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Keys to Selecting a Prediction Model for Carcass Composition from Computed Tomography Images

Font-i-Furnols M*, Carabus A and Gispert M

IRTA-Product Quality, Finca Camps i Armet, 17121 Monells, Girona, Catalonia, Spain

*Corresponding Author:
Font-i-Furnols M
IRTA-Product Quality, Finca Camps i Armet
17121 Monells, Girona, Catalonia, Spain
Tel: 34972630052
E-mail: [email protected]

Received date: February 15, 2016; Accepted date: February 28, 2016; Published date: March 6, 2016

Citation: Font-i-Furnols M, Carabus A, Gispert M (2016) Keys to Selecting a Prediction Model for Carcass Composition from Computed Tomography Images. J Tomogr Simul 1:104.

Copyright: © 2016 Font-i-Furnols M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Abstract

Linear, nonlinear and volume measurements obtained from computed tomography (CT) images of live pigs are good predictors of carcass characteristics there are different ways to analyse the goodness of a prediction equation, including the decomposition of the predicted error and the biases and coefficient of determination. The present paper compares the goodness of fit of individual prediction equations within three different genotypes and the prediction obtained by a global equation for the different genotypes at the same time comparison is performed by means of the error decomposition, the standard deviation of the bias and the coefficient of model determination The results showed a good mean square prediction error and a high error due to disturbances (random effects) for most of the predictions; however, the prediction of lean obtained by the global equation and applied to the specific genotypes presented a low error due to disturbances and a high error due to central tendency different results are obtained when comparing individual and global equations for the estimation of lean without the distinction of the genotype predicted In general, the comparison shows that both equations are properly developed and useful; however, the utility is not the same for both of them.

Keywords

Error decomposition; Coefficient of model determination; Computed tomography; Pigs body composition

Introduction

Mathematical prediction models are used to explain the behaviour of natural processes they are useful for researchers, industries and policy makers to explain knowledge or discoveries acquired in scientific trials and/or to challenge old dogmas [1] they are commonly used in livestock animals to assist companies in making decisions; thus, model usefulness must be assessed by its sustainability for a particular purpose this means that adequate statistical analysis is an indispensable step during the development, evaluation, and revision phases of a model the swine and pork industry have used prediction models over the years to assess the growing rate of the animals [2,3], as well as the mortality [4], prolificity [5], behaviour [6], tissue development and deposition [7] and carcass composition [8-10].

When talking about livestock animals, there are different types of prediction models, such as linear regression, allometric, and quadratic [11] , and a model’s goodness depends on a mixture of different factors: R2, coefficient of variation, root mean square error and, mainly, its utility moreover, there are a huge variety of predictors for several characteristics of live pigs in swine, for example, predictors can be obtained for live animals on the farm by observing the animals or measuring them with devices, such as vision systems or ultrasounds [12], in the laboratory using samples obtained in vivo during growth [13] or, recently, using images obtained with the use of new technologies or devices, such as dual X-ray absorptiometry, magnetic resonance imaging [14,15] and computed tomography (CT) [7,16,17].

The aim of this paper was to compare and discuss the goodness of fit by genotype (GEN) and globally (all GEN together) of two methodologies for predicting the carcass composition of live pigs: (1) individual equations developed for each GEN obtained by Font-i- Furnols et al. [11] and (2) global equations developed for the three GEN together obtained by Carabus et al. [17] The prediction equations were obtained using the measurements of the pig body obtained from CT image analysis as predictors and the weight of the carcass pieces and tissues obtained by manual dissection as the reference values (observed or “true” values).

Materials and Methods

The present paper makes a comparison between the prediction equations obtained by Font-i-Furnols et al. [11] and Carabus et al. [17] using data from the same animals.

Animals and computed tomography scanning

In brief, the study included 90 gilts of 3 different GEN, 30 (Duroc × (Landrace × Large White)) (DU), 30 (Pietrain × (Landrace × Large White)) (PI) and 30 (Landrace × Large White) (LA), with no parental relation within the breeds Landrace and Large White from different companies The entire bodies of the animals were CT scanned with a General Electric HiSpeed Zx/I tomographer at different target body weights (TBW): 30, 70, 100 and 120 kg A total of 15 animals (five for each GEN) were scanned at 30, 70 and 100 kg and 45 animals (15 for each gen) were scanned at 120 kg The instrumental settings of the CT were: 140 kV, 145 mA, matrix dimensions of 512×512, axial, 7 mm thick (30 kg TBW) and 10 mm thick (70, 100 and 120 kg TBW) A custom-built cradle (PVC, Ø 030 m, length of 12 m for the 30 kg pigs and Ø 046 m, length of 18 m for the 70, 100 and 120 kg pigs) was used to hold the pigs during scanning Pigs had free access to water and were fastened for a minimum of 8 hr before weighing and scanning Pigs were sedated to minimize disturbances in the CT images due to movement.

Dissections

After scanning, animals were slaughtered The left half carcasses were kept refrigerated at 2°C for 24 to 48 hr until dissected Each carcass was prepared and cut following the European Union reference method [18]. Thereafter, four primal cuts plus tenderloin were weighed and manually dissected Lean, subcutaneous fat, including the skin, intermuscular fat, and bone of most of the cuts were separated with a knife by trained technicians, and the weights of all of these tissues were recorded to obtain the total amount of different fat, lean and bone in the primal cuts, considering all of the tenderloin weight as lean Only dissected carcasses were used for the development of prediction equations.

Computed tomography image analysis

The distribution of density volume based on the Hounsfield scale (in Hounsfield units [HU]) was obtained from CT images using the VisualPork software package, which was developed for that purpose by the University of Girona and the IRTA [19,20] The partial volumes estimated between −149 and −1, between 0 and 140, and between 141 and 1,400 HU were associated with fat, muscle and bone volume, respectively, and were used as independent variables in the regression analysis Volumes between −1,000 and −150 HU, which belong mainly to the less dense parts of the viscera, were considered only in calculating the total volume.

Moreover, CT phenotypic measurements (thickness, lengths and areas) were manually obtained in a reduced set of images as detailed in Font-i-Furnols et al. [11] and Carabus et al. [17].

Variables of interest to be predicted. Equations, using CT predictors, were derived to predict the total amounts of fat (subcutaneous and intermuscular fat of the four primal cuts) and lean (lean of the four primal cuts + tenderloin), as well as the shoulder weight, the loin and its subcutaneous fat weights, the belly weight and the ham and its fat, lean and bone weights.

Prediction equations

The prediction equations were carried out following two different approaches:

One approach included an individual equation for each GEN and was developed by Font-i-Furnols et al.. [11] Four types of regressions equations for the same parameter estimation were obtained: (1) linear regressions using CT volumes or CT ratios of volumes as predictors, (2) quadratic regressions using the previous CT volumes or CT ratios of volumes and their squared value as predictors, (3) allometric equations (y = axb linearized as logy = loga + b·logx), in which CT predictors were chosen as for the previous regression models and (4) linear regression using CT volumes, CT ratios of volumes and direct physical measurements recorded on loin and ham images as predictors Predictors were selected using the stepwise procedure of SAS (selected criteria: P < 015) and subjective criteria maximizing the coefficient of determination (R2) and minimizing root mean square error (RMSE) The criterion to choose the best prediction equation of this methodology was the lowest CVp (100 × (RMSE of prediction by cross-validation /mean)) The selected prediction equation was the one used in the present work.

Carabus et al. [17] presented the same equation for the three GEN to apply the equation on animals of different GEN and to a set of animals of different SEX (results not analysed in the present paper) For that, it was necessary to establish a criterion based on the accuracy and the decomposition of the mean square predicted error (MSPE) The accuracy and precision of each equation were evaluated by R2 and the Root Mean Square Error (RMSE) Moreover, to investigate the lack of fit of the equations for both datasets, without the distinction of GEN or SEX, the MSEP was decomposed and compared Ideally, most of the error should reside in the random component of MSEP [1] If the proportion of random error for any of the groups was lower than 070, another regression was performed using different predictors Furthermore, when necessary to standardize the variance, the dependent and independent variables were transformed into natural logarithms.

Statistical analysis

The criteria selected to compare both models for each parameter predicted were found by decomposing the error into (1) error due to central tendency (ECT), (2) error due to regression (ER) and (3) error due to disturbances or random effects (ED) [1,21] ECT indicates how the average of the predicted values deviates from the observed values average, ER measures the deviation of the regression coefficient of the slope from one and ED is the unexplained variance due to random effects or disturbances A good prediction is expected to have a high ED error, considering that ECT and ER errors can be eliminated by linear corrections of the predictions [22] The decomposition was carried out as follows:

MSE= ECT + ET + ED

image

image

image

where imageis the mean of the predicted values,image the mean of the observed values, Sp the standard deviation of the predicted values, So the standard deviation of the observed values, and r the coefficient of correlation between the predicted and observed values ECT, ER and ED are expressed in proportion, thus their sum is one.

The decomposition of the prediction errors obtained using the equations developed by Font-i-Furnols et al. [11] and Carabus et al. [17] were analysed by first considering the prediction and observed values of all of the GEN at the same time globally and then considering them by each GEN individually The bias between the dissection and the predictions of Font-i-Furnols et al. [11] and Carabus et al. [17] was analysed, and the standard deviation was obtained as a measure of imprecision, also considering both all three GEN together and each GEN separately Moreover, the coefficient of model determination (CD), which is the ratio of the total variance of the observed data to the square of the difference between the predicted and the mean of the observed data, was calculated for both predictions using the data of the three GEN together and for each GEN separately It is calculated as follows [1]:

image

where imageis the observed ith value, imageis the mean of the observed values and image is the predicted ith value The CD statistic represents the proportion of the total variance of the observed values explained by the predicted values [23].

Results and Discussion

The decomposition of the error in both methodologies, when predictions of all of the animals (three GEN) were considered together, is presented in Table 1 Both methodologies showed high ED (>95% in all of the cases), indicating that the prediction is correct all of the estimated parameters presented a similar MSPE between both equations and also a high proportion of random error; however, the global equations developed by Carabus et al. [17] did present better results for the ED, exhibiting values higher than >099 in 10 of the 11 predicted parameters only the estimation of the weight of the four main cuts was lower.

Estimated parameter (kg)
Individual equations approach Global equation approach
Font-i-Furnolset al [11] Carabuset al [17]
MSPE ECT ER ED MSPE ECT ER ED
Leana 382 0 1 999 410 0 1 999
Fatb 148 2 17 981 156 0 1 999
Four cutsc 1077 0 1 999 1204 24 18 958
Ham 138 0 3 997 147 0 0 1000
Ham fat 27 7 29 964 24 0 0 1000
Ham lean 95 18 13 969 110 0 0 1000
Ham bone 1 7 12 981 5 4 5 999
Loin 83 0 2 998 89 0 0 1000
Loin fat 31 12 11 978 28 0 1 999
Shoulder 43 0 1 999 46 0 0 1000
Belly 32 1 12 987 34 0 3 997

Table 1: Decomposition of the mean square prediction error (MSPE) considering all of the genotypes together in error due to central tendency (ECT), error due to regression (ER) and error due to disturbances (ED) depending on the prediction approach.

This high ED is most likely because this was the criterion for selecting the prediction equation in that paper. This means that these equations are useful for the entire population of DU, LA and PI studied in Carabus et al. [17] and Font-i-Furnols et al. [11] Moreover, the genotypes used are the typical ones used for commercial conditions in Spain, thus these equations could also be useful for a large number of animals the coefficient of model determination and the standard deviation of the bias for both approaches when all of the GEN were considered together are presented in Table 2 the highest imprecision (standard deviation of the bias) was for the weight of the four main cuts in both approaches the CD values close to one indicate a good prediction, while CD values lower than 1 indicate over prediction of the model and CD values higher than 1 indicate under prediction of the model.

Estimated parameter (kg) Individual equations approach Global equation approach
Font-i-Furnolset al [11] Carabuset al [17]
CD SDBias CD SDBias
Leana 100 37 101 48
Fatb 99 25 101 29
Four cutsc 101 66 98 62
Ham 100 37 101 38
Ham fat 97 15 102 16
Ham lean 105 31 102 33
Ham bone 105 3 101 2
Loin 102 27 101 25
Loin fat 99 19 103 20
Shoulder 102 27 101 19
Belly 104 26 102 26

Table 2: Coefficient of model determination (CD) and standard deviation of the bias (SDBias) of the prediction approaches considering all of the genotypes together.

The individual equation approach [11] presents almost all of the CD values as close to 1 Only the ham lean and bone were slightly under predicted (5%), and, for the rest of the parameters, the over- or under prediction was less than 5% Regarding the global equation approach [17], it generally yields CD values close to one and always with a variation lower than 5% This can be related with the fact that this approach was carried out considering all of the GEN together

The comparison of the errors using individual equations within GEN is presented in Table 3. In general, both methodologies presented high ED, which means that the prediction is correct, and, as expected, equations from Font-i-Furnols et al.[11] developed individually for each specific GEN showed higher levels of accuracy when comparing both predictions within GEN Table 3 shows the estimated parameters and the distribution of the predicted errors by each approach within GEN The individual equations approach of Font-i-Furnols et al. [11], which developed one individual equation for each GEN, generally showed better results (lower MSPE and higher ED) than the global equation approach of Carabus et al. [17], which developed a global equation for all of the GEN together and for pigs of a different genotype and different sexes.

Estimated parameter (kg)   Individual equations approach Global equation approach
  Font-i-Furnolset al [11] Carabuset al [17]
GEN MSPE ECT ER ED MSPE ECT ER ED
Leana DU 125 18 1 981 173 296 132 572
  LA 181 20 9 971 224 87 2 911
  PI 132 2 4 994 313 428 34 538
Fatb DU 78 24 28 948 89 26 48 926
  LA 51 4 12 984 82 8 27 966
  PI 71 10 46 945 87 64 11 925
Four cutsc DU 122 5 3 992 52 9 20 972
  LA 886 2 4 993 111 4 9 987
  PI 366 13 11 975 1099 237 94 669
Ham DU 64 18 2 979 180 402 195 403
  LA 61 9 12 979 114 0 140 859
  PI 75 48 36 916 174 423 16 561
Ham fat DU 14 0 1 999 21 53 29 918
  LA 11 3 5 995 27 37 78 884
  PI 42 46 159 795 28 1 38 962
Ham lean DU 46 7 10 983 60 14 187 799
  LA 69 6 3 994 88 125 11 864
  PI 180 41 22 937 190 94 6 900
Ham bone DU 0 6 3 991 4 58 3 940
  LA 1 16 36 948 1 6 46 948
  PI 1 3 6 991 1 103 23 874
Loin DU 101 2 1 999 88 11 64 925
  LA 77 2 65 993 63 102 3 895
  PI 56 1 1 998 45 56 86 858
Loin fat DU 25 2 2 998 56 2 55 943
  LA 23 0 12 988 20 29 22 949
  PI 69 37 133 830 54 23 140 837
Shoulder DU 35 4 2 996 24 65 4 931
  LA 152 0 0 1000 45 54 2 946
  PI 44 3 2 999 48 2 3 995
Belly DU 41 2 1 1000 44 310-5 3 997
  LA 97 3 6 991 78 11 1 989
  PI 76 0 0 1000 88 9 1 990

Table 3: Decomposition of the mean square prediction error (MSPE) considering the genotypes (DU = Duroc x (Landrace × Large White); LA = Landrace × Large White; PI = PI × (Landrace × Large White)) separately and together in error due to central tendency (ECT), error due to regression (ER) and error due to disturbances (ED) depending on the prediction approach.

This makes sense because different equations for each GEN would allow a better adjustment within genotype than more general equations However, as in the prediction of the fat, good results are obtained from both predictions It is important to notice that the number and type of animals used to obtain these predictions were not the same in both cases Individual equations within GEN were obtained from a reduced number of animals, which were the animals of each GEN that were CT scanned, slaughtered and dissected, while global equations had more than three times as many reference samples because there were the animals from the three GEN together plus some additional animals from another GEN and different sexes Nevertheless, although the global approach [17] yielded predictions more useful for a larger population than the individual ones [11], sometimes they are also less accurate.

One of the worst results from the global equation approach was found in the prediction of the total lean When decomposing the error of the estimated lean for the individual equations approach within GEN, it can be observed that the MSPE is lower than 0200 kg and that the ED is higher than 95%, but the same decomposition of the error by GEN for the global equation approach within GEN does show different results The error for DU and PI presented a low ED and a high ECT Figures 1 and 2 present the visual decomposition of the error for the individual and global equations within GEN, respectively Figure 1 shows no difference between the lines and no tendency in the biases Figure 2 shows the higher ECT in the DU and PI lines In this case, for PI pigs, there is an underestimation at all levels of the ham’s lean, although it is higher at higher levels.

tomography-simulation-estimation

Figure 1: Residuals of the estimation of the lean obtained by (a) the individual equations approach [11].

tomography-simulation-Residuals

Figure 2: Residuals of the estimation of the lean obtained by the global equation approach [17].

In DU pigs, there is an overestimation at higher lean content, also indicating the high ER In the case of LA, the decomposition shows high ED and a slightly high ECT, which can be seen in the plot, because the regression line is slightly superior to the zero line (slight overestimation) A similar situation occurred with the weight of the ham It presented a very low MSPE for the individual equations approach and a good distribution of the errors (Table 3, Figures 3 and 4) However, the decomposition of the errors for the global equation approach was worse, mainly for the DU and PI lines (Table 3, Figures 3 and 4) They presented low values for ED (<060), high values for ECT (>040) and DU and medium values for ER (>019) LA also presented an ER of 014 Thus, in this case, for PI pigs, there is an underestimation at all levels of the ham’s lean (high ECT) In DU pigs, there is an overestimation only at higher lean content, indicating the high ECT and also the high ER The high ER obtained for LA pigs can also be seen in the plot because there is an overestimation at lower lean content and an underestimation at higher lean content In this case, the ECT is low because the positive and negative biases are compensated.

Estimated parameter (kg)   Individual equations approach Global equation approach
  Font-i-Furnolset al[11] Carabuset al [17]
GEN CD SDBias CD SDBias
Leana DU 100 35 97 35
  LA 100 42 100 45
  PI 101 36 104 42
Fatb DU 98 28 97 29
  LA 99 23 103 28
  PI 98 26 102 29
Four cutsc DU 100 35 99 23
  LA 102 94 101 33
  PI 99 60 95 91
Ham DU 101 26 91 32
  LA 102 41 108 32
  PI 97 43 105 31
Ham fat DU 102 12 97 14
  LA 100 11 111 16
  PI 89 20 96 17
Ham lean DU 103 21 92 24
  LA 101 26 106 28
  PI 109 42 107 42
Ham bone DU 102 2 101 2
  LA 107 3 105 2
  PI 105 4 98 2
Loin DU 102 32 106 29
  LA 103 28 100 24
  PI 101 24 96 21
Loin fat DU 102 16 114 24
  LA 104 15 105 14
  PI 89 26 90 23
Shoulder DU 101 19 100 15
  LA 104 39 101 21
  PI 101 21 102 22
Belly DU 102 20 103 21
  LA 106 31 102 28
  PI 103 28 102 30

Table 4: Coefficient of model determination (CD) and standard deviation of the bias (SDBias) of the prediction approaches considering the genotypes (DU = Duroc × (Landrace × Large White); LA = Landrace × Large White; PI = Pietrain × (Landrace × Large White)) individually.

tomography-simulation-equations

Figure 3: Residuals of the estimation of the lean of the ham obtained by the individual equations approach [11].

tomography-simulation-approach

Figure 4: Residuals of the estimation of the lean of the ham obtained by the global equation approach [17].

The coefficient of model determination and the standard deviation of the bias for both approaches when the GEN were considered separately are presented in Table 4 Although the lean of the four main cuts’ estimation had lower ED values in the global equation approach than the individual equations approach, no differences in CD and in the standard deviation of the bias can be seen between the two approaches, with CD being lower than 5% for all of the GEN Ham fat in the individual equations approaches a CD value of 089 for PI GEN, indicating an over prediction, while, in the global equation approach, the CD value of LA was 111, indicating an under prediction In both cases, the error of disturbances was lower than in the other GEN Loin fat estimation also presented some different CD values, from 1: 089 for PI in the individual equations approach and 114 and 090 for DU and PI, respectively, in the global equation approach For PI in both approaches, the ED was lower than 85%.

Thus, except for certain parameters and GEN mentioned above, the CD generally reflects a small shift in the predicted and observed values, indicating the good model predictions.

Conclusion

Linear, nonlinear and volume measurements obtained from CT images at specific anatomical positions in live pigs are good predictors of carcass characteristics There are different methodologies to obtain a prediction equation depending on the purpose, including prediction models that are useful only for a specific type of animal (eg, the same genotype) or generalized for several types of animals (eg, different genotypes and sexes) The comparison performed in the present work shows that both approaches for predicting carcass and cut compositions from CT images of growing live pigs are properly developed and useful Errors are similar for the majority of the parameters, although the predictions are slightly better for some parameters if individual specific equations were used However, the global equation permits generalization of the predictions to a larger number of animals; thus, it is preferable to use it when the population is mixed or when the parameter estimated does not need a high level of accuracy for a specific line When this is needed, such as in the case of breeding companies, it is preferable to use individual equations specifically developed for that GEN Nevertheless, when choosing individual equations, it is important to increase the size of the sample to have greater confidence in the results.

Acknowledgements

The present study was supported by the Instituto Nacional de Investigaciones Agrarias-INIA (Evaluación in vivo del crecimiento alométrico de los tejidos muscular y adiposo de los cerdos segun la genética y el sexo mediante tomografía computerizada RTA2010-00014-00-00) INIA is also thanked for the scholarship provided to Anna Carabus The authors wish to thank Carles Francàs, Albert Rossell, Agustí Quintana, Albert Brun, Tania Avila and Goretti Gordo for their invaluable technical assistance.

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