Estimating body volumes and surface areas of animals from cross-sections.

Background: Body mass and surface area are among the most important biological properties, but such information is lacking for some extant organisms and most extinct species. Numerous methods have been developed for body size estimation of animals for this reason. There are two main categories of mass-estimating approaches: extant-scaling approaches and volumetric-density approaches. Extant-scaling approaches determine the relationships between linear skeletal measurements and body mass using regression equations. Volumetric-density approaches, on the other hand, are all based on models. The models are of various types, including physical models, 2D images, and 3D virtual reconstructions. Once the models are constructed, their volumes are acquired using Archimedes' Principle, math formulae, or 3D software. Then densities are assigned to convert volumes to masses. The acquisition of surface area is similar to volume estimation by changing math formulae or software commands. This article presents a new 2D volumetric-density approach called the cross-sectional method (CSM). Methods: The CSM integrates biological cross-sections to estimate volume and surface area accurately. It requires a side view or dorsal/ventral view image, a series of cross-sectional silhouettes and some measurements to perform the calculation. To evaluate the performance of the CSM, two other 2D volumetric-density approaches (Graphic Double Integration (GDI) and Paleomass) are compared with it. Results: The CSM produces very accurate results, with average error rates around 0.20% in volume and 1.21% in area respectively. It has higher accuracy than GDI or Paleomass in estimating the volumes and areas of irregular-shaped biological structures. Discussion: Most previous 2D volumetric-density approaches assume an elliptical or superelliptical approximation of animal cross-sections. Such an approximation does not always have good performance. The CSM processes the true profiles directly rather than approximating and can deal with any shape. It can process objects that have gradually changing cross-sections. This study also suggests that more attention should be paid to the careful acquisition of cross-sections of animals in 2D volumetric-density approaches, otherwise serious errors may be introduced during the estimations. Combined with 2D modeling techniques, the CSM can be considered as an alternative to 3D modeling under certain conditions. It can reduce the complexity of making reconstructions while ensuring the reliability of the results.