3D reconstruction of dental specimens from 2D histological images and microCT-scans

Direct comparison of experimental and theoretical results in biomechanical studies requires a careful reconstruction of specimen surfaces to achieve a satisfactory congruence for validation. In this paper a semi-automatic approach is described to reconstruct triangular boundary representations from images originating from, either histological sections or microCT-, CT- or MRI-data, respectively. In a user-guided first step, planar 2D contours were extracted for every material of interest, using image segmentation techniques. In a second step, standard 2D triangulation algorithms were used to derive high quality mesh representations of the underlying surfaces. This was accomplished by converting the 2D meshes into 3D meshes by a novel lifting procedure. The meshes can be imported as is into finite element programme packages such as Marc/Mentat or COSMOS/M. Accuracy and feasibility of the algorithm is demonstrated by reconstructing several specimens as examples and comparing simulated results with available measurements performed on the original objects.     

A tool to model 3D coarse-root development with annual resolution

Dynamic root-development models are indispensable for biomechanical and biomass allocation studies, and also play an important role in understanding slope stability. There are few root-development models in the literature, and there is a specific lack of dynamic models. Therefore, the aim of this study is to develop a 3D growth-development model for coarse roots, which is species independent, as long as annual rings are formed. In order to implement this model, the objectives are (I) to interpolate annual growth layers, and (II) to evaluate the interpolations and annual volume computations. The model developed is a combination of 3D laser scans and 2D tree-ring data. A FARO laser ScanArm is used to acquire the coarse-root structure. A MATLAB program then integrates the ring-width measurements into the 3D model. A weighted interpolation algorithm is used to compute cross sections at any point within the model to obtain growth layers. The algorithm considers both the root structure and the ring-width data. The model reconstructed ring profiles with a mean absolute error for mean ring chronologies of <9% and for single radii of <20%. The interpolation accuracy was dependent on the number of input sections and root curvature. Total volume computations deviated by 3.5?C6.6% from the reference model. A new robust root-modelling tool was developed which allows for annual volume computations and sophisticated root-development analyses.     

Visualizing 3D data obtained from microscopy on the Internet

The Internet is a powerful communication medium increasingly exploited by business and science alike, especially in structural biology and bioinformatics. The traditional presentation of static two-dimensional images of real-world objects on the limited medium of paper can now be shown interactively in three dimensions. Many facets of this new capability have already been developed, particularly in the form of VRML (virtual reality modeling language), but there is a need to extend this capability for visualizing scientific data. Here we introduce a real-time isosurfacing node for VRML, based on the marching cube approach, allowing interactive isosurfacing. A second node does three-dimensional (3D) texture-based volume-rendering for a variety of representations. The use of computers in the microscopic and structural biosciences is extensive, and many scientific file formats exist. To overcome the problem of accessing such data from VRML and other tools, we implemented extensions to SGI's IFL (image format library). IFL is a file format abstraction layer defining communication between a program and a data file. These technologies are developed in support of the BioImage project, aiming to establish a database prototype for multidimensional microscopic data with the ability to view the data within a 3D interactive environment.     

Three-Dimensional Mapping of Soil Chemical Characteristics at Micrometric Scale by Combining 2D SEM-EDX Data and 3D X-Ray CT Images

There is currently a significant need to improve our understanding of the factors that control a number of critical soil processes by integrating physical, chemical and biological measurements on soils at microscopic scales to help produce 3D maps of the related properties. Because of technological limitations, most chemical and biological measurements can be carried out only on exposed soil surfaces or 2-dimensional cuts through soil samples. Methods need to be developed to produce 3D maps of soil properties based on spatial sequences of 2D maps. In this general context, the objective of the research described here was to develop a method to generate 3D maps of soil chemical properties at the microscale by combining 2D SEM-EDX data with 3D X-ray computed tomography images. A statistical approach using the regression tree method and ordinary kriging applied to the residuals was developed and applied to predict the 3D spatial distribution of carbon, silicon, iron, and oxygen at the microscale. The spatial correlation between the X-ray grayscale intensities and the chemical maps made it possible to use a regression-tree model as an initial step to predict the 3D chemical composition. For chemical elements, e.g., iron, that are sparsely distributed in a soil sample, the regression-tree model provides a good prediction, explaining as much as 90% of the variability in some of the data. However, for chemical elements that are more homogenously distributed, such as carbon, silicon, or oxygen, the additional kriging of the regression tree residuals improved significantly the prediction with an increase in the R² value from 0.221 to 0.324 for carbon, 0.312 to 0.423 for silicon, and 0.218 to 0.374 for oxygen, respectively. The present research develops for the first time an integrated experimental and theoretical framework, which combines geostatistical methods with imaging techniques to unveil the 3-D chemical structure of soil at very fine scales. The methodology presented in this study can be easily adapted and applied to other types of data such as bacterial or fungal population densities for the 3D characterization of microbial distribution.     

Combined method of whole mount and block-face imaging: Acquisition of 3D data of gene expression pattern from conventional in situ hybridization

Visualization of spatiotemporal expression of a gene of interest is a fundamental technique for analyzing the involvements of genes in organ development. In situ hybridization (ISH) is one of the most popular methods for visualizing gene expression. When conventional ISH is performed on sections or whole-mount specimens, the gene expression pattern is represented in 2-dimensional (2D) microscopic images or in the surface view of the specimen. To obtain 3-dimensional (3D) data of gene expression from conventional ISH, the “serial section method” has traditionally been employed. However, this method requires an extensive amount of time and labor because it requires researchers to collect a tremendous number of sections, label all sections by ISH, and image them before 3D reconstruction. Here, we proposed a rapid and low-cost 3D imaging method that can create 3D gene expression patterns from conventional ISH-labeled specimens. Our method consists of a combination of whole-mount ISH and Correlative Microscopy and Blockface imaging (CoMBI). The whole-mount ISH-labeled specimens were sliced using a microtome or cryostat, and all block-faces were imaged and used to reconstruct 3D images by CoMBI. The 3D data acquired using our method showed sufficient quality to analyze the morphology and gene expression patterns in the developing mouse heart. In addition, 2D microscopic images of the sections can be obtained when needed. Correlating 2D microscopic images and 3D data can help annotate gene expression patterns and understand the anatomy of developing organs. These results indicated that our method can be useful in the field of developmental biology.     

Streamlined,Inexpensive 3D Printing of the Brain and Skull

Neuroimaging technologies such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) collect three-dimensional data (3D) that is typically viewed on two-dimensional (2D) screens. Actual 3D models, however, allow interaction with real objects such as implantable electrode grids, potentially improving patient specific neurosurgical planning and personalized clinical education. Desktop 3D printers can now produce relatively inexpensive, good quality prints. We describe our process for reliably generating life-sized 3D brain prints from MRIs and 3D skull prints from CTs. We have integrated a standardized, primarily open-source process for 3D printing brains and skulls. We describe how to convert clinical neuroimaging Digital Imaging and Communications in Medicine (DICOM) images to stereolithography (STL) files, a common 3D object file format that can be sent to 3D printing services. We additionally share how to convert these STL files to machine instruction gcode files, for reliable in-house printing on desktop, open-source 3D printers. We have successfully printed over 19 patient brain hemispheres from 7 patients on two different open-source desktop 3D printers. Each brain hemisphere costs approximately $3–4 in consumable plastic filament as described, and the total process takes 14–17 hours, almost all of which is unsupervised (preprocessing = 4–6 hr; printing = 9–11 hr, post-processing = <30 min). Printing a matching portion of a skull costs $1–5 in consumable plastic filament and takes less than 14 hr, in total. We have developed a streamlined, cost-effective process for 3D printing brain and skull models. We surveyed healthcare providers and patients who confirmed that rapid-prototype patient specific 3D models may help interdisciplinary surgical planning and patient education. The methods we describe can be applied for other clinical, research, and educational purposes.     

ESyPred3D: Prediction of proteins 3D structures

MOTIVATION: Homology or comparative modeling is currently the most accurate method to predict the three-dimensional structure of proteins. It generally consists in four steps: (1) databanks searching to identify the structural homolog, (2) target-template alignment, (3) model building and optimization, and (4) model evaluation. The target-template alignment step is generally accepted as the most critical step in homology modeling. RESULTS: We present here ESyPred3D, a new automated homology modeling program. The method gets benefit of the increased alignment performances of a new alignment strategy. Alignments are obtained by combining, weighting and screening the results of several multiple alignment programs. The final three-dimensional structure is build using the modeling package MODELLER. ESyPred3D was tested on 13 targets in the CASP4 experiment (Critical Assessment of Techniques for Proteins Structural Prediction). Our alignment strategy obtains better results compared to PSI-BLAST alignments and ESyPred3D alignments are among the most accurate compared to those of participants having used the same template. AVAILABILITY: ESyPred3D is available through its web site at http://www.fundp.ac.be/urbm/bioinfo/esypred/ CONTACT: christophe.lambert@fundp.ac.be; http://www.fundp.ac.be/~lambertc     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

MATRAS: A program for protein 3D structure comparison

The recent accumulation of large amounts of 3D structural data warrants a sensitive and automatic method to compare and classify these structures. We developed a web server for comparing protein 3D structures using the program Matras (http://biunit.aist-nara.ac.jp/matras). An advantage of Matras is its structure similarity score, which is defined as the log-odds of the probabilities, similar to Dayhoff's substitution model of amino acids. This score is designed to detect evolutionarily related (homologous) structural similarities. Our web server has three main services. The first one is a pairwise 3D alignment, which is simply align two structures. A user can assign structures by either inputting PDB codes or by uploading PDB format files in the local machine. The second service is a multiple 3D alignment, which compares several protein structures. This program employs the progressive alignment algorithm, in which pairwise 3D alignments are assembled in the proper order. The third service is a 3D library search, which compares one query structure against a large number of library structures. We hope this server provides useful tools for insights into protein 3D structures.     

3D parallel coordinate systems--a new data visualization method in the context of microscopy-based multicolor tissue cytometry.

BACKGROUND: Presentation of multiple interactions is of vital importance in the new field of cytomics. Quantitative analysis of multi- and polychromatic stained cells in tissue will serve as a basis for medical diagnosis and prediction of disease in forthcoming years. A major problem associated with huge interdependent data sets is visualization. Therefore, alternative and easy-to-handle strategies for data visualization as well as data meta-evaluation (population analysis, cross-correlation, co-expression analysis) were developed. METHODS: To facilitate human comprehension of complex data, 3D parallel coordinate systems have been developed and used in automated microscopy-based multicolor tissue cytometry (MMTC). Frozen sections of human skin were stained using the combination anti-CD45-PE, anti-CD14-APC, and SytoxGreen as well as the appropriate single and double negative controls. Stained sections were analyzed using automated confocal laser microscopy and semiquantitative MMTC-analysis with TissueQuest 2.0. The 3D parallel coordinate plots are generated from semiquantitative immunofluorescent data of single cells. The 2D and 3D parallel coordinate plots were produced by further processing using the Matlab environment (Mathworks, USA). RESULTS: Current techniques in data visualization primarily utilize scattergrams, where two parameters are plotted against each other on linear or logarithmic scales. However, data evaluation on cartesian x/y-scattergrams is, in general, only of limited value in multiparameter analysis. Dot plots suffer from serious problems, and in particular, do not meet the requirements of polychromatic high-context tissue cytometry of millions of cells. The 3D parallel coordinate plot replaces the vast amount of scattergrams that are usually needed for the cross-correlation analysis. As a result, the scientist is able to perform the data meta-evaluation by using one single plot. On the basis of 2D parallel coordinate systems, a density isosurface is created for representing the event population in an intuitive way. CONCLUSIONS: The proposed method opens new possibilities to represent and explore multidimensional data in the perspective of cytomics and other life sciences, e.g., DNA chip array technology. Current protocols in immunofluorescence permit simultaneous staining of up to 17 markers. Showing the cross-correlation between these markers requires 136 scattergrams, which is a prohibitively high number. The improved data visualization method allows the observation of such complex patterns in only one 3D plot and could take advantage of the latest developments in 3D imaging.     

Molecular mechanism of 1,25-dihydroxyvitamin D3 inhibition of adipogenesis in 3T3-L1 cells

We have investigated the molecular mechanism whereby 1,25-dihydroxyvitamin D3 [1,25(OH)2D3] inhibits adipogenesis in vitro. 1,25(OH)2D3 blocks 3T3-L1 cell differentiation into adipocytes in a dose-dependent manner; however, the inhibition is ineffective 24-48 h after the differentiation is initiated, suggesting that 1,25(OH)2D3 inhibits only the early events of the adipogenic program. Treatment of 3T3-L1 cells with 1,25(OH)2D3 does not block the mitotic clonal expansion or C/EBPbeta induction; rather, 1,25(OH)2D3 blocks the expression of C/EBPalpha, peroxisome proliferator-activated receptor-gamma (PPARgamma), sterol regulatory element-binding protein-1, and other downstream adipocyte markers. The inhibition by 1,25(OH)2D3 is reversible, since removal of 1,25(OH)2D3 from the medium restores the adipogenic process with only a temporal delay. Interestingly, although the vitamin D receptor (VDR) protein is barely detectable in 3T3-L1 preadipocytes, its levels are dramatically increased during the early phase of adipogenesis, peaking at 4-8 h and subsiding afterward throughout the rest of the differentiation program; 1,25(OH)2D3 treatment appears to stabilize the VDR protein levels. Consistently, adenovirus-mediated overexpression of human (h) VDR in 3T3-L1 cells completely blocks the adipogenic program, confirming that VDR is inhibitory. Inhibition of adipocyte differentiation by 1,25(OH)2D3 is ameliorated by troglitazone, a specific PPARgamma antagonist; conversely, hVDR partially suppresses the transacting activity of PPARgamma but not of C/EBPbeta or C/EBPalpha. Moreover, 1,25(OH)2D3 markedly suppresses C/EBPalpha and PPARgamma mRNA levels in mouse epididymal fat tissue culture. Taken together, these data indicate that the blockade of 3T3-L1 cell differentiation by 1,25(OH)2D3 occurs at the postclonal expansion stages and involves direct suppression of C/EBPalpha and PPARgamma upregulation, antagonization of PPARgamma activity, and stabilization of the inhibitory VDR protein.     

Characterization of the capillary network in skeletal muscles from 3D data

In this review we present immunohistochemical methods for visualization of capillaries and muscle fibres in thick muscle sections. Special attention is paid to the procedures that preserve good morphology. Applying confocal microscopy and virtual 3D stereological grids, or tracing of capillaries in virtual reality, length of capillaries within a muscle volume or length of capillaries adjacent to a muscle fibre per fibre length, fibre surface area or fibre volume can be evaluated by an unbiased approach. Moreover, 3D models of capillaries and muscle fibres can be produced. Comparison of the developed methods with counting capillary profiles from 2D sections is discussed and the reader is warned that counting capillary profiles from 2D sections can underestimate the capillary length by as much as 75 percent. Application of the described 3D methodology is illustrated by the anatomical remodelling of capillarity during acute denervation and early reinnervation in the rat soleus and extensor digitorum longus muscles.     

Reconstruction of axial tomographic high resolution data from confocal fluorescence microscopy: a method for improving 3D FISH images.

Fluorescent confocal laser scanning microscopy allows an improved imaging of microscopic objects in three dimensions. However, the resolution along the axial direction is three times worse than the resolution in lateral directions. A method to overcome this axial limitation is tilting the object under the microscope, in a way that the direction of the optical axis points into different directions relative to the sample. A new technique for a simultaneous reconstruction from a number of such axial tomographic confocal data sets was developed and used for high resolution reconstruction of 3D-data both from experimental and virtual microscopic data sets. The reconstructed images have a highly improved 3D resolution, which is comparable to the lateral resolution of a single deconvolved data set. Axial tomographic imaging in combination with simultaneous data reconstruction also opens the possibility for a more precise quantification of 3D data. The color images of this publication can be accessed from http://www.esacp.org/acp/2000/20-1/heintzmann.++ +htm. At this web address an interactive 3D viewer is additionally provided for browsing the 3D data. This java applet displays three orthogonal slices of the data set which are dynamically updated by user mouse clicks or keystrokes.     

GCI: A network server for interactive 3D graphics

The Graphics Command Interpreter (GCI) is an independent server module that can be interfaced to any program that needs interactive three-dimensional (3D) graphics capabilities. The principal advantage of GCI is its simplicity. Only a limited set of powerful features have been implemented, including object management, global and local transformations, rotation, translation, clipping, scaling, viewport operations, window management, menu handling and picking.GCI and the master (client) program it serves run concurrently, communicating over a local or remote TCP/IP network. GCI sets up socket communication and provides a 3D graphics window and a terminal emulator for the master program. Communication between the two programs is via ASCII strings over standard I/O channels. The implied language for messages is very simple. GCI interprets messages from the master program and implements them as changes of graphical objects or as text messages to the user. GCI provides the user with facilities to manipulate the view of the displayed 3D objects interactively, independently of the master program, and to communicate mouse-controlled selection of menu items or 3D points as well as keyboard strings to the master program.The program is written in C and initially implemented using the Silicon Graphics GL graphics library. As the need to link special libraries to the master program is completely avoided, GCI can very easily be interfaced to existing programs written in any language and running on any operating system capable of TCP/IP communication. The program is freely available.     

Cross-sectional interpolation of annual rings within a 3D root model

Ring width of a given year can be highly variable throughout the cross section of a stem. This is especially true for roots. Therefore, the entire circumference of tree rings is often needed for studies focusing on specific reactions of individual trees on certain environmental conditions. Also, ring reconstructions are of interest for biomass calculations estimated by the cross-sectional area. The aim of the study is thus to reconstruct tree rings of cross sections within a 3D root-surface model, which will be the basis for an upcoming 3D root-development model. A FARO ScanArm was used for the acquisition of the 3D root structure (Technologies Inc., 2010). Afterwards ring-width data was measured along 4 radii per cross section and the resulting ring boundaries were integrated into the 3D root model. A weighted interpolation algorithm was used to reconstruct entire ring-width profiles of the cross sections. The algorithm considered the ring-width variations of the adjacent radii as well as the outer shape of the cross section. Hence, the intention was to estimate ring width around the root circumference using ring widths measured along 4 radii and the surface dimensions of roots. Interpolated ring-width data was compared to the measured tree-ring data as a control for the developed interpolation algorithm. Comparisons between modelled and empirical values showed a mean absolute error of about 0.06 mm deviation, and with a few exceptions the growth patterns could be accurately simulated. This has permitted additional radii measurements to be replaced by model interpolations.     

Effect of segmentation errors on 3D-to-2D registration of implant models in X-ray images

In many biomedical applications, it is desirable to estimate the three-dimensional (3D) position and orientation (pose) of a metallic rigid object (such as a knee or hip implant) from its projection in a two-dimensional (2D) X-ray image. If the geometry of the object is known, as well as the details of the image formation process, then the pose of the object with respect to the sensor can be determined. A common method for 3D-to-2D registration is to first segment the silhouette contour from the X-ray image; that is, identify all points in the image that belong to the 2D silhouette and not to the background. This segmentation step is then followed by a search for the 3D pose that will best match the observed contour with a predicted contour. Although the silhouette of a metallic object is often clearly visible in an X-ray image, adjacent tissue and occlusions can make the exact location of the silhouette contour difficult to determine in places. Occlusion can occur when another object (such as another implant component) partially blocks the view of the object of interest. In this paper, we argue that common methods for segmentation can produce errors in the location of the 2D contour, and hence errors in the resulting 3D estimate of the pose. We show, on a typical fluoroscopy image of a knee implant component, that interactive and automatic methods for segmentation result in segmented contours that vary significantly. We show how the variability in the 2D contours (quantified by two different metrics) corresponds to variability in the 3D poses. Finally, we illustrate how traditional segmentation methods can fail completely in the (not uncommon) cases of images with occlusion.     

High quality 3D imaging of vertebrate microremains using X-ray synchrotron phase contrast microtomography

Vertebrate microremains, particularly teeth, represent a substantial part of known vertebrate biodiversity. Many groups, such as Mesozoic mammals, are known mostly through isolated teeth. Classical imaging techniques of such complex millimetric to inframillime-tric objects are most often limited by problems of manipulation, depth of focus or limited orientation. The methods generally used are stereomicroscopy (including in-focus z-series reconstruction) and Scanning Electron Microscopy (SEM), which provide good images. Nevertheless, both provide 2D static images or partial and directional 3D data, making complete observation difficult. Propagation phase contrast synchrotron X-ray microtomography is a powerful technique alleviating these limitations. Thanks to submicron resolution and to the edge detection effect, it rapidly provides 3D data from minute samples with levels of quality and detail unattainable using conventional microtomographs. Complex morphology of small specimens can be studied with unlimited orientation possibilities and, when coupled with 3D printing, it allows enlarged 3D reproductions of such small and fragile fossils.     

Registration of 2D histological sections with 3D micro-CT datasets from small animal vertebrae and tibiae

The aim of this study was the registration of digitized thin 2D sections of mouse vertebrae and tibiae used for histomorphometry of trabecular bone structure into 3D micro computed tomography (μCT) datasets of the samples from which the sections were prepared. Intensity-based and segmentation-based registrations (SegRegs) of 2D sections and 3D μCT datasets were applied. As the 2D sections were deformed during their preparation, affine registration for the vertebrae was used instead of rigid registration. Tibiae sections were additionally cut on the distal end, which subsequently undergone more deformation so that elastic registration was necessary. The Jaccard distance was used as registration quality measure. The quality of intensity-based registrations and SegRegs was practically equal, although precision errors of the elastic registration of segmentation masks in tibiae were lower, while those in vertebrae were lower for the intensity-based registration. Results of SegReg significantly depended on the segmentation of the μCT datasets. Accuracy errors were reduced from approximately 64% to 42% when applying affine instead of rigid transformations for the vertebrae and from about 43% to 24% when using B-spline instead of rigid transformations for the tibiae. Accuracy errors can also be caused by the difference in spatial resolution between the thin sections (pixel size: 7.25 μm) and the μCT data (voxel size: 15 μm). In the vertebrae, average deformations amounted to a 6.7% shortening along the direction of sectioning and a 4% extension along the perpendicular direction corresponding to 0.13–0.17 mm. Maximum offsets in the mouse tibiae were 0.16 mm on average.     

Integrating 2D and 3D shell morphology to disentangle the palaeobiology of ammonoids: a virtual approach

Based on data derived from computed tomography, we demonstrate that integrating 2D and 3D morphological data from ammonoid shells represents an important new approach for investigating the palaeobiology of ammonoids. Characterization of ammonite morphology has long been constrained to 2D data, with only a few studies collecting ontogenetic data in 180° steps. Here we combine this traditional approach with 3D data collected from high‐resolution nano‐computed tomography. Ontogenetic morphological data on the hollow shell of a juvenile ammonite Kosmoceras (Jurassic, Callovian) was collected. 2D data was collected in 10° steps and show significant changes in shell morphology. Preserved hollow spines show multiple mineralized membranes never reported before, representing temporal changes in the ammonoid mantle tissue. 3D data show that chamber volumes do not always increase exponentially, as was generally assumed, but may represent a proxy for life events, such as stress phases. Furthermore, chamber volume cannot be simply derived from septal spacing in forms comparable to Kosmoceras. Vogel numbers represent a 3D parameter for chamber shape, and those for Kosmoceras are similar to other ammonoids (Arnsbergites, Amauroceras) and modern cephalopods (Nautilus, Spirula). Two methods to virtually document the suture line ontogeny, used to document phylogenetic relationships of larger taxonomic entities, were applied for the first time and present a promising alternative to hand drawings. The curvature of the chamber surfaces increases during ontogeny due to increasing strength of ornamentation and septal complexity. As this may allow for faster handling of cameral liquid, it could compensate for decreasing SA/V ratios through ontogeny.