The experimental objectives of trials using CT scans are quite varied, ranging from the study of the effects of drought on sheep carcass composition (Ball et al. 1998), use in study of deer (Jopson et al. 1997), estimation of genetic parameters for sheep carcass traits (Kvame and Vangen 2007), fat distribution assessment in pigs (Kolstad 2001), estimation of body composition in commercial turkeys (Brenøe and Kolstad 2000), and determination of the volume of specific muscles in sheep carcasses (Navajas et al. 2006). CT scanning animals over time is also important in investigating longitudinal changes to carcass composition when livestock are subjected to varying treatments or management plans or more simply understanding breed differences. As CT scanning is non-destructive, it is ideally suited to this task. However, a CT scan does not measure tissue type directly. After image processing, the scan provides an estimate of the denseness of the tissues at each of the given pixels. These pixels can be mixed, that is, consisting of two or even three tissue types in the area defined in a pixel. In addition, the density of tissue types varies depending on location on the carcass. As a result, the same CT number can represent a pixel that is comprised mainly (or wholly) of different tissues at the boundaries of these tissue CSIRO 2009

densities. Therefore, an effective statistical analysis needs to be able to estimate the proportion of tissue present in a scan given the known mixing that takes place at tissue boundaries. Given that bone is more dense than muscle, which in turn is more dense than fat, previous studies (Jopson et al. 1997; Ball et al. 1998; Brenøe and Kolstad 2000; Kolstad 2001; Kvame and Vangen 2007) have applied a simple boundary approach which assumes that pixels within a specified range may be designated to one of these three tissues. In this paper, we will use a Bayesian mixture model to estimate tissue proportions in individual scans. We will then use the Cavalieri and trapezoidal methods to estimate the proportion and weight of each tissue type in the carcass, and compare these results to those we obtained by using the established fixed boundary method commonly applied to sheep. Materials and methods Experimental objectives The overall aim of this work is to estimate the volume of the three tissue types present in the entire live carcass of an animal. Generally, CT scans are taken either at pre-determined reference points on the animal, or, more commonly, as in this study, a series of scans is taken at a set distance apart along the length of the carcass. As these are live animals, the next requirement is to remove the non-carcass miscellanea from the images. In this analysis, this operation was performed

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manually, using ImageJ 1.38x software (US National Institutes of Health, Bethesda, MD, USA), by an experienced technician. The resulting 15 images which are to be used in this analysis can be seen in Fig. 1. An alternative approach is to use an automated segmentation algorithm, such as the one developed by Glasbey and Young (2002). Carcass in this paper will henceforth refer to the CT scan data of a live sheep with the non-carcass components removed from the data.

C. L. Alston et al.

The next stage of the process is to determine the area of the three tissue types present in each of the 15 CT scans. This is needed to estimate the volume of each tissue in the carcass using either the Cavalieri approach or the trapezoidal method (Thompson and Kinghorn 1992). It is common for this to be done using fixed boundaries to allocate each of the pixels in the scan to one of the three tissue types present in the scan. However, viewing Fig. 2, which incorporates a commonly used set of

Fig. 1. Individual slices from computed tomography scanning of a live sheep, which were used to estimate the volume of different tissue types in the carcass.

A new method for calculating the volume of primary tissue types

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Houndsfield number Fig. 2. Histograms of Hounsfield numbers for each of the 15 computed tomography scans to be analysed. Grey vertical lines indicate boundaries commonly used in sheep studies (Kvame and Vangen 2007) to allocate pixels to fat (y –23), muscle (–23 < y 146) and bone (y > 146) components.

boundaries in sheep studies (Kvame and Vangen 2007), it is clear that fat and muscle tissues are not well separated. Additionally, the changing shape of the histograms over the carcass profile indicates that the density of these tissues is varying. Consequently, fixed boundaries would have different levels of accuracy depending on the region in which the scan was taken. The third stage of the process is to use the statistical analysis of each scan to estimate the percentage or volume of the carcass attributable to fat, muscle and bone. Further, researchers may also wish to estimate the weight of the carcass, if the animal were to be

slaughtered, and the weight of each of the different tissues in this carcass. Bayesian Normal mixture model for estimating CT scan proportions In the studies mentioned above (see ‘Introduction’), the percentage or volume of tissue type in a carcass was measured using fixed boundaries. This technique entails determining appropriate CT numbers by which to classify each pixel into a tissue type.

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In this analysis we use the Bayesian Normal mixture model proposed by Alston et al. (2005) to determine the proportion of each tissue type present in a scan. This approach is more flexible than one with fixed boundaries, allowing the density of tissues to vary over regions of the carcass, and also allowing pixels to be categorised not only by their CT (Hounsfield) number, but also by allocation of neighbouring pixels. In the Normal mixture model, the data from the N pixels in the CT scan, y = (y1,. . .,yN), are represented by a Normal mixture likelihood given by; " # N X k Y 1 1 yi mj 2 : ð1Þ lj qffiffiffiffiffiffiffiffiffiffi exp gðyÞ g^ðyÞ ¼ 2 sj 2ps2j i¼1 j¼1 Here, k is the number of Normal components in the mixture. This representation provides a parametric framework to describe the complex densities of tissue that are derived from the scans that can be interpreted and computed with relative ease. In particular, skewed densities can be represented through the addition of two or more Normal components. These skewed densities can be the result of tissue characteristics themselves, or may be the result of combining tissues of the same type from different locations on the carcass; for example, fat density may vary as it is taken from two different locations and then combined in the data. The parameter lj represents the probability of pixel i belonging to the jth component. In effect, this is the probability that the tissue of an individual pixel isPeither fat, muscle or bone. These probabilities sum to 1 ( kj¼1 lj ¼ 1). In a Bayesian setting, one can introduce indicator vectors zi = (zi1,. . .,zik) to represent the unobserved component membership of the pixel yi(i = 1,. . .,N). These are subsequently treated as other parameters to be estimated in the modelling procedure. To allow the model to use the spatial information provided by 1st order neighbours, Alston et al. (2005) assume zi is drawn from a hidden Markov random field (MRF) with a joint distribution described by a Potts model (Potts 1952); ! X 1 ð2Þ zi zqi ; pðzjbÞ ¼ CðbÞ exp b iqi

where C(b) P is a normalising constant, qi indicates a neighbour of pixel i, i~qi is the sum over all neighbouring pairs and zizqi = 1$ if zi = zqi, otherwise zizqi = 0. The parameter b estimates the level of spatial homogeneity in component membership between neighbouring pixels in the image. A zero value for b indicates that the allocation of pixels to component groups is independent of their neighbours. Positive values for b infer that neighbouring pixels tend to have similar component memberships. Prior distributions In this analysis, we work with the log-transform of the Hounsfield numbers to aid in the computational aspects of the chosen mixture model. These Hounsfield numbers have the value of the lowest reading added before transformation to ensure they are nonnegative. On the original scale, the distribution of bone would result in very large numbers of components being necessary to

adequately describe its skewed distribution. We use conjugate priors as they are both biologically reasonable and computationally convenient. By using conjugate priors, the conditional posterior distributions of the parameters to be estimated are in readily simulated forms, and, hence, we are able to use the Gibbs sampler for parameter estimation. The prior distributions of the component means (mj) in this analysis are taken as p(mj|s2j ) ~N(xj, s2j / nj), where xj is taken as the mean of the data (yi) and nj, which represents an equivalent sample size and hence level of precision attributable to the prior, is fixed at 100. As the numbers of pixels in any one image is always greater than 24 000, setting nj at this small value (nj < 0.005N) assures us that component means are not unduly influenced by this prior. Another reasonable approach to setting the hyperparameter for xj would be to have a separate value representing each of the three tissue types. This could be based on the currently used boundaries and components with a mean lower than each boundary assigned this value. We have tested both these approaches, and find with these data that there is no discernible difference in the resulting parameter estimates. The prior distributions for the component variances (s2j ) were taken as p(s2j ) ~InverseGamma(nj, s2j ), where we set nj = 4.05 and s2j = 0.5125. These hyperparameters were obtained by inspection of the data in order to obtain prior estimates for the variance that are in keeping with the observed data and also allow for a range of component variances to accommodate the different tissue distributions. Finally, we use a prior distribution for the spatial parameter of p(b) ~Uniform(z, d). A lower bound of z = 0 was chosen as it is theoretically expected from viewing the images that neighbouring pixels are similar in value, and hence we expect positive spatial correlation between the allocation variables (zi). An upper bound of d = 3 was selected as a reasonable level at which the neighbour allocations could influence but not completely determine the allocation of a pixel to a component group. In the analysis, all estimated values of b were less than 2, so this is a reasonable bound to impose. Estimation Gibbs sampler The parameters of the mixture model in Eqn (1) were estimated using a two stage Gibbs sampler, as detailed by Alston et al. (2005), which we reiterate briefly here. Stage 1: Allocate pixels to a component (1) Simulate updated values zi using pðzi jzqi ; y; b; m; sÞ Multinomialð1; wi1 ; vi2 ; . . . ; wik Þ;

ð3Þ

where wij represents the posterior probability that pixel i(yi) belongs to component j, given the current estimates of mj, s2j and b and the previous allocation of its neighbouring pixels (zqi): qffiffiffiffiffiffiffiffiffiffi1 y m 2 exp 12 i sj j þbU ðzqi ; jÞ 2ps2j : ð4Þ wij ¼ 2 Pk pffiffiffiffiffiffiffiffiffiffi2 1 1 yi mt 2pst exp 2 st þbU ðzqi ; tÞ t¼1



Here, zqi are the first order neighbours of pixel yi and U(zqi, j) is the number of pixels in the neighbourhood of zi allocated to component j in the previous iteration. It is evident from this representation that using the Potts model allows the four neighbouring pixels to have an influence on the allocation of pixel i, whilst still allowing the pixel value itself (yi), to influence the allocation. This is considered to be a suitable level of influence between data and neighbours in terms of allocation. ^ ¼ PN wij = PN Pk wit to be (2) Update estimate of l i¼1 i¼1 t¼1 used in calculation of tissue proportions and weights. (3)PCalculate the following values for use in stage 2; mj ¼ Ni¼1 zij , N 1 X y ¼ zij yi mj i¼1

and ^s2j ¼

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zij ðyi yj Þ2 :

ð5Þ

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Stage 2: Update parameter estimates (1) Update values for unknown parameters (mj and s2j ) from their conditional posteriors. In this case, ! s2j mj yj þ nj jj ; ð6Þ ; mj N mj þ nj mj þ nj

s2j InverseGamma

mj þvj þ1 1 2 2 mj nj 2 ; sj þ s^j þ : ðy j Þ 2 2 mj þnj j j ð7Þ

(2) Update the estimate of the spatial parameter b using a Metropolis-Hastings step (Rydén and Titterington1998). Using this approach, the pseudo-likelihood is used in place of Eqn 2, thereby avoiding the need to calculate the normalising constant C(b). We draw bnew ~Unif(0, 3) and accept bnew with ( ) ^ new jm; s; z; yÞ pðb ; prob ¼ min 1; ^ current jm; s; z; yÞ pðb otherwise retain existing b. Starting values In this analysis, for each scan, we start with a mixture model containing three components (k = 3), the known number of tissues in each scan. To initiate the Gibbs sampler we need to set starting values for both the component memberships (zi0) and the parameter values (b0, mj0, sj02). When k = 3, we set the starting values of m0 = (4.0, 5.5, 7.0), which approximately correspond to the log-transform of the midpoint of the usual boundaries imposed on the pixels for 2; s 2; s 2 Þ is the classification. The value given to s20 ¼ ðs sample variance of the data. The initial group memberships (zi0) are then determined assuming the usual independent mixture model with l0 = (1/3, 1/3, 1/3). After initially fitting a model with k = 3, we then sequentially add components and test for an improvement in overall density fit using the BIC statistic (Kass and Raftery 1995). Starting values are then set for the new model (k = 4, 5, . . ., K) using the targeted addition of components scheme proposed by Alston et al. (2007).

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The aim of this scheme is to identify regions where the density estimate is under fitting the observed data, hence implying that the model may benefit from an additional component in these regions. One of these regions is randomly chosen, based on the amount of under fit, and a new starting value for m0 and s02 is simulated. See Alston et al. (2007) for full implementation details. In all models (k = 3, 4, 5, . . ., K), starting values of b0 are drawn from its prior distribution, which in this case is a Unif(0, 3). Volume calculation In this analysis we have used both the Cavalieri and trapezoidal methods to calculate tissue volumes in a whole carcass based on 15 equally spaced CT scans, taken 4 cm apart. Most animal science papers to date have used the Cavalieri method, and it has proven to be reliable in most situations (Gundersen and Jensen 1987; Gundersen et al. 1988). An estimate of volume using Cavalieri’s method is calculated as; V Cav ¼ d ·

m X

areag t · areamax ;

ð8Þ

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where m is the number of CT scans taken (15), d is the distance the CT scans are apart, in this case, 4 cm. The value of t is the thickness of each slice (g), in this example, 1 cm and areamax is the maximum area of any of the m scans. The approach of Cavalieri relies on CT scans being taken at equal distances of separation. For experiments in which this is not achievable, it is useful to have an alternative means of volume assessment. For such cases, we consider using the trapezoidal method where volume calculations are given by " # m1 X 1 areag ; V Trap equal:dist ¼ d ðarea1 þ aream Þ þ ð9Þ 2 g¼2 when spacings are equal, and by V Trap

unequal:dist

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ðareag þ areagþ1 Þ ; 2

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when scans are taken at varying distances. Here, dg,g+1 is the distance between scan g and scan g+1. As noted by Rosen and Harry (1990), the trapezoidal method will require a reasonable number of scans to provide accurate volume estimates. Calculating tissue weight is straightforward. We use the established conversion to grams per cubic centimetre given by Fullerton (1980); Estdensityðg=cm3 Þ ¼ 1:0062 þ Hu · 0:00106:

ð11Þ

To estimate the weight of each tissue we the equation Tissueweight ¼ tissue · 0:00106Þ · NumPixtissue · ðpixels=cm3 Þ1 ð1:0062 þ Hu 1000 ð12Þ tissue is the mean Hounsfield number for pixels where Hu allocated to the tissue of interest and NumPixtissue is the

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Table 1. Estimated number of components for the Bayesian mixture model of each of the 15 images in the study and the total number of pixels in each scan

number of pixels allocated to the tissue type. The number of pixels/cm3 is 113.78 in this dataset. Results

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The Gibbs sampler outlined above (see ‘Bayesian Normal mixture model for estimating CT scan proportions’) was run for 110 000 iterations for each CT scan for all values of k required. Estimates of mixture parameters were based on the final 100 000 iterations. The number of components required in each scan is given in Table 1. The number of components needed to adequately model the density of each scan ranged between 6 and 10. These components are allocated to the three primary tissue types based on the mean (mj) estimate of each component during post-processing of the output. The resulting estimates and 95% credible intervals for tissue proportions for each of the 15 scans can be seen in Fig. 3. As scans are taken at 4-cm spacings, the smooth transitions in tissue proportion are biologically tenable. The only scans displaying a sizeable change were for the bone component between scans 13 and 14, this being explained by scan 14 passing through the pelvic region of the carcass where the bone component is proportionally large. The width of the 95% credible intervals, which were based 0.30

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46 550 53 561 55 032 52 347 41 528 28 091 24 480 24 397 27 547 33 061 39 613 52 106 66 422 65 693 36 326

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on allocation of pixels to tissue types in the last 1000 iterations of the Gibbs sampler, indicates the model is stable around these estimates.

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Image number Fig. 3. Estimated proportions and 95% credible intervals of (a) fat, (b) muscle and (c) bone, in each of the 15 computed tomography scan images using the Bayesian mixture model.



Table 2. Mixture model estimates with 95% credible intervals (in parentheses) for the percentage and weight of tissue components in carcass The boundary method only provides point estimates. Boundaries are defined as fat, y –23; muscle, –23 < y 146; and bone, y > 146

The estimates of the probabilities (lj) and the number of pixels in each scan (Table 1) are then used to calculate the area of tissue in each of the CT scans. These 15 area estimates are then used to estimate the overall proportion of tissue types in the carcass (Table 2). Using the mixture model results, the Cavalieri and trapezoidal methods yield estimates of tissue proportions that are in close agreement with each other and the findings of an extensive study published by Thompson and Atkins (1980). Additionally, a chemical analysis of this carcass indicated a fat percentage of 20.2% (4.47 kg), which is also in close agreement of these estimates. However, the results obtained using the boundary approach indicated that the proportion of fat and bone in this carcass is being overestimated quite substantially. Although it is of less scientific interest, the weight of the carcass and individual tissues therein was also estimated (Table 2). A weight measurement of the carcass at slaughter was 25.4 kg, which again shows a close agreement with the estimates obtained using the mixture model approach particularly given the error that is associated with manually editing images to extract the unwanted viscera from the live animal CT scans. Fig. 4 illustrates the mean CT number for the pixels allocated to each tissue type over the 15 scans. These smooth transitions between values reinforce the earlier observation from Fig. 2 that

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Percentage (%) (23.13, 23.30) 23.03 (22.94, 23.10) (62.20, 62.39) 61.89 (61.80, 61.98) (14.44, 14.52) 14.75 (14.72, 14.79)

Weight (kg) Carcass 22.88 (22.882, 22.883) 23.773 (23.771, 23.776) Fat 4.54 (4.52, 4.56) 4.77 (4.75, 4.78) Muscle 13.97 (13.95, 13.99) 14.35 (14.33, 14.38) Bone 4.37 (4.36, 4.38) 4.64 (4.63, 4.65)

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Image number Fig. 4. Estimated mean computed tomography (CT) number (Hounsfield numbers) and 95% credible intervals corresponding to (a) fat, (b) muscle and (c) bone tissue in each of the 15 CT scan images using the Bayesian mixture model.

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major outcome of interest. This idea is illustrated in Table 2, which shows that the estimate of fat under the boundary allocation has values far exceeding the chemical analysis, the mixture model estimates and the findings by Thompson and Atkins (1980). Discussion In this paper we have built on our previous publications (Alston et al. 2004, 2005, 2007) which focussed on the mixture model analysis for individual CT scans. This work demonstrates that the results from a mixture model analysis can be used for volume calculation of tissue types in live sheep using CT scan data and is analytically feasible for routine use. The use of the Bayesian Normal mixture model to estimate tissue volume and allocate pixels to each of the three tissue types is shown to be advantageous to the standard practice of imposing fixed boundaries to achieve these estimates. The change in mean Hounsfield numbers for the allocated tissues along carcass regions, along with the illustrated change in histogram densities, provides clear evidence that information may be misinterpreted if assessment is made using a standard boundary model. It seems likely that fixed boundaries need to be calibrated for factors such as breed, sex and age, rather then applying a standard set to all sheep in general. An additional benefit of the mixture model over the standard boundary technique is the ability to calculate measures of certainty around estimates, such as credible intervals. The boundary method provides a point estimate only, hence, giving no means of assessing uncertainty. The computation of the mixture model is more burdensome than the boundary method. However, our current research has shown (B. Carson, R. Murison, C. Alston, unpubl. data), with deft programming and the exploitation of parallel computing, the proposed Gibbs sampler could be implemented for use in live animal experimental work, based on the current computing power available to most modern researchers. We have also demonstrated that the trapezoidal method is comparable to the more frequently used Cavalieri method, and it may be of use in situations where it is difficult to scan animals at equal spacings. Acknowledgements The authors would like to thank Dr Kelly Pearce for providing the chemical composition values and Ms Neroli Smith for her involvement with collating and editing CT images. We also acknowledge Meat and Livestock Australia for their original funding of the project that has made this data available.

References Alston CL, Mengersen KL, Thompson JM, Littlefield PJ, Perry D, Ball AJ (2004) Statistical analysis of sheep CAT scan images using a Bayesian mixture model. Australian Journal of Agricultural Research 55(1), 57–68. doi: 10.1071/AR03017 Alston CL, Mengersen KL, Thompson JM, Littlefield PJ, Perry D, Ball AJ (2005) Extending the Bayesian mixture model to incorporate spatial information in analysing sheep CAT scan images. Australian Journal of Agricultural Research 56(4), 373–388. doi: 10.1071/AR04211

Alston CL, Mengersen KL, Robert CP, Thompson JM, Littlefield PJ, Perry D, Ball AJ (2007) Bayesian mixture models in a longitudinal setting for analysing sheep CAT scan images. Computational Statistics & Data Analysis 51(9), 4282–4296. doi: 10.1016/j.csda.2006.05.013 Ball AJ, Thompson JM, Alston CL, Blakely AR, Hinch GN (1998) Changes in maintenance energy requirements of mature sheep fed at different levels of feed intake at maintenance, weight loss and realimentation. Livestock Production Science 53, 191–204. doi: 10.1016/S0301-6226(97)00160-7 Brenøe UT, Kolstad K (2000) Body composition and development measured repeatedly by computer tomography during growth in two types of turkeys. Poultry Science 79, 546–552. Fullerton GD (1980) Fundamentals of CT tissue characterization. In ‘Medical physics of CT and ultrasound: tissue imaging and characterization. Medical physics monograph 6’. (Eds GD Fullerton, JA Zagzebski) pp. 125–162. (American Institute of Physics: New York) Glasbey CA, Young MJ (2002) Maximum a posteriori estimation of image boundaries by dynamic programming. Applied Statistics 51, 209–221. doi: 10.1111/1467-9876.00264 Gundersen HJG, Jensen EB (1987) The efficiency of systematic sampling in sterology and its prediction. Journal of Microscopy 147(3), 229–263. Gundersen HJG, Bendtsen TF, Korbo L, Marcussen N, Møller A, et al. (1988) Some new, simple and efficient stereological methods and their use in pathological research and diagnosis. APMIS 96(5), 379–394. Jopson NB, Thompson JM, Fennessy PF (1997) Tissue mobilisation rates in male fallow deer (Dama dama) as determined by computed tomography: the effects of natural and enforced food restriction. Animal Science 65, 311–320. Kass RE, Raftery AE (1995) Bayes factors. Journal of the American Statistical Association 90(430), 773–795. doi: 10.2307/2291091 Kolstad K (2001) Fat deposition and distribution measured by computer tomography in three genetic groups of pigs. Livestock Production Science 67, 281–292. doi: 10.1016/S0301-6226(00)00195-0 Kvame T, Vangen O (2007) Selection for lean weight based on ultrasound and CT in a meat line of sheep. Livestock Science 106, 232–242. doi: 10.1016/j.livsci.2006.08.007 Navajas EA, Glasbey CA, McLean KA, Fisher AV, Charteris AJL, Lambe NR, Bünger L, Simm G (2006) In vivo measurements of muscle volume by automatic image analysis of spiral computed tomography scans. Animal Science 82, 545–553. doi: 10.1079/ASC200662 Potts RB (1952) Some generalized order-disorder transitions. Proceedings of the Cambridge Philosophical Society 48, 106–109. doi: 10.1017/ S0305004100027419 Rosen GD, Harry JD (1990) Brain volume estimation from serial section measurements: a comparison of methodologies. Journal of Neuroscience Methods 35(2), 115–124. doi: 10.1016/0165-0270(90)90101-K Rydén T, Titterington DM (1998) Computational Bayesian analysis of hidden Markov models. Journal of Computational and Graphical Statistics 7(2), 194–211. doi: 10.2307/1390813 Thompson JM, Atkins KD (1980) Use of carcase measurements to predict percentage carcase composition in crossbred lambs. Australian Journal of Agricultural Research and Animal Husbandry 20, 144–150. doi: 10.1071/ EA9800144 Thompson J, Kinghorn B (1992) CATMAN – A program to measure CAT-scans for prediction of body components in live animals. Proceedings of the Australian Association of Animal Breeding and Genetics 10, 560–564.

Manuscript received 6 March 2009, accepted 18 May 2009

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