Modeling of human muscle and its deformation.

There is a lack of volume preserving and reasonable deformation of human muscles during bones and joints movement in the field of digital orthopedics. A novel approach for modeling of human muscle and its deformation was put forward to effectively assist doctors in guiding patients to carry out rehabilitation exercises. Firstly, based on Magnetic Resonance Imaging (MRI) data, the generated slice images were used to extract the outer contour lines and then the corresponding contour lines and optimal matching points of the adjacent layer images were connected to construct the three-dimensional (3D) geometric models of the muscles; Secondly, the mapping relationship between parameters can be established through hierarchical definition of the muscle characteristics to realize the volume-preserving deformation of muscle; Finally, the movement of human joints can be realized based on the constraint range of joint movement, and the vector-valued dynamic fourth-order differential equation was proposed to make the characteristic curve dynamically simulate the process of muscle deformation, thereby forming the corresponding relationship between bone movement and muscle deformation. The effectiveness and feasibility of this method have been verified in our experiments with biceps brachii and triceps brachii as examples. The maximum volume errors of biceps brachii and triceps brachii during the deformation process were less than 0.6%, which can be ignored within a certain allowable error range, reflecting that the parametric method was used to realize the reasonable volume-preserving deformation of human muscle.

Non-Auxetic Mechanical Metamaterials.

The concept of "mechanical metamaterials" has become increasingly popular, since their macro-scale characteristics can be designed to exhibit unusual combinations of mechanical properties on the micro-scale. The advances in additive manufacturing (AM, three-dimensional printing) techniques have boosted the fabrication of these mechanical metamaterials by facilitating a precise control over their micro-architecture. Although mechanical metamaterials with negative Poisson's ratios (i.e., auxetic metamaterials) have received much attention before and have been reviewed multiple times, no comparable review exists for architected materials with positive Poisson's ratios. Therefore, this review will focus on the topology-property relationships of non-auxetic mechanical metamaterials in general and five topological designs in particular. These include the designs based on the diamond, cube, truncated cube, rhombic dodecahedron, and the truncated cuboctahedron unit cells. We reviewed the mechanical properties and fatigue behavior of these architected materials, while considering the effects of other factors such as those of the AM process. In addition, we systematically analyzed the experimental, computational, and analytical data and solutions available in the literature for the titanium alloy Ti-6Al-4V. Compression dominated lattices, such as the (truncated) cube, showed the highest mechanical properties. All of the proposed unit cells showed a normalized fatigue strength below that of solid titanium (i.e., 40% of the yield stress), in the range of 12⁻36% of their yield stress. The unit cells discussed in this review could potentially be applied in bone-mimicking porous structures.

Helicity is the only integral invariant of volume-preserving transformations.

We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional I defined on exact divergence-free vector fields of class C(1) on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.

Volumetric relief map for intracranial cerebrospinal fluid distribution analysis.

Cerebrospinal fluid imaging plays a significant role in the clinical diagnosis of brain disorders, such as hydrocephalus and Alzheimer's disease. While three-dimensional images of cerebrospinal fluid are very detailed, the complex structures they contain can be time-consuming and laborious to interpret. This paper presents a simple technique that represents the intracranial cerebrospinal fluid distribution as a two-dimensional image in such a way that the total fluid volume is preserved. We call this a volumetric relief map, and show its effectiveness in a characterization and analysis of fluid distributions and networks in hydrocephalus patients and healthy adults.

Avoiding symmetry-breaking spatial non-uniformity in deformable image registration via a quasi-volume-preserving constraint.

The choice of a reference image typically influences the results of deformable image registration, thereby making it asymmetric. This is a consequence of a spatially non-uniform weighting in the cost function integral that leads to general registration inaccuracy. The inhomogeneous integral measure--which is the local volume change in the transformation, thus varying through the course of the registration--causes image regions to contribute differently to the objective function. More importantly, the optimization algorithm is allowed to minimize the cost function by manipulating the volume change, instead of aligning the images. The approaches that restore symmetry to deformable registration successfully achieve inverse-consistency, but do not eliminate the regional bias that is the source of the error. In this work, we address the root of the problem: the non-uniformity of the cost function integral. We introduce a new quasi-volume-preserving constraint that allows for volume change only in areas with well-matching image intensities, and show that such a constraint puts a bound on the error arising from spatial non-uniformity. We demonstrate the advantages of adding the proposed constraint to standard (asymmetric and symmetrized) demons and diffeomorphic demons algorithms through experiments on synthetic images, and real X-ray and 2D/3D brain MRI data. Specifically, the results show that our approach leads to image alignment with more accurate matching of manually defined neuroanatomical structures, better tradeoff between image intensity matching and registration-induced distortion, improved native symmetry, and lower susceptibility to local optima. In summary, the inclusion of this space- and time-varying constraint leads to better image registration along every dimension that we have measured it.

SYMMETRIC NON-RIGID IMAGE REGISTRATION VIA AN ADAPTIVE QUASI-VOLUME-PRESERVING CONSTRAINT.

The standard implementation of non-rigid image registration is asymmetric, even though symmetry might be an intrinsic attribute of the particular application, e.g., pairwise image alignment. Current approaches to restore symmetry to non-rigid registration, although successful in achieving inverse-consistency, generally alter the objective function through implicit inclusion of a non-uniform weight in the integral that is computed on the native space of an input image. This inhomogeneous integral measure, which varies through the course of the registration, results in regional biases by allowing image regions to contribute differently to the objective function. In this work, instead of symmetrizing the objective function, we address the root of the problem: the non-uniformity of the integral in both the asymmetric and the symmetrized implementations. We introduce a new quasi-volume-preserving constraint that keeps the forward and backward objective functions arbitrarily close to each other - hence the registration symmetry - without compromising the uniformity of the integrals. We show the advantages of our method through experiments on synthetic images and real X-ray and MRI data.

A new method for estimating carbon dioxide emissions from transportation at fine spatial scales.

Detailed estimates of carbon dioxide (CO2) emissions at fine spatial scales are useful to both modelers and decision makers who are faced with the problem of global warming and climate change. Globally, transport related emissions of carbon dioxide are growing. This letter presents a new method based on the volume-preserving principle in the areal interpolation literature to disaggregate transportation-related CO2 emission estimates from the county-level scale to a 1 km2 grid scale. The proposed volume-preserving interpolation (VPI) method, together with the distance-decay principle, were used to derive emission weights for each grid based on its proximity to highways, roads, railroads, waterways, and airports. The total CO2 emission value summed from the grids within a county is made to be equal to the original county-level estimate, thus enforcing the volume-preserving property. The method was applied to downscale the transportation-related CO2 emission values by county (i.e. parish) for the state of Louisiana into 1 km2 grids. The results reveal a more realistic spatial pattern of CO2 emission from transportation, which can be used to identify the emission 'hot spots'. Of the four highest transportation-related CO2 emission hotspots in Louisiana, high-emission grids literally covered the entire East Baton Rouge Parish and Orleans Parish, whereas CO2 emission in Jefferson Parish (New Orleans suburb) and Caddo Parish (city of Shreveport) were more unevenly distributed. We argue that the new method is sound in principle, flexible in practice, and the resultant estimates are more accurate than previous gridding approaches.