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arXiv2010

General analysis of mathematical models for bone remodeling

Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modelling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we find that the parameter regime most likely realized in nature lies very close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. Some evidence implicates such dynamical transitions as a potential mechanism leading to forms of Paget's disease.

q-bio.TO↗

arXiv2010

Kramers-Kronig analysis of biological skin

A treatise on the optical property of biological tissue is presented. Water is postulated to be a topological basis and serves to discriminate published skin data. Electromagnetic theory governing dielectric behavior is concisely detailed pertaining to certain optical constants and Kramers-Kronig relation. The Kramers-Kronig relation defining dispersion index is emulated through the discrete Hilbert transform. An accrued absorption set is populated with empirical absorption data for biological skin, pure liquid water and interpolated values. Kramers-Kronig analysis of biological skin yields a comprehensive description of the complex index of refraction from DC to x-ray frequencies.

q-bio.TO↗

arXiv2010

Parametric identification of a functional-structural tree growth model and application to beech trees (Fagus sylvatica)

Functional-structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains a critical issue. We present the GreenLab approach for modelling tree growth. It simulates tree growth plasticity in response to changes of their internal level of trophic competition, especially topological development and cambial growth. The model includes a simplified representation of tree architecture, based on a species-specific description of branching patterns. We study whether those simplifications allow enough flexibility to reproduce with the same set of parameters the growth of two observed understorey beech trees (Fagus sylvatica L.) of different ages in different environmental conditions. The parametric identification of the model is global, i.e. all parameters are estimated simultaneously, potentially providing a better description of interactions between sub-processes. As a result, the source-sink dynamics throughout tree development is retrieved. Simulated and measured trees were compared for their trunk profiles (fresh masses and dimensions of every growth units, ring diameters at different heights) and compartment masses of their order 2 branches. Possible improvements of this method by including topological criteria are discussed.

math.DS↗

arXiv2010

Computational challenges of tumor spheroid modeling

The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we put forward general considerations that apply to any fine-grained numerical model of tumors. We discuss ways to bypass computational limitations and discuss our incremental approach, where each step is validated by experimental observations on a quantitative basis. We present a few results on the growth of tumor cells in closed and open environments and of tumor spheroids. This study suggests new ways to explore the initial growth phase of solid tumors and to optimize anti-tumor treatments.

q-bio.TO↗

arXiv2010

Preliminary Functional-Structural Modeling on Poplar (Salicaceae)

Poplar is one of the best fast-growing trees in the world, widely used for windbreak and wood product. Although architecture of poplar has direct impact on its applications, it has not been descried in previous poplar models, probably because of the difficulties raised by measurement, data processing and parameterization. In this paper, the functional-structural model GreenLab is calibrated by using poplar data of 3, 4, 5, 6 years old. The data was acquired by simplifying measurement. The architecture was also simplified by classifying the branches into several types (physiological age) using clustering analysis, which decrease the number of parameters. By multi-fitting the sampled data of each tree, the model parameters were identified and the plant architectures at different tree ages were simulated.

math.DS↗

arXiv2010

Modeling branching effects on source-sink relationships of the cotton plant

Compared with classical process-based models, the functional-structural plant models provide more efficient tools to explore the impact of changes in plant structures on plant functioning. In this paper we investigated the effects of branches on the sourcesink interaction for the cotton plant (Gossypium hirsutum L.) based on a two-treatment experiment conducted on cotton grown in the field: the singlestem plants and the plants with only two vegetative branches. It was observed that the branched cotton had more organs for the whole plant but the organs on the trunk were smaller than those on the single-stem cotton. The phytomer production of the branches was four or five growth cycles delayed compared with the main stem. The organs on the trunk had similar dynamics of expansion for both treatments. Effects of branches were evaluated by using the functionalstructural model GREENLAB. It allowed estimating the coefficients of sink strength to differentiate the biomass acquisition abilities of organs between different physiological ages. We found that the presence of the two vegetative branches increased the ground projection area of plant leaves and had led to slight changes on the directly measured parameters; the potential relative sink strengths of organs were found similar for the two treatments.

math.DS↗

arXiv2011

Abnormality of the placental vasculature affects placental thickness

Our empirical modeling suggests that deformation of placental vascular growth is associated with abnormal placental chorionic surface shape. Altered chorionic surface shape is associated with lowered placental functional efficiency. We hypothesize that placentas with deformed chorionic surface vascular trees and reduced functional efficiency also have irregular vascular arborization that will be reflected in increased variability of placental thickness and a lower mean thickness. We find that non-centrality of the umbilical cord insertion is strongly and significantly correlated with disk thickness (Spearman's rho=0.128, p=0.002). Deformed shape is strongly and significantly associated with lower overall thickness and higher variability of thickness with beta between -0.173 and -0.254 (p<0.001) . Both lower mean thickness and high variability of thickness are strongly correlated with higher beta (reduced placental efficiency) (p<0.001 and p=0.038 respectively). Greater thickness variability is correlated with higher beta independent of the other placental shape variables p=0.004.

q-bio.TO↗

arXiv2011

A Phyllotactic Approach to the Structure of Collagen Fibrils

Collagen fibrils, cable-like assemblies of long biological molecules, are dominant components of connective tissues. Their determinant morphological and functional roles motivated a large number of studies concerning their formation and structure. However, these two points are still open questions and, particularly, that of their organization which is certainly dense but not strictly that of a crystal. We examine here how the algorithm of phyllotaxis could contribute to the analysis of the structure of collagen fibrils. Such an algorithm indeed leads to organizations giving to each element of the assembly the most homogeneous and isotropic dense environment in a situation of cylindrical symmetry. The scattered intensity expected from a phyllotactic distribution of triple helices in collagen fibrils well agrees with the major features observed along the equatorial direction of their X ray patterns. Following this approach, the aggregation of triple helices in fibrils should be considered within the frame of soft condensed matter studies rather than that of molecular crystal studies.

cond-mat.soft↗

arXiv2011

Evaluation of a Novel Approach for Automatic Volume Determination of Glioblastomas Based on Several Manual Expert Segmentations

The glioblastoma multiforme is the most common malignant primary brain tumor and is one of the highest malignant human neoplasms. During the course of disease, the evaluation of tumor volume is an essential part of the clinical follow-up. However, manual segmentation for acquisition of tumor volume is a time-consuming process. In this paper, a new approach for the automatic segmentation and volume determination of glioblastomas (glioblastoma multiforme) is presented and evaluated. The approach uses a user-defined seed point inside the glioma to set up a directed 3D graph. The nodes of the graph are obtained by sampling along rays that are sent through the surface points of a polyhedron. After the graph has been constructed, the minimal s-t cut is calculated to separate the glioblastoma from the background. For evaluation, 12 Magnetic Resonance Imaging (MRI) data sets were manually segmented slice by slice, by neurosurgeons with several years of experience in the resection of gliomas. Afterwards, the manual segmentations were compared with the results of the presented approach via the Dice Similarity Coefficient (DSC). For a better assessment of the DSC results, the manual segmentations of the experts were also compared with each other and evaluated via the DSC. In addition, the 12 data sets were segmented once again by one of the neurosurgeons after a period of two weeks, to also measure the intra-physician deviation of the DSC.

cs.CV↗

arXiv2011

A Flexible Semi-Automatic Approach for Glioblastoma multiforme Segmentation

Gliomas are the most common primary brain tumors, evolving from the cerebral supportive cells. For clinical follow-up, the evaluation of the preoperative tumor volume is essential. Volumetric assessment of tumor volume with manual segmentation of its outlines is a time-consuming process that can be overcome with the help of segmentation methods. In this paper, a flexible semi-automatic approach for grade IV glioma segmentation is presented. The approach uses a novel segmentation scheme for spherical objects that creates a directed 3D graph. Thereafter, the minimal cost closed set on the graph is computed via a polynomial time s-t cut, creating an optimal segmentation of the tumor. The user can improve the results by specifying an arbitrary number of additional seed points to support the algorithm with grey value information and geometrical constraints. The presented method is tested on 12 magnetic resonance imaging datasets. The ground truth of the tumor boundaries are manually extracted by neurosurgeons. The segmented gliomas are compared with a one click method, and the semi-automatic approach yields an average Dice Similarity Coefficient (DSC) of 77.72% and 83.91%, respectively.

cs.CE↗

arXiv2011

Pituitary Adenoma Segmentation

Sellar tumors are approximately 10-15% among all intracranial neoplasms. The most common sellar lesion is the pituitary adenoma. Manual segmentation is a time-consuming process that can be shortened by using adequate algorithms. In this contribution, we present a segmentation method for pituitary adenoma. The method is based on an algorithm we developed recently in previous work where the novel segmentation scheme was successfully used for segmentation of glioblastoma multiforme and provided an average Dice Similarity Coefficient (DSC) of 77%. This scheme is used for automatic adenoma segmentation. In our experimental evaluation, neurosurgeons with strong experiences in the treatment of pituitary adenoma performed manual slice-by-slice segmentation of 10 magnetic resonance imaging (MRI) cases. Afterwards, the segmentations were compared with the segmentation results of the proposed method via the DSC. The average DSC for all data sets was 77.49% +/- 4.52%. Compared with a manual segmentation that took, on the average, 3.91 +/- 0.54 minutes, the overall segmentation in our implementation required less than 4 seconds.

cs.CE↗

arXiv2011

A simple model of cerebral blood flow dependence on arterial blood pressure

It is shown that the dependence of the cerebral blood flow (CBF) on mean arterial blood pressure (MABP) can be described with a simple model having the following assumptions. Below certain MABP (denoted as MABP1) there are no autoregulatory or feedback mechanisms influencing CBF. Between MABP1 and MABP2 (MABP at which breakthrough accurs) there is a linear (on MABP) dependent feedback with a sloap depending very much on the individual considered. The classical autoregulation model with a plateau in between MABP1 and MABP2 is a particular case of this model. The model describes well the experiments performed on dogs (Harper 1966), for which the individual feedback sloap parameter varied to great extent, indicating the importance of mesurments on individuals against averaged mesurments (or measurments on diffent individuals) which superficially support the classical autoregulation. New effect of decreased CBF, while increasing MABP, was observed.

physics.bio-ph↗

arXiv2011

Mathematical Properties of Pump-Leak Models of Cell Volume Control and Electrolyte Balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.

q-bio.CB↗

arXiv2011

Stimulation of human red blood cells leads to Ca2+-mediated intercellular adhesion

Red blood cells (RBCs) are a major component of blood clots, which form physiologically as a response to injury or pathologically in thrombosis. The active participation of RBCs in thrombus solidification has been previously proposed but not yet experimentally proven. Holographic optical tweezers and single-cell force spectroscopy were used to study potential cell-cell adhesion between RBCs. Irreversible intercellular adhesion of RBCs could be induced by stimulation with lysophosphatidic acid (LPA), a compound known to be released by activated platelets. We identified Ca2+ as an essential player in the signaling cascade by directly inducing Ca2+ influx using A23187. Elevation of the internal Ca2+ concentration leads to an intercellular adhesion of RBCs similar to that induced by LPA stimulation. Using single-cell force spectroscopy, the adhesion of the RBCs was identified to be approximately 100 pN, a value large enough to be of significance inside a blood clot or in pathological situations like the vasco-occlusive crisis in sickle cell disease patients.

physics.bio-ph↗

arXiv2011

A validated model of serum anti-Mullerian hormone from conception to menopause

Background: Anti-Mullerian hormone (AMH) is a product of growing ovarian follicles. The concentration of AMH in blood may also reflect the non-growing follicle (NGF) population, i.e. the ovarian reserve, and be of value in predicting reproductive lifespan. A full description of AMH production up to the menopause has not been reported. Methodology/Principal Findings: By searching the published literature for AMH concentrations in healthy pre-menopausal females, and using our own data (combined n = 3,260) we have generated and robustly validated the first model of AMH concentration from conception to menopause. This model shows that 34% of the variation in AMH is due to age alone. We have shown that AMH peaks at age 24.5 years, followed by a decline to the menopause. We have also shown that there is a neonatal peak and a potential pre-pubertal peak. Our model allows us to generate normative data at all ages. Conclusions/Significance: These data highlight key inflection points in ovarian follicle dynamics. This first validated model of circulating AMH in healthy females describes a transition period in early adulthood, after which AMH reflects the progressive loss of the NGF pool. The existence of a neonatal increase in gonadal activity is confirmed for females. An improved understanding of the relationship between circulating AMH and age will lead more accurate assessment of ovarian reserve for the individual woman.

q-bio.TO↗

arXiv2011

The OPFOS microscopy family: High-resolution optical-sectioning of biomedical specimens

We report on the recently emerging (Laser) Light Sheet based Fluorescence Microscopy field (LSFM). The techniques used in this field allow to study and visualize biomedical objects non-destructively in high-resolution through virtual optical sectioning with sheets of laser light. Fluorescence originating in the cross section of the sheet and sample is recorded orthogonally with a camera. In this paper, the first implementation of LSFM to image biomedical tissue in three dimensions - Orthogonal-Plane Fluorescence Optical Sectioning microscopy (OPFOS) - is discussed. Since then many similar and derived methods have surfaced (SPIM, Ultramicroscopy, HR-OPFOS, mSPIM, DSLM, TSLIM...) which we all briefly discuss. All these optical sectioning methods create images showing histological detail. We illustrate the applicability of LSFM on several specimen types with application in biomedical and life sciences.

physics.ins-det↗

arXiv2011

Realistic 3D computer model of the gerbil middle ear, featuring accurate morphology of bone and soft tissue structures

In order to improve realism in middle ear (ME) finite element modeling (FEM), comprehensive and precise morphological data are needed. To date, micro-scale X-ray computed tomography (μCT) recordings have been used as geometric input data for FEM models of the ME ossicles. Previously, attempts were made to obtain this data on ME soft tissue structures as well. However, due to low X-ray absorption of soft tissue, quality of these images is limited. Another popular approach is using histological sections as data for 3D models, delivering high in-plane resolution for the sections, but the technique is destructive in nature and registration of the sections is difficult. We combine data from high-resolution μCT recordings with data from high-resolution orthogonal-plane fluorescence optical-sectioning microscopy (OPFOS), both obtained on the same gerbil specimen. State-of-the-art μCT delivers high-resolution data on the three-dimensional shape of ossicles and other ME bony structures, while the OPFOS setup generates data of unprecedented quality both on bone and soft tissue ME structures. Each of these techniques is tomographic and non-destructive, and delivers sets of automatically aligned virtual sections. The datasets coming from different techniques need to be registered with respect to each other. By combining both datasets, we obtain a complete high-resolution morphological model of all functional components in the gerbil ME. The resulting three-dimensional model can be readily imported in FEM software and is made freely available to the research community. In this paper, we discuss the methods used, present the resulting merged model and discuss morphological properties of the soft tissue structures, such as muscles and ligaments.

q-bio.TO↗

arXiv2011

Structure and Growth in the Living Tissue and in Carbon Nanotubes

The topological organisation of cells in a model of living tissue (the crypt of intestinal epithelium) is identical to the topological organisation of atoms in carbon nanotubes. The existing models of growth of these two structures contain identical elements. It is proposed that the growth of carbon nanotubes can depend also on other mechanisms postulated in the crypt model where the growth in the bottom is transmitted to the cylinder, and, in this case, the growth of nanotubes should involve the same peculiar lattice transformations as the ones found in the crypt models. The crypt models also suggest a possible initiation of growth in the nanotubes by the loss of carbon atoms. We consider the crystalline structures that can be formed from graphene and the structures of the living tissues as one distinct class of structures.

cond-mat.mes-hall↗