Shell form in the biconvex articulate Brachiopoda: a geometric analysis

Paleobiology ◽  
1980 ◽  
Vol 6 (1) ◽  
pp. 57-76 ◽  
Author(s):  
George R. McGhee
Keyword(s):  
Geometric Model ◽  
Geometric Analysis ◽  
Small Region ◽  
Shell Morphology ◽  
Shell Surface ◽  
Absolute Size ◽  
Shell Form ◽  
Geometric Space ◽  
Biological Optimization ◽  
Area And Volume

Using a geometric model of shell morphology, it is demonstrated that biconvex brachiopods occupy only a small region of the potential geometric space available to organisms with planispiral exoskeletons composed of two articulated valves. Measurements taken for a sample of 324 genera of the articulate orders Pentamerida, Rhynchonellida, Spiriferida, and Terebratulida were analyzed using a simple geometric model of shell form and ontogeny. The frequency distribution of brachiopod shell morphologies exhibited by the four orders represents the biological optimization of the spatial relationships between area and volume. Biconvex brachiopods develop shells which are designed to minimize shell surface area while maximizing internal shell volume. The means by which optimization is achieved is related directly to the effects of increase in absolute size during ontogeny. The boundaries upon shell geometries utilizable by biconvex brachiopods are determined by (1) limitations of articulation, and (2) limitations of surface and volume.

scholarly journals Turning turtle: scaling relationships and self-righting ability in Chelydra serpentina

2021 ◽  
Vol 288 (1946) ◽  
pp. 20210213
Author(s):  
Ilan M. Ruhr ◽  
Kayleigh A. R. Rose ◽  
William I. Sellers ◽  
Dane A. Crossley ◽  
Jonathan R. Codd
Keyword(s):  
Body Mass ◽  
Geometric Model ◽  
Shell Morphology ◽  
Shell Shape ◽  
Chelydra Serpentina ◽  
Older Individuals ◽  
Neck Length ◽  
Energy Increase ◽  
Scaling Relationships ◽  
Simple Scaling

Testudines are susceptible to inversion and self-righting using their necks, limbs or both, to generate enough mechanical force to flip over. We investigated how shell morphology, neck length and self-righting biomechanics scale with body mass during ontogeny in Chelydra serpentina , which uses neck-powered self-righting. We found that younger turtles flipped over twice as fast as older individuals. A simple geometric model predicted the relationships of shell shape and self-righting time with body mass. Conversely, neck force, power output and kinetic energy increase with body mass at rates greater than predicted. These findings were correlated with relatively longer necks in younger turtles than would be predicted by geometric similarity. Therefore, younger turtles self-right with lower biomechanical costs than predicted by simple scaling theory. Considering younger turtles are more prone to inverting and their shells offer less protection, faster and less costly self-righting would be advantageous in overcoming the detriments of inversion.

Geometric Analysis of the Proximal Medullary Cavity of the Femur in the German Shepherd Dog

1998 ◽  
Vol 11 (01) ◽  
pp. 29-36 ◽  
Author(s):  
J. A. Helsen ◽  
M. Mulier ◽  
D. Mattheeuws ◽  
S. V. N. Jaecques
Keyword(s):  
Body Mass ◽  
Hip Prosthesis ◽  
Geometric Model ◽  
Geometric Analysis ◽  
Helix Angle ◽  
Medullary Cavity ◽  
Geometric Parameters ◽  
German Shepherd ◽  
Human Femur ◽  
Press Fit

SummaryForty-one cadaver femora of German Shepherd dogs were prepared for implantation of a cementless total hip prosthesis by reaming of the proximal medullary cavity with standard orthopaedic instruments. Silicone paste imprints of the cavity were taken and measured with a 3 D laser reflection system. Data were processed statistically according to a geometric model with these parameters: distal diameter Ø dist , medio-frontal radius r, laterofrontal angle α, medio-frontal angle β, helix angle γ and increment eccentricity δ e . Correlations between body mass and Ø disv body mass and r, body mass and β were moderately significant (p <0.05, p <0.06, p <0.05 resp.). Other correlations between body mass and parameters were not significant. Simple weighing of a German Shepherd is not a useful predictor of the internal dimensions of the proximal femur.The distribution of the most important parameter Ø dist was compared with the range of Ø dist sizes of the iso-elastic veterinary hip prosthesis (IVHP). This comparison showed that the test sample of 41 bones could be fitted with four IVHP sizes. However, 25 femora out of 41 do not fit into the available r values of the IVHP assortment. Less than adequate proximal canal fill will be the result if an IVHP is implanted, unless substantial reaming is done proximomedially.It was shown that measurements on radiographs of intact dog cadaver femora do not yield equivalent results to the imprints. Moreover, comparison of the internal dimensions of the medullary cavity of the human femur showed that a press-fit human prosthesis cannot be geometrically proportional to the IVHP.Dimensions of reamed cavities of forty-one cadaver femora of German Shepherd dogs were measured with a system of silicone imprinting and 3D laser reflectometry. Data were processed statistically according to a geometric model with seven parameters. Correlations between parameters and body mass were moderately significant for three parameters and not significant for the others. Distributions of the geometric parameters were calculated and implications with respect to prosthesis design are discussed. A comparison with geometric parameters obtained from radiographs was made and the significance of the differences is discussed. Finally, a comparison with the geometric parameters of the medullary cavity of the human femur is made.

A geometric model for measurement of surface distance, surface area, and volume from tomographic images

1992 ◽  
Vol 19 (2) ◽  
pp. 419-431 ◽  
Author(s):  
Jack L. Lancaster ◽  
David Eberly ◽  
Abdalmajeid Alyassin ◽  
J. Hunter Downs ◽  
Peter T. Fox
Keyword(s):  
Surface Area ◽  
Geometric Model ◽  
Tomographic Images ◽  
Surface Distance ◽  
Area And Volume

scholarly journals A model for planktic foraminiferal shell growth

Paleobiology ◽  
1993 ◽  
Vol 19 (1) ◽  
pp. 71-91 ◽  
Author(s):  
Miguel Signes ◽  
Jelle Bijma ◽  
Christoph Hemleben ◽  
Rolf Ott
Keyword(s):  
Surface Area ◽  
Adult Stage ◽  
Growth Parameters ◽  
Shell Growth ◽  
Shell Morphology ◽  
Shell Surface ◽  
Laws Of Growth ◽  
Juvenile Stages ◽  
Fine Tune ◽  
Logarithmic Growth

In this paper we analyze the laws of growth that control planktic foraminiferal shell morphology. We assume that isometry is the key toward the understanding of their ontogeny. Hence, our null hypothesis is that these organisms construct isometric shells. To test this hypothesis, geometric models of their shells have been generated with a personal computer. It is demonstrated that early chambers in log-spirally coiled structures cannot follow a strict isometric arrangement. In the real world, the centers of juvenile chambers deviate from the logarithmic growth curve. Juvenile stages are generally more planispiral and contain more chambers per whorl than adult stages. These traits are shown to be essential in order to keep volumes of consecutive chambers in geometric progression. We are convinced that the neanic stage marks the constructional bridge from a juvenile set of growth parameters to an adult one. The adult stage can be strictly isometric, that is, the effective shape is constant and the increase in volume after a chamber addition is proportional to the preexisting volume of the shell.The shell volume is related to the biomass, the ratio of outer shell surface area to shell volume is related to the respiration rate and the ratio of the total shell surface area to shell volume is related to the total calcification effort. The influence of the parameters of the model on these relationships is investigated. Only the initial radius and the rate of radius increase affect the relationships between shell volume and surface area. The other shape parameters merely provide a fine tune-up of these relationships. Size itself plays a major role during foraminiferal development.

scholarly journals Multiscale imaging and registration-driven model for pulmonary acinar mechanics in the mouse

2013 ◽  
Vol 114 (8) ◽  
pp. 971-978 ◽  
Author(s):  
Haribalan Kumar ◽  
Dragoş M. Vasilescu ◽  
Youbing Yin ◽  
Eric A. Hoffman ◽  
Merryn H. Tawhai ◽  
...  
Keyword(s):  
Solid Mechanics ◽  
Geometric Model ◽  
Mouse Lung ◽  
Alveolar Wall ◽  
Inflation Pressure ◽  
Vascular Perfusion ◽  
Intact Mouse ◽  
Geometric Similarity ◽  
Multiple Resolutions ◽  
Area And Volume

A registration-based multiscale method to obtain a deforming geometric model of mouse acinus is presented. An intact mouse lung was fixed by means of vascular perfusion at a hydrostatic inflation pressure of 20 cmH2O. Microcomputed tomography (μCT) scans were obtained at multiple resolutions. Substructural morphometric analysis of a complete acinus was performed by computing a surface-to-volume (S/V) ratio directly from the 3D reconstruction of the acinar geometry. A geometric similarity is observed to exist in the acinus where S/V is approximately preserved anywhere in the model. Using multiscale registration, the shape of the acinus at an elevated inflation pressure of 25 cmH2O is estimated. Changes in the alveolar geometry suggest that the deformation within the acinus is not isotropic. In particular, the expansion of the acinus (from 20 to 25 cmH2O) is accompanied by an increase in both surface area and volume in such a way that the S/V ratio is not significantly altered. The developed method forms a useful tool in registration-driven fluid and solid mechanics studies as displacement of the alveolar wall becomes available in a discrete sense.

Topology of Spade Drills for Wood Drilling Operations Part 2: Spade Drill Point Cutting Geometry Analysis

2005 ◽  
Vol 127 (2) ◽  
pp. 310-318
Author(s):  
Hanxin Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
Software Package ◽  
Geometric Model ◽  
Geometric Analysis ◽  
Analysis Procedure ◽  
Angle Distribution ◽  
Cutting Geometry ◽  
Drilling Operations ◽  
Drill Point ◽  
Geometric Elements ◽  
Geometry Analysis

Based on the spade drill point’s mathematical models established in Part 1 of this paper, a detailed methodology for the analysis of the cutting edges and angle distributions along these edges is given. The analysis addresses the most important geometric elements of the bit including the tip, major cutting edge, and the chisel edge profiles, as well as the rake and clearance angle distribution along these cutting edges. In unison, the geometric model of the spade bit and the analysis procedure described in this part of the paper have laid the foundation for a methodology and a software package for a detailed geometric analysis of all relevant cutting mechanics related geometric entities of the drill. This, in turn, constitutes the first prerequisite for assessing the cutting performance of these tools.

Geometric Modeling of the Nasal Valve

2017 ◽  
Vol 33 (04) ◽  
pp. 444-450 ◽  
Author(s):  
Wasnard Victor ◽  
Matthew Sclafani ◽  
Anthony Sclafani
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Geometric Analysis ◽  
Lateral Wall ◽  
Nasal Valve ◽  
Total Change ◽  
Cross Sectional ◽  
Cantilevered Beam ◽  
Nasal Function ◽  
Length Reduction

AbstractWe have used a simple geometric model to examine forces affecting the nasal valve after dorsal reduction and spreader graft placement. The study was designed on the geometric modeling of the internal nasal valve (INV). Published measurements of the leptorrhine nose were used to construct a geometric model of the INV. The changes in the cross-sectional area (CSA) occurring after reduction rhinoplasty were calculated algebraically, as was the effect of these changes on the tendency of the lateral wall of the INV to collapse. The effect of spreader grafting on the CSA was determined, and the total change in CSA of the INV in various scenarios was determined and compared with the reported normal CSA. Relative to published norms, the gain in CSA from spreader grafting can be significant if thick grafts are used. When the lateral wall of the INV is conceptualized as a cantilevered beam fixed medially, the reduction of length reduction of the lateral segment of the INV can significantly reduce the tendency for the inward collapse of the lateral wall. The reduction in CSA of the INV associated with dorsal nasal reduction can be ameliorated through the placement of spreader grafts. Moreover, the reduction in length of the INV sidewall also limits inward collapse, assuming it is firmly reattached to the dorsal septum. An enhanced appreciation of the physical properties of the INV anticipated through a simplified geometric analysis will be invaluable to the rhinological surgeon interested in enhancing nasal function.

The bio-geometry of mollusc shells

Paleobiology ◽  
1998 ◽  
Vol 24 (1) ◽  
pp. 133-149 ◽  
Author(s):  
Sean H. Rice
Keyword(s):  
Growth Rate ◽  
The Body ◽  
Growth Strategy ◽  
Shell Morphology ◽  
Spiral Growth ◽  
Time Interval ◽  
Shell Form ◽  
New Material ◽  
Morphological Transformations ◽  
Shell Production

The shells of gastropods and cephalopods grow by production of new material, by the mantle, at the lip of the shell. I derive a model of shell form that allows us to describe the morphology of a shell in terms of independently definable biological parameters. These are (1) the relative rates of shell production at different points around the aperture, (2) the total amount of shell produced per time interval, (3) the growth rate of the aperture, (4) aperture shape, and (5) the orientation of the animal within the shell. Describing shell form in these terms allows us to see what biological changes must occur in development in order to change one shell morphology into another and what constraints are associated with particular morphological transformations. The model shows that it is developmentally easy to derive a slightly coiled limpet shell from that of a high-spired ancestor, but difficult to take the next step to a fully conical limpet. Many, if not most, real gastropod shells are not conical but rather have a convex or concave profile. I show that these forms result from a decoupling of shell production rates from the growth rate of the animal within the shell. The model also shows how truly different forms, such as vermetid snails and heteromorph ammonites, escaped the confines of spiral growth–sometimes by rotating the body within the shell, and sometimes by taking up a growth strategy that does not constrain them to coil. This model is compatible with shell morphometric models that have been widely discussed in the literature but strives toward a different goal: understanding the relationships between the various biological processes involved in shell development.

A New Geometric Model for Three-Dimensional Braided Composites

2014 ◽  
Vol 662 ◽  
pp. 15-19 ◽  
Author(s):  
Chen Bing Ni ◽  
Gao Feng Wei
Keyword(s):  
Cross Section ◽  
Geometric Model ◽  
Geometric Analysis ◽  
Three Dimensional ◽  
Structural Features ◽  
Unit Cell ◽  
Braided Composites ◽  
Unit Cells ◽  
Analysis Models ◽  
Surface Unit Cell

According to the structural features of 3-D braided composites, the whole structure is divided into three types of sub-unit cells, these are the interior unit cell, the surface unit cell and the corner unit cell. Considering the bending of fiber bundle and the deformation of cross-section which are caused by the space fiber extrusion and twist together, the corresponding geometric analysis models for every type of sub-unit cell are established, and the engineering elastic constants of the 3-D braided composites are predicted. The results show that the calculated results well agree with the experimental results, and the effectiveness of the model is verified.

Within-basin variation in the shell morphology and growth rate of a freshwater mussel

1988 ◽  
Vol 66 (7) ◽  
pp. 1704-1708 ◽  
Author(s):  
Robert C. Bailey ◽  
Roger H. Green
Keyword(s):  
Growth Rate ◽  
Morphometric Analysis ◽  
Lake Erie ◽  
Freshwater Mussel ◽  
Shell Morphology ◽  
High Exposure ◽  
Shell Form ◽  
Habitat Variation ◽  
Ratio Variables

We measured a correlation between the habitat of the freshwater mussel Lampsilis radiata siliquoidea (Barnes, 1823) from several sites in Inner Long Point Bay, Lake Erie, and its shell morphology and growth rate. Morphometric analysis revealed that mussels in more exposed areas of the bay (areas with more turbulence and sandier sediments) had thicker shells than those from less exposed areas (areas with little turbulence and muddier sediments). Two growth rate analyses showed that the mussels from high exposure areas also grew faster. The results demonstrate the importance of (i) a multivariate consideration of shell form (as opposed to the use of ratio variables) when assessing form–habitat correlations, (ii) quantitatively defining habitat variation in examining such relationships, and (iii) measuring form–habitat relationships among more than two sites in a given basin or stream reach.

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