A three-dimensional mathematical model of the human masticatory system predicting maximum possible bite forces

A three-dimensional mathematical model of the human masticatory system, containing 16 muscle forces and two joint reaction forces, is described. The model allows simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. The system parameters for the model were obtained from a cadaver head. Maximum possible bite forces were computed using optimization techniques; the optimization criterion we used was the minimizing of the relative activity of the most active muscle. The model predicts that at each specific bite point, bite forces can be generated in a wide range of directions, and that the magnitude of the maximum bite force depends on its direction. The relationship between bite force direction and its maximum magnitude depends on bite point location and mandibular position. In general, the direction of the largest possible bite force does not coincide with the direction perpendicular to the occlusal plane.     

The effects of aponeurosis geometry on strain injury susceptibility explored with a 3D muscle model

In the musculoskeletal system, some muscles are injured more frequently than others. For example, the biceps femoris longhead (BFLH) is the most commonly injured hamstring muscle. It is thought that acute injuries result from large strains within the muscle tissue, but the mechanism behind this type of strain injury is still poorly understood. The purpose of this study was to build computational models to analyze the stretch distributions within the BFLH muscle and to explore the effects of aponeurosis geometry on the magnitude and location of peak stretches within the model. We created a three-dimensional finite element (FE) model of the BFLH based on magnetic resonance (MR) images. We also created a series of simplified models with a similar geometry to the MR-based model. We analyzed the stretches predicted by the MR-based model during lengthening contractions to determine the region of peak local fiber stretch. The peak along-fiber stretch was 1.64 and was located adjacent to the proximal myotendinous junction (MTJ). In contrast, the average along-fiber stretch across all the muscle tissue was 0.95. By analyzing the simple models, we found that varying the dimensions of the aponeuroses (width, length, and thickness) had a substantial impact on the location and magnitude of peak stretches within the muscle. Specifically, the difference in widths between the proximal and distal aponeurosis in the BFLH contributed most to the location and magnitude of peak stretch, as decreasing the proximal aponeurosis width by 80% increased peak average stretches along the proximal MTJ by greater than 60% while slightly decreasing stretches along the distal MTJ. These results suggest that the aponeurosis morphology of the BFLH plays a significant role in determining stretch distributions throughout the muscle. Furthermore, this study introduces the new hypothesis that aponeurosis widths may be important in determining muscle injury susceptibility.     

A simple method for in vivo measurement of implant rod three-dimensional geometry during scoliosis surgery

Scoliosis is defined as a spinal pathology characterized as a three-dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-dimensional geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective geometry has been shown to be successful in the reconstruction of a three-dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-dimensional geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-dimensional geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-dimensional geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-dimensional implant rod geometry in vivo.     

A mathematical model of the patellofemoral joint

A mathematical model of the patellofemoral joint taking into account movements and forces in the sagittal plane is described. The system parameters of the model are the locations of the attachments of the quadriceps muscle and the patellar ligament, the length of the patellar ligament, the dimensions of the patella and the geometry of the articulating surfaces. They were obtained from ten autopsy knees. The model enables calculation of the relative position of the patella, patellar ligament and quadriceps tendon, the location of the patellofemoral contact point and the magnitude of the patellofemoral compression force and the force in the patellar ligament as a function of the location of the tibial tuberosity at different flexion-extension angles of the knee. The model is validated by comparing model data with experimentally determined data.     

Perspective: Emerging strategies for determining atomic-resolution structures of macromolecular complexes within cells

In principle, electron cryo-tomography (cryo-ET) of thin portions of cells provides high-resolution images of the three-dimensional spatial arrangement of all members of the proteome. In practice, however, radiation damage creates a tension between recording images at many different tilt angles, but at correspondingly reduced exposure levels, versus limiting the number of tilt angles in order to improve the signal-to-noise ratio (SNR). Either way, it is challenging to read the available information out at the level of atomic structure. Here, we first review work that explores the optimal strategy for data collection, which currently seems to favor the use of a limited angular range for tilting the sample or even the use of a single image to record the high-resolution information. Looking then to the future, we point to the alternative of so-called “deconvolution microscopy”, which may be applied to tilt-series or optically-sectioned, focal series data. Recording data as a focal series has the advantage that little or no translational alignment of frames might be needed, and a three-dimensional reconstruction might require only 2/3 the number of images as does standard tomography. We also point to the unexploited potential of phase plates to increase the contrast, and thus to reduce the electron exposure levels while retaining the ability align and merge the data. In turn, using much lower exposures per image could have the advantage that high-resolution information is retained throughout the full data-set, whether recorded as a tilt series or a focal series of images.     

Three-dimensional surface reconstruction software system for IBM personal computers

Surface and volumetric three-dimensional imaging methods have found application in fields as diverse as diagnostic medical imaging and paleontological research. The acquisition, modeling, classification, and computer graphics rendering of discrete image volumes will be introduced. Applications in diagnosis (craniofacial, orthopedic, cardiovascular, and others) as well as reconstruction methods for generic serial sections will be described. C language software for three-dimensional reconstruction which operates on an IBM PC/AT clone is described.     

FURTHER OBSERVATIONS ON THE FINE STRUCTURE OF THE MACRONUCLEUS IN TOKOPHRYA INFUSIONUM

In a previous paper (8) an organized structure was described in the macronuclei of certain old organisms of Tokophrya infusionum. It was found that the same honeycomb structure appears in great abundance in the macronuclei of overfed organisms. This permitted a better three-dimensional reconstruction of the described structure. Since the defined structure may be experimentally induced, it offers an opportunity for further more detailed studies as to its nature and meaning.     

The deutocerebrum of the cockroach Blaberus craniifer burm. Spatial organization of the sensory glomeruli

The objective of this work is to describe the glomerular organization of the deutocerebrum in Blaberus craniifer and to test the hypothesis that the glomeruli are identifiable. The problem is studied using the techniques of analytical geometry, i.e., by measuring the location of the glomeruli in cartesian coordinate systems. Computerized geometrical and statistical techniques are described for the three-dimensional reconstruction and quantitative study of these brain structures. The invariance of the glomerular organization, and consequently the identifiability of the glomeruli, is based on three criteria: (1) the number of glomeruli per hemideutocerebrum (hDTC) is a constant (109); (2) the position of the glomeruli is symmetrical in the two sides of one individual and identical in the same side of two individuals, except for small local variations, (3) the dimensions of two positionally homologous glomeruli are statistically equal in the same and in different individuals, except for a macroglomerulus which is found only in the male. The causes of variability, from experimental and biological origin, are discussed and quantitatively evaluated. The interindividual biological variability, not ascribable to differences in size between brains, expressed as a 95% interval, is estimated to be 27 μm for the location of glomeruli and 12 μm for the diameter of glomeruli.     

双源CT测量前交叉韧带单束重建术后隧道位置的临床研究

目的:应用双源CT(Dual-source computer tomography,DSCT)测量前交叉韧带(Anterior cruciate ligament,ACL)单束重建术后胫骨、股骨隧道位置,并对隧道位置进行评价。方法:对2013年1月至2014年6月我科收治的92例(男64例,女28例,平均年龄31.2岁)ACL单束重建患者术后膝关节进行双源CT三维重建,应用Adobe Photoshop CS6软件圈画隧道中心并采用Lorenz法测量胫骨隧道中心点相对位置百分比(Tx,Ty),采用Bernard四格表法测量股骨隧道中心点相对位置百分比(Fx,Fy)。结果:Tx平均为(54.54±3.42)%,Ty平均为(39.58±6.72)%,Fx平均为(28.98±6.51)%,Fy平均为(28.04±8.70)%。男、女性及左、右膝之间Tx、Ty、Fx、Fy的差异均无统计学意义(P0.05)。结论:双源CT能够清晰,三维显示ACL术后隧道,可以用来评估隧道位置,为改进前交叉韧带损伤后的手术方式及个体化解剖重建提供帮助。     

Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.     

Confocal scanning microscopy: three-dimensional biological imaging

Confocal scanning optical microscopy, arguably the most significant in biological light microscopy in this decade, enables one to obtain quantitative non-invasive optical sections through labelled biological specimens, virtually free from out-of-focus blur. A set of these optical sections collected at a series of focal levels through an object constitutes a three-dimensional image which may then be processed digitally for display as a computer reconstruction, a stereo pair or an animation sequence.     

Numerical simulations of Trichel pulses in a negative corona in air

Numerical simulations of a negative corona in air demonstrate that the experimentally observed regime of self-oscillations, known as Trichel pulses, is well described by a three-dimensional axisymmetric model that is based on the standard transport equations and in which only the ion-induced secondary electron emission at the cathode is taken into account. The quantitative difference between the measured and calculated values of the mean current and the pulse repetition rate most likely stems from the insufficiently large dimensions of the computation region and from the fact that the point shape adopted in simulations somewhat inexactly conforms to that used in experiments. It was found that the transverse discharge structure near the cathode radically changes during the pulse. Specifically, as the current grows, a cathode sheath forms at the discharge axis and expands over the cathode surface. When the current falls off, the cathode sheath is rapidly destroyed; as a result, the characteristic field structure is well defined only near the discharge axis and becomes virtually indistinguishable as the current decreases by an order of magnitude.     

3D FSPGR (fast spoiled gradient echo) magnetic resonance imaging in the diagnosis of focal cortical dysplasia in children

Small dysplastic lesions of the cerebral cortex are often missed by conventional MRI methods. The identification of subtle structural abnormalities by traditional multiplanar rectilinear slices is often limited by the complex convolutional pattern of the brain. We used a method of FSPGR (fast spoiled gradient-echo) of three-dimensional MRI data that improves the anatomical display of the sulcal structure of the hemispheric convexities. It also reduces the asymmetric sampling of gray-white matter that may lead to false-positive results. We present 5 from 12 patients with dysplastic cortical lesions in whom conventional two-dimensional and three-dimensional MRI with multiplanar reformatting was initially considered normal. Subsequent studies using 3D FSPGR identified various types of focal cortical dysplasia in all. These results indicate that an increase in the detection of subtle focal dysplastic lesions may be accomplished when one improves the anatomical display of the brain sulcal structure by performing 3D FSPGR.     

THE ULTRASTRUCTURE OF GLENODINIOPSIS STEINII (DINOPHYCEAE)

The freshwater dinoflagellate Glenodiniopsis steinii Wolsoszyńska was examined using computer-assisted three-dimensional reconstruction of serially sectioned cells observed with the transmission electron microscope and images from the scanning electron microscope. Vegetative cells contain ultrastructure typical of freshwater dinoflagellates including trichocysts, mitochondria, Golgi bodies, starch grains, and lipid bodies. The chloroplast is a single, multilobed structure, not multiple discoid chloroplasts as previously described. The “C” shape of the nucleus is apparently due in part to the size and location of the pusule.     

Cold-Sensitive Mutations of Dictyostelium Myosin Heavy Chain Highlight Functional Domains of the Myosin Motor

Dictyostelium provides a powerful environment for characterization of myosin II function. It provides well-established biochemical methods for in vitro analysis of myosin's properties as well as an array of molecular genetic tools. The absence of myosin function results in an array of phenotypes that can be used to genetically manipulate myosin function. We have previously reported methods for the isolation and identification of rapid-effect cold-sensitive myosin II mutations in Dictyostelium. Here, we report the development and utilization of a rapid method for localizing these point mutations. We have also sequenced 19 mutants. The mutations show distinct clustering with respect to three-dimensional location and biochemically characterized functional domains of the protein. We conclude that these mutants represent powerful tools for understanding the mechanisms driving this protein motor.     

Three-dimensional image reconstruction from ordered arrays of 70S ribosomes

A better understanding of the molecular mechanism of protein biosynthesis still awaits a reliable model for the ribosomal particle. We describe here the application of a diffraction technique, namely three-dimensional image reconstruction from two-dimensional sheets of 70S ribosomes from Bacillus stearothermophilus at 47 A resolution. The three-dimensional model obtained by these studies shows clearly the two subunits, the contact points between them, an empty space large enough to accommodate the components of protein biosynthesis, the location of regions rich in RNA and a possible binding site for mRNA. The tunnel within the 50S particle which may provide the path taken by the nascent polypeptide chain in partially resolved.     

Helical structure of unidirectionally shadowed metal replicas of cyanide hydratase from Gloeocercospora sorghi

The helical filaments of the cyanide hydratase from Gloeocercospora sorghi have been reconstructed in three dimensions from freeze dried, unidirectionally shadowed specimens using iterative real-space helical reconstruction. The average power spectrum of all selected images has three clear reflections on different layer lines. The reconstruction is complicated by the fact that three possible indexing schemes are possible and reconstructions using the starting symmetries based on each of these indexing schemes converge on three-dimensional volumes which appear plausible. Because only one side is visible in shadowed specimens, it is necessary to examine the phases from a single filament by cryo-electron microscopy in order to make an unequivocal assignment of the symmetry. Because of the novel nature of the reconstruction method used here, conventional cryo-EM methods were also used to determine a second reconstruction, allowing us to make comparisons between the two. The filament is shown to have a left-handed one-start helix with D(1) symmetry, 5.46 dimers per turn and a pitch of 7.15nm. The reconstruction suggests the presence of an interaction across the groove not previously seen in nitrilase helical fibres.     

A simplified approach for modeling diffusion into cells

Regulation of the intracellular concentration of substrates is essential for the maintenance of a stable cellular environment. Diffusion and reaction processes supply and consume substrates within cells and determine their steady-state concentrations. To realistically represent these processes by computer simulation they must be modeled in three dimensions. Yet three-dimensional models are inherently computing intensive. This study describes a method, which substantially simplifies the modeling of diffusion into a polyhedral body (a cube), that was used as a model representation of a cell. The method is applied to a case study of oxygen diffusion into nitrogen-fixing, rhizobia-infected cells in legume nodules. The method involved generating a one-dimensional representation of the three-dimensional problem to provide a "surface area profile" of three-dimensional diffusion. The one-dimensional models were significantly easier to program, several orders of magnitude faster to solve and in this study were validated by assessing their results against those of comparable three-dimensional models of diffusion into the same body. The results show the one-dimensional method to be a close approximation of a three-dimensional source-sink problem with systematic differences below 10% for fractional oxygenation of leghemoglobin, cell respiration and nitrogenase activity. Larger differences between models (up to 45%) in the predicted average and innermost O(2)concentrations had no effects on the physiological conclusions of the study, but were attributed to the poorer resolution of the three- than the one-dimensional model, and to an inherent simplification in the derivation of the one-dimensional surface area profiles. The one-dimensional modeling approach was found to be a simple, yet powerful tool for the study of diffusion and reaction in biological systems.     

Prediction of the location of structural domains in globular proteins

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation |i-j| in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.