Use of the boundary element method for biological morphometrics

McAlarney, Mona E.

doi:10.1016/0021-9290(94)00111-g

Cited by 10 publications

(5 citation statements)

References 11 publications

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“…FE analysis as well as other related morphometric techniquessuch as the macroelement method (MEM) and the boundary element method (BEM), also called the boundary integral equation method (BIE), among others-is useful for the assessment of complex shape changes in structures such as cranial bones. It seems that of all the available morphometric techniques, BEM offers the advantage of eliminating arbitrary internal subdivisions because it uses information based on the outline of the structure under study, thus making the use of distinct anatomical landmark points within specific reference frames unnecessary (McAlarney, 1995). This is particularly useful for structures with inherent material homogeneity and potentially complicated shapes, such as dental implants (Wolfe, 1993), or in cases of shapes which change complexly over time, making the reproducibility of landmarks very difficult.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Mechanical Behavior of the Jaws and Their Related Structures By Finite Element (Fe) Analysis

Korioth

Versluis

1997

Critical Reviews in Oral Biology & Medicine

175

121

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In this paper, we provide a review of mechanical finite element analyses applied to the maxillary and/or mandibular bone with their associated natural and restored structures. It includes a description of the principles and the relevant variables involved, and their critical application to published finite element models ranging from three-dimensional reconstructions of the jaws to detailed investigations on the behavior of natural and restored teeth, as well as basic materials science. The survey revealed that many outstanding FE approaches related to natural and restored dental structures had already been done 10-20 years ago. Several three-dimensional mandibular models are currently available, but a more realistic correlation with physiological chewing and biting tasks is needed. Many FE models lack experimentally derived material properties, sensitivity analyses, or validation attempts, and yield too much significance to their predictive, quantitative outcome. A combination of direct validation and, most importantly, the complete assessment of methodical changes in all relevant variables involved in the modeled system probably indicates a good FE modeling approach. A numerical method for addressing mechanical problems is a powerful contemporary research tool. FE analyses can provide precise insight into the complex mechanical behavior of natural and restored craniofacial structures affected by three-dimensional stress fields which are still very difficult to assess otherwise.

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Section: Introductionmentioning

confidence: 99%

Modeling the Mechanical Behavior of the Jaws and Their Related Structures By Finite Element (Fe) Analysis

Korioth

Versluis

1997

Critical Reviews in Oral Biology & Medicine

175

121

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“…Two types of FEM have been applied in morphometric studies, namely homogeneous FE, in which shape changes within an element are assumed to be uniform throughout (Bookstein 1986; Moss et al 1987), and non-homogeneous FE, whereby interpolation is used to model the deformation as a non-linear function of the changes observed at landmarks (Lewis et al 1980; Cheverud et al 1983; McAlarney 1995; McAlarney and Chiu 1997). …”

Section: Interpolating Splinesmentioning

confidence: 99%

The Measurement of Local Variation in Shape

et al. 2012

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Geometric morphometrics comprises tools for measuring and analyzing shape as captured by an entire set of landmark configurations. Many interesting questions in evolutionary, genetic, and developmental research, however, are only meaningful at a local level, where a focus on “parts” or “traits” takes priority over properties of wholes. To study variational properties of such traits, current approaches partition configurations into subsets of landmarks which are then studied separately. This approach is unable to fully capture both variational and spatial characteristics of these subsets because interpretability of shape differences is context-dependent. Landmarks omitted from a partition usually contain information about that partition’s shape. We present an interpolation-based approach that can be used to model shape differences at a local, infinitesimal level as a function of information available globally. This approach belongs in a large family of methods that see shape differences as continuous “fields” spanning an entire structure, for which landmarks serve as reference parameters rather than as data. We show, via analyses of simulated and real data, how interpolation models provide a more accurate representation of regional shapes than partitioned data. A key difference of this interpolation approach from current morphometric practice is that one must assume an explicit interpolation model, which in turn implies a particular kind of behavior of the regions between landmarks. This choice presents novel methodological challenges, but also an opportunity to incorporate and test biomechanical models that have sought to explain tissue-level processes underlying the generation of morphological shape.

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“…5 and especially rather close to the sinusoidal portion of the partially inserted Padé graph. [31][32][33] When this graph portion is approximated by another best approximation that is not limited by a continual growth of the graph, this leads to an intersection at P. Particular portions of the right third of the figure between P and B ͑gradually shaded area͒ are important for clarifying the interaction of the propagating compressional waves with the tissue's dentinal tubules and their main orientation in cross sections. The two horizontal cross sections contribute to the data set in a rather distinct manner because the ultrasonic beam axes at P ͑and above P͒ are perpendicular to the specimen's surfaces and almost perpendicular to the orientation of the dentinal tubules.…”

Section: Tubule Density and Tubule Orientation At Intercept Pmentioning

confidence: 99%

“…This means that the RP provided is "upgradable" as well as "release compatible" to adaptive simulations that utilize finite elements and a certain group of macro-elements. 32 Furthermore, the presented RPs and Table II can be quite useful for the purpose of excluding individual Poisson's ratios that might not be observed, reporting any imaginary parts of complex Poisson's ratios, as well as for modeling attempts that account for a pronounced anisotropy in the Poisson's ratio of wet dentin. 37 In addition to using the exact relationship between p-wave velocity and unidirectional Young's modulus, it is considered advantageous to utilize expanded alternative formulas as inputs for a new concept involving a continuum theory of microstructured brittle materials.…”

Section: F Padé Shape Functions and Distinct Approximationsmentioning

confidence: 99%

Lateral distribution of ultrasound velocity in horizontal layers of human teeth

John

2006

The Journal of the Acoustical Society of America

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The speed of ultrasound at 20 MHz differs inside human teeth depending on which tissues are involved. At least two out of four dental tissues exhibit variations in the longitudinal velocity (CL). The aim of this in vitro study is to describe the laterally varying propagation velocity of tangentially propagating longitudinal waves. At a distance of 5 mm from the crown reference, the CL is determined using longitudinal sections and a pulse-echo technique. Several graphs are combined to account for the corono-apical decrease in CL and the laterally varying CL distribution along horizontally adjacent relative tooth width portions. The laterally increasing CL of 21 specimens at radial locations rises from 2900 to 4000 m/s. A mathematical evaluation reveals an optimal horizontal formula of the form CL(5 mm) = a + bX2 ln(X), where X is the standardized lateral parameter relative to individual tooth width w, which is compensated for offsets. Individual residuals and a, b coefficients of the corresponding approximations are provided. Individual mean errors range from 7 m/s (SD=6 m/s) to 92 m/s (SD=79 m/s). The lower contour of the envelope curve of all CL distributions is described by taking up a formerly introduced equation [J. Acoust. Soc. Am. 116, 545 (2004)].

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Use of the boundary element method for biological morphometrics

Cited by 10 publications

References 11 publications

Modeling the Mechanical Behavior of the Jaws and Their Related Structures By Finite Element (Fe) Analysis

Modeling the Mechanical Behavior of the Jaws and Their Related Structures By Finite Element (Fe) Analysis

The Measurement of Local Variation in Shape

Lateral distribution of ultrasound velocity in horizontal layers of human teeth

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