Related papers: Estimation of erythrocyte surface area in mammals
We begin by studying the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over the unit sphere in n-dimensions and use this…
The intersection of two orthogonal cylinders represents a classical problem in computational geometry with direct applications to engineering design, manufacturing, and numerical simulation. While analytical solutions exist for the fully…
The manuscript provides formulas for the volume of a body defined by the intersection of a solid cone and a solid sphere as a function of the sphere radius, of the distance between cone apex and sphere center, and of the cone aperture…
Sickle cell disease causes erythrocytes to become sickle-shaped, affecting their movement in the bloodstream and reducing oxygen delivery. It has a high global prevalence and places a significant burden on healthcare systems, especially in…
We study the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of their major semi-axes. We write down an explicit formula as an integral over the unit sphere, use the formula to derive convexity…
We write down estimates for the surface area, and more generally, integral mean curvatures of an ellipsoid E in n-dimensional Euclidean space in terms of the lengths of the major semi-axes. We give applications to estimating the area of…
It is shown that the model proposed by Canham quantitatively describes the observed biconcave shape of human erythrocytes.
We present simple parametric equations in terms of Jacobi elliptic functions that provide a realistic model of the shape of human normal erythrocytes as well as of variations in size (anisocytosis) and shape (poikilocytosis) thereof. We…
This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…
The red blood cells or erythrocytes are biconcave shaped cells and consist mostly in a membrane delimiting a cytosol with a high concentration in hemoglobin. This membrane is highly deformable and allows the cells to go through narrow…
Understanding the physics of blood is challenging due to its nature as a suspension of soft particles and the fact that typical problems involve different scales. This is valid also for numerical investigations. In fact, many computational…
Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…
We study red blood cells using the Helfrich-Canham functional: due to their lipid bilayer structure, RBCs are naturally modeled using the theory of elastic surfaces. In this study, we demonstrate that Cassinian ovals, except for the…
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We present a solution of a question from S. Campi, P.…
Atherosclerotic lesions within carotid and cerebral vessels are likely to influence hemodynamics and manifest into vascular pathologies, including Alzheimers Disease and ischemic stroke. Hemodynamics are influenced by changes in luminal…
The derivatives with respect to the variable $r$ of $\pi r^2$ and $\frac{4}{3}\pi r^3$ are $2\pi r$ and $4\pi r^2$, respectively. This relates, through the derivative, the area enclosed in a circle to the length of that circle and,…
An example of the volume and boundary face area of a curved polyhedron for the case of regular spherical and hyperbolic tetrahedron is discussed. An exact formula is explicitly derived as a function of the scalar curvature and the edge…
We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the…
We give an explicit estimate of the area of a closed surface by the diameter and a lower bound of curvature. This is better than Calabi-Cao's estimate for a nonnegatively curved two-sphere.
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…