Abstract
The body surface area (BSA) of an organism is one of the important parameters for evaluating physiological functions. In drug development, normalization by BSA is an appropriate method for extrapolating doses between species. The BSA of animals has generally been estimated by multiplying the k value by 2/3 of the power of the body weight (BW) (Meeh’s formula). In mathematics, if it is assumed that the density and body shape of the animals are essentially constant, the BSA is proportional to BW2/3. In this study, we measured the BSA and volume (V) of 72 laboratory rabbits (48 males and 24 females of New Zealand White rabbits [NZW]), using a computed tomography scanner. After BSA and V determination, the k value, density, and sphericity were calculated. We analyzed variations in the k value, density, and body shape of laboratory rabbits. The mean k value of the 72 NZW was 11.0. We advocate using Meeh’s formula, as follows, for estimating BSA of laboratory rabbits (NZW): 100 × BSA [m2] = 11.0 × BW [kg]2/3.
Keywords: body surface area, computed tomography, CT image, CT scanner, rabbit
Introduction
The body surface area (BSA) of an organism is one of the parameters used for evaluating physiological functions, such as an essential requirement in calculating the cardiac index [5], assessing the basal metabolic rate [3, 8], and determining the burn surface area as a percentage of the total. BSA has also been used as a criterion for drug dosage determination since the 1950s [13]. In drug development, the no observed adverse effect levels in laboratory animal species have been converted to human equivalent doses using scaling factors. Normalization by BSA (i.e., conversion of a dosage from mg/kg to mg/m2) is an appropriate method for extrapolating doses between species. The Food and Drug Administration Center for Drug Evaluation and Research guidance recommends the use of BSA to estimate starting doses in the initial clinical trials for therapeutics in volunteer subjects [2]. In addition, the procedures for assessing dermal toxicity are described in the guidelines issued by the Organization for Economic Cooperation and Development and these guidelines recommend that the test substance be applied to not less than 10% of the total BSA [10,11,12]. Thus, accurately determining the BSA of laboratory animals is extremely important.
The BSA of animals has generally been estimated by multiplying a constant by 2/3 of the power of the measured body weight (BW) [9]. Using BSA values, which have been determined by classic methods such as skinning, triangulation, surface integrator, paper cover, the mold method, and the perimeter method, the k values (100 × BSA [m2] = k × BW [kg]2/3, i.e., Meeh’s formula) for various species have been published. The k value for rabbits was reported to be 5.7–10.0 by Spector [14], and 12.0–12.9 by Fougère and Wynn [4]. Additionally, Bai et al. reported the k value of Japanese White rabbits (JW) to be 11.30–11.35 [1]. Owing to the complex structural features of animal bodies, it is difficult to accurately measure the BSA of animals. Despite obvious limitations in their accuracy and reproducibility, these classic methods are still currently used to determine the BSA values.
Computed tomography (CT) scanners can generate detailed 3-dimensional (3D) images of an object, and the analysis of these CT images is expected to determine BSA more precisely than the classic measurement techniques. In previous reports [6, 7], we measured the BSA of laboratory miniature pigs using a CT scanner and 3D analysis software. Applying our measurement results, we calculated the k value for peripubertal- or mature-miniature pigs to be 7.98 [6] and the k value for juvenile miniature pigs to be 8.58 [7].
For rabbits, Zehnder et al. measured the BSA of 12 rabbits (multiple breeds of rabbits including New Zealand White rabbits [NZW]) using a CT scanner and analyzed the CT images using their own procedure. They reported the k value for rabbits to be 9.9 [15]. In the present study, we measured the BSA of 72 laboratory rabbits (NZW) using a CT scanner and employing our measurement methods to verify the k value of laboratory rabbits.
In mathematics, if it is assumed that the density and body shape of the animals are essentially constant, the BSA is proportional to BW2/3. In other words, density and sphericity (i.e., index of the body shape) are inversely correlated with the k value. Therefore, we determined the volume (V) of the rabbits from the CT images and calculated density and sphericity. We analyzed variations in the k value, density, and body shape of laboratory rabbits.
Materials and Methods
Animals
NZW (Kbl: NZW) were obtained from Kitayama LABES Co., Ltd., Nagano, Japan. The BSA and V were measured for 72 rabbits (42 males at 11–41 weeks of age, 6 males at 260 weeks of age, and 24 females at 15–36 weeks of age) that had been used in other non-clinical studies and euthanized by anesthesia with sodium pentobarbital according to the protocols of the previous studies. No critical abnormalities in clinical signs or BW changes were noted in these rabbits during the time that they were alive. All studies were conducted in compliance with the Guidelines for Management and Welfare of Experimental Animals of Nihon Bioresearch Inc.
Experimental procedures
The BSA measuring methods followed those described previously [6], except for the slice thickness and the reconstruction interval (previously, the slice thickness and the reconstruction interval were 5 mm and 2.5 mm, but were 3 mm and 1.5 mm, respectively, in the present study); these were modified based on body size. The body of each rabbit was set in the prone position for whole-body CT scanning on the day of euthanasia. Images were obtained using a Multislice CT scanner (Alexion TSX 033A, Toshiba Medical Systems Co., Ltd., Tochigi, Japan, tube voltage: 120 kV, tube current: 150 mA, helical pitch: 5.5). The BSA of each animal was determined from the 3D CT images (Fig. 1) using high-speed 3D analysis software (TRI-3D/VOL, Ratoc System Engineering Co., Ltd., Tokyo, Japan). Analysis of the 3D CT images was based on the computer graphics algorithm known as Marching Cubes and Discriminant Analysis Method. As shown in Fig. 1, the fur of the rabbits was not reflected the analyzed 3D CT images, because the fur including abundant air has a very low CT value. After the BSA had been determined, the k value was calculated.
Fig.1.
CT images of NZW. (A) NZW in dorsal aspect. (B) In lateral side.
The V of each animal was determined from axial multi-planar reconstruction (MPR) of CT images. The total area of each section of the CT images was calculated using image processing software (Win ROOF, Mitani Co., Fukui, Japan) and multiplying the value by 1.5 mm (the reconstruction interval). After V had been determined, the density (= BW [kg]/V [l]) and the sphericity (= π1/3[6V]2/3/100 BSA) were calculated. The significant figure was set to three digits.
Statistical methods
The mean, SD, coefficient of variation (CV), the median, the correlation coefficient between the BW (r), and the probability of r (P) for the k value, the density, and the sphericity were calculated using statistical software (Pharmaco Basic, Scientist Press Co., Ltd., Tokyo, Japan).
Accuracy confirmation
To confirm the accuracy of the method used in this study, the surface areas and V of 2 acrylic cuboids (small cuboid: d=15 cm, w=15 cm, and h=15.5 cm; calculated surface area=0.138 m2, calculated V=3.49 l, and large cuboid: d=27 cm, w=27 cm, and h=30 cm; calculated surface area=0.470 m2, calculated V=21.9 l) were measured. For the small cuboid, a diagonal of the bottom of the cuboid form was set parallel to the moving direction of the bed of the CT scanner. For the large cuboid, 2 sides of the bottom were set parallel to the moving direction (Fig. 2). Measurements were repeated 5 times employing the same method as that used for the rabbits.
Fig.2.
Direction of the CT scanning of an acrylic cuboid. (A) For the small cuboid, a diagonal of the bottom was set parallel to a moving direction. (B) For the large cuboid, 2 sides of the bottom were set parallel to a moving direction. Square; bottom of the cuboid, arrow; moving direction of the bed of the CT scanner.
Results
Male (11–41 weeks of age)
As shown in Table 1, the mean age of the 42 male rabbits was 16.6 weeks (median: 12.0 weeks), and their BWs ranged from 2.22 to 3.69 kg (mean: 2.79 kg, median: 2.63 kg). The BSA and the V values ranged from 0.185 to 0.269 m2 and from 2.04 to 3.53 l, respectively.
Table 1. Age, BW, BSA, V, k value, density, and sphericity in male NZW (11–41 weeks of age).
| Age (week) | BW (kg) | BSA (m2) | V (l) | k value | density (kg/l) | sphericity | |
|---|---|---|---|---|---|---|---|
| 11 | 2.22 | 0.191 | 2.04 | 11.2 | 1.09 | 0.407 | |
| 11 | 2.26 | 0.187 | 2.04 | 10.9 | 1.11 | 0.416 | |
| 12 | 2.29 | 0.195 | 2.37 | 11.2 | 0.97 | 0.441 | |
| 11 | 2.33 | 0.190 | 2.11 | 10.8 | 1.10 | 0.419 | |
| 11 | 2.34 | 0.190 | 2.18 | 10.8 | 1.07 | 0.428 | |
| 12 | 2.34 | 0.198 | 2.27 | 11.2 | 1.03 | 0.422 | |
| 11 | 2.35 | 0.185 | 2.18 | 10.5 | 1.08 | 0.439 | |
| 11 | 2.38 | 0.202 | 2.17 | 11.3 | 1.10 | 0.401 | |
| 12 | 2.43 | 0.209 | 2.45 | 11.6 | 0.99 | 0.421 | |
| 12 | 2.48 | 0.209 | 2.45 | 11.4 | 1.01 | 0.421 | |
| 12 | 2.50 | 0.209 | 2.50 | 11.3 | 1.00 | 0.426 | |
| 11 | 2.51 | 0.206 | 2.27 | 11.2 | 1.11 | 0.405 | |
| 11 | 2.51 | 0.206 | 2.28 | 11.2 | 1.10 | 0.407 | |
| 11 | 2.52 | 0.205 | 2.35 | 11.1 | 1.07 | 0.417 | |
| 12 | 2.53 | 0.209 | 2.47 | 11.3 | 1.02 | 0.423 | |
| 12 | 2.57 | 0.211 | 2.48 | 11.2 | 1.04 | 0.420 | |
| 12 | 2.57 | 0.210 | 2.60 | 11.2 | 0.99 | 0.435 | |
| 12 | 2.58 | 0.212 | 2.58 | 11.3 | 1.00 | 0.429 | |
| 12 | 2.59 | 0.212 | 2.57 | 11.2 | 1.01 | 0.428 | |
| 12 | 2.60 | 0.206 | 2.46 | 10.9 | 1.06 | 0.428 | |
| 12 | 2.61 | 0.213 | 2.51 | 11.2 | 1.04 | 0.419 | |
| 12 | 2.64 | 0.212 | 2.64 | 11.1 | 1.00 | 0.436 | |
| 16 | 2.67 | 0.215 | 2.53 | 11.2 | 1.06 | 0.418 | |
| 12 | 2.68 | 0.218 | 2.68 | 11.3 | 1.00 | 0.428 | |
| 18 | 2.78 | 0.220 | 2.64 | 11.1 | 1.05 | 0.420 | |
| 24 | 2.82 | 0.232 | 2.66 | 11.6 | 1.06 | 0.400 | |
| 18 | 2.89 | 0.224 | 2.75 | 11.0 | 1.05 | 0.424 | |
| 18 | 2.92 | 0.229 | 2.77 | 11.2 | 1.05 | 0.417 | |
| 18 | 2.95 | 0.232 | 2.77 | 11.3 | 1.06 | 0.411 | |
| 18 | 3.04 | 0.229 | 2.83 | 10.9 | 1.07 | 0.423 | |
| 24 | 3.06 | 0.236 | 2.94 | 11.2 | 1.04 | 0.421 | |
| 18 | 3.06 | 0.242 | 2.98 | 11.5 | 1.03 | 0.414 | |
| 24 | 3.19 | 0.243 | 3.06 | 11.2 | 1.04 | 0.419 | |
| 16 | 3.20 | 0.233 | 2.79 | 10.7 | 1.15 | 0.411 | |
| 24 | 3.23 | 0.253 | 3.03 | 11.6 | 1.07 | 0.400 | |
| 16 | 3.27 | 0.230 | 2.83 | 10.4 | 1.16 | 0.421 | |
| 24 | 3.33 | 0.248 | 3.18 | 11.1 | 1.05 | 0.422 | |
| 24 | 3.45 | 0.254 | 3.25 | 11.1 | 1.06 | 0.418 | |
| 24 | 3.49 | 0.247 | 3.21 | 10.7 | 1.09 | 0.426 | |
| 24 | 3.64 | 0.257 | 3.47 | 10.9 | 1.05 | 0.431 | |
| 41 | 3.66 | 0.269 | 3.48 | 11.3 | 1.05 | 0.413 | |
| 41 | 3.69 | 0.256 | 3.53 | 10.7 | 1.05 | 0.438 | |
| Mean | 16.6 | 2.79 | 0.220 | 2.65 | 11.1 | 1.05 | 0.421 |
| SD | 7.4 | 0.42 | 0.022 | 0.39 | 0.3 | 0.04 | 0.010 |
| CV | 2.46% | 3.97% | 2.40% | ||||
| Median | 12.0 | 2.63 | 0.213 | 2.59 | 11.2 | 1.05 | 0.421 |
The mean ± SD, CV, the median, r, and P for the k value were calculated to be 11.1 ± 0.3, 2.46%, 11.2, −0.189, and 0.231, respectively; those for density were 1.05 ± 0.04, 3.97%, 1.05, 0.175, and 0.266; and those for sphericity were 0.421 ± 0.010, 2.40%, 0.421, −0.017, and 0.917 (Fig. 3).
Fig.3.
Scatter diagrams representing the k value, the density, or the sphericity on the vertical axis and the BW on the horizontal axis in the 42 male (11–41 weeks of age) or the 24 female (15–36 weeks of age) NZW.
The CV for the k value, density, and sphericity each were small (<4%), and P>0.05 for all of these values. These results suggest that these values could be essentially constant in male NZW at 11–41 weeks of age.
Male (260 weeks of age)
As shown in Table 2, the BWs of the 6 male rabbits ranged from 3.89 to 4.27 kg (mean: 4.05 kg, median: 4.04 kg). The BSA and the V values ranged from 0.271 to 0.287 m2 and from 3.59 to 4.10 l, respectively.
Table 2. BW, BSA, V, k value, density, and sphericity in male NZW (260 weeks of age).
| BW (kg) | BSA (m2) | V (l) | k value | density (kg/l) | sphericity | |
|---|---|---|---|---|---|---|
| 3.89 | 0.272 | 3.76 | 11.0 | 1.03 | 0.430 | |
| 3.89 | 0.271 | 3.59 | 11.0 | 1.08 | 0.418 | |
| 4.04 | 0.276 | 3.86 | 10.9 | 1.05 | 0.431 | |
| 4.04 | 0.276 | 3.78 | 10.9 | 1.07 | 0.425 | |
| 4.14 | 0.279 | 3.99 | 10.8 | 1.04 | 0.436 | |
| 4.27 | 0.287 | 4.10 | 10.9 | 1.04 | 0.432 | |
| Mean | 4.05 | 0.277 | 3.85 | 10.9 | 1.05 | 0.429 |
| SD | 0.15 | 0.006 | 0.18 | 0.1 | 0.02 | 0.006 |
| Median | 4.04 | 0.276 | 3.82 | 10.9 | 1.05 | 0.431 |
The calculated k value, density, and sphericity ranged from 10.8 to 11.0 (mean ± SD: 10.9 ± 0.1, median: 10.9), 1.03 to 1.08 (mean ± SD: 1.05 ± 0.02, median: 1.05), and 0.418 to 0.436 (mean ± SD: 0.429 ± 0.006, median: 0.431), respectively.
All k values, densities, and sphericities were within the range of these values and the mean ± 2 SD at 11–41 weeks of age. Therefore, our results suggest that these values are essentially equal in male NZW at 260 and 11–41 weeks of age. The mean ± SD of the k value of the 48 males (42 males at 11–41 weeks of age and 6 males at 260 weeks of age) was 11.1 ± 0.3.
Female (15–36 weeks of age)
As shown in Table 3, the mean age of the 24 female rabbits was 21.8 weeks (median: 19.0 weeks), and their BWs ranged from 2.71 to 3.99 kg (mean: 3.25 kg, median: 3.23 kg). The BSA and the V values ranged from 0.213 to 0.268 m2 and from 2.70 to 3.74 l, respectively.
Table 3. Age, BW, BSA, V, k value, density, and sphericity in female NZW.
| Age (week) | BW (kg) | BSA (m2) | V (l) | k value | density (kg/l) | sphericity | |
|---|---|---|---|---|---|---|---|
| 15 | 2.71 | 0.213 | 2.70 | 11.0 | 1.00 | 0.440 | |
| 15 | 2.93 | 0.225 | 2.87 | 11.0 | 1.02 | 0.434 | |
| 15 | 2.94 | 0.221 | 2.92 | 10.8 | 1.01 | 0.447 | |
| 15 | 3.00 | 0.233 | 3.02 | 11.2 | 0.99 | 0.434 | |
| 19 | 3.00 | 0.221 | 2.87 | 10.6 | 1.05 | 0.442 | |
| 23 | 3.02 | 0.228 | 2.87 | 10.9 | 1.05 | 0.428 | |
| 15 | 3.05 | 0.224 | 2.89 | 10.7 | 1.06 | 0.438 | |
| 19 | 3.05 | 0.232 | 3.02 | 11.0 | 1.01 | 0.436 | |
| 15 | 3.06 | 0.237 | 3.06 | 11.2 | 1.00 | 0.430 | |
| 19 | 3.11 | 0.233 | 2.96 | 10.9 | 1.05 | 0.428 | |
| 19 | 3.14 | 0.241 | 2.82 | 11.2 | 1.11 | 0.401 | |
| 15 | 3.21 | 0.239 | 3.16 | 11.0 | 1.02 | 0.436 | |
| 23 | 3.24 | 0.238 | 3.11 | 10.9 | 1.04 | 0.433 | |
| 23 | 3.25 | 0.246 | 3.07 | 11.2 | 1.06 | 0.415 | |
| 23 | 3.26 | 0.238 | 3.12 | 10.8 | 1.04 | 0.434 | |
| 36 | 3.33 | 0.244 | 3.11 | 10.9 | 1.07 | 0.422 | |
| 19 | 3.35 | 0.248 | 3.18 | 11.1 | 1.05 | 0.422 | |
| 23 | 3.43 | 0.245 | 3.31 | 10.8 | 1.04 | 0.438 | |
| 19 | 3.45 | 0.245 | 3.28 | 10.7 | 1.05 | 0.436 | |
| 23 | 3.50 | 0.246 | 3.39 | 10.7 | 1.03 | 0.444 | |
| 23 | 3.51 | 0.260 | 3.37 | 11.3 | 1.04 | 0.418 | |
| 36 | 3.70 | 0.268 | 3.55 | 11.2 | 1.04 | 0.420 | |
| 36 | 3.82 | 0.263 | 3.74 | 10.8 | 1.02 | 0.443 | |
| 36 | 3.99 | 0.265 | 3.60 | 10.5 | 1.11 | 0.429 | |
| Mean | 21.8 | 3.25 | 0.240 | 3.12 | 10.9 | 1.04 | 0.431 |
| SD | 7.2 | 0.30 | 0.014 | 0.26 | 0.2 | 0.03 | 0.011 |
| CV | 1.98% | 2.89% | 2.47% | ||||
| Median | 19.0 | 3.23 | 0.239 | 3.09 | 10.9 | 1.04 | 0.434 |
The mean ± SD, CV, the median, r, and P for the k value were calculated to be 10.9 ± 0.2, 1.98%, 10.9, −0.222, and 0.298, respectively; those for density were 1.04 ± 0.03, 2.89%, 1.04, 0.428, and 0.037; and those for sphericity were 0.431 ± 0.011, 2.47%, 0.434, −0.153, and 0.475 (Fig. 3).
The r for density was 0.428 and P<0.05. Hence, density showed a positive correlation with BW; however, the CV for density was slight (2.89%). Furthermore, the value of r for sphericity was −0.153. Thereby, the CV for the k value was small (1.98%), and the P for the k value was higher than 0.05. It follows that the k value hardly correlated with BW. We consider that the k value is essentially constant in female NZW at 15–36 weeks of age.
Surface area and V of the cuboid
The mean ± SD and CV of surface area of the small cuboid were 0.138 ± 0.001 m2 and 0.08%, respectively. The average value of the measured surface area was entirely in agreement with the calculated value (0.138 m2). The mean ± SD and CV of surface area of the large cuboid were 0.476 ± 0.012 m2 and 0.26%, respectively. The average value was 101% of the calculated value (0.470 m2).
The mean ± SD and CV of V of the small cuboid were 3.48 ± 0.04 l and 1.29%, respectively. The average value of the measured V was 99.7% of the calculated value (3.49 l). The mean ± SD and CV of V of the large cuboid were 21.9 ± 0.00 l and 0.00%, respectively. The average value of the measured V was entirely in agreement with the calculated value (21.9 l).
Discussion
Formula for BSA of laboratory rabbits (NZW)
Applying the results of the present measurement, the mean k value of the 48 males was 11.1, and the mean k value of the 24 females was 10.9. The difference between the mean k values of the males and the females was very slight. We propose the following formula for estimating BSA of laboratory rabbits (NZW): 100 × BSA [m2] = 11.0 × BW [kg]2/3 on the basis of the mean k value of the 72 NZW.
Comparison with the previous k value
Based on the results of this study, the k value of NZW was determined to be 11.0. In comparison with the previous data, the k value in this study was larger than the k values (5.7–10.0) for rabbits determined by use of skinning and triangulation reported by Spector [14], and smaller than the k value (12.0–12.9) reported by Fougère and Wynn (The method of BSA determination was not shown.) [4]. Additionally, the present k value was slightly smaller than the k values (11.30–11.35) of JW determined by use of paper cover and skinning reported by Bai et al. [1]. It have been pointed out that the accuracy and reproducibility of these classic methods have limitations [6].
The present k value was larger than the k value (9.9) of rabbits (NZW, Mini-lop, Netherland Dwarf, Dutch Belted, Chinchilla, Flemish Giant, and breed unknown) analyzed the CT images using their own procedure reported by Zehnder [15]. The surface area of the small cuboid was computed to be 0.111 ± 0.001 m2 (mean ± SD) from the MPR of CT images by Zehnder’s procedure (i.e., summing the lengths of contour for each slice and multiplying this total length by the reconstruction interval. Additionally, the areas of the end slices were added to this value [15]). The average value computed by Zehnder’s procedure was 80.4% of the calculated value (0.138 m2). In mathematics, the lengths of 2 vertical sides of the contour for each slice (2 × h of cuboid = 2 × 15.5 cm = 31 cm) should be multiplied by 2.12 mm (1.5 mm × √2). The total multiplied length is the 2 sides of the bottom of the cuboid form (15 + 15 = 30 cm) to transform from the lengths of the contour into surface area (31 cm × 30 cm + 2 × 225 cm2 [the areas of the top and bottom square] = 0.138 m2); however, Zehnder’s procedure multiplied by 1.5 mm and total multiplied length is the diagonal of the bottom (21.2 cm: total of the reconstruction interval) (Fig. 2A). Thereby, the surface area of the small cuboid computed by Zehnder’s procedure was small (31 cm × 21.2 cm + 2 × 225 cm2 = 0.111 m2). To be more precise, the BSA and the k value computed by Zehnder’s procedure may be smaller than the actual value.
Although the difference between the present k value of NZW and the previous data for rabbits might be attributable to the differences in the density and body shape of the measured rabbits, the difference in the measurement method should also be considered. Since accuracy and reproducibility were confirmed by measuring the surface area and the V of the acrylic cuboids, we concluded the measurement method employed in this study was reliable. Furthermore, we expect that the k value for other laboratory animals will be verified by this measuring method.
Conflict of Interest
The authors declare that there is no conflict of interest.
Acknowledgments
The authors wish to thank all members of Nihon Bioresearch Inc., for their help and support during this study.
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