Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues.

UNLABELLED: Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech. MODEL: Mechanobiol. 13 1003-23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material.

A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations.

Instructing others to move is fundamental for many populations, whether animal or cellular. In many instances, these commands are transmitted by contact, such that an instruction is relayed directly (e.g. by touch) from signaller to receiver: for cells, this can occur via receptor-ligand mediated interactions at their membranes, potentially at a distance if a cell extends long filopodia. Given that commands ranging from attractive to repelling can be transmitted over variable distances and between cells of the same (homotypic) or different (heterotypic) type, these mechanisms can clearly have a significant impact on the organisation of a tissue. In this paper, we extend a system of nonlocal partial differential equations (integrodifferential equations) to provide a general modelling framework to explore these processes, performing linear stability and numerical analyses to reveal its capacity to trigger the self-organisation of tissues. We demonstrate the potential of the framework via two illustrative applications: the contact-mediated dispersal of neural crest populations and the self-organisation of pigmentation patterns in zebrafish.

Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion.

The ability to invade tissue is one of the hallmarks of cancer. Cancer cells achieve this through the secretion of matrix degrading enzymes, cell proliferation, loss of cell-cell adhesion, enhanced cell-matrix adhesion and active migration. Invasion of tissue by the cancer cells is one of the key components in the metastatic cascade, whereby cancer cells spread to distant parts of the host and initiate the growth of secondary tumours (metastases). A better understanding of the complex processes involved in cancer invasion may ultimately lead to treatments being developed which can localise cancer and prevent metastasis. In this paper we formulate a novel continuum model of cancer cell invasion of tissue which explicitly incorporates the important biological processes of cell-cell and cell-matrix adhesion. This is achieved using non-local (integral) terms in a system of partial differential equations where the cells use a so-called "sensing radius"R to detect their environment. We show that in the limit as R-->0 the non-local model converges to a related system of reaction-diffusion-taxis equations. A numerical exploration of this model using computational simulations shows that it can form the basis for future models incorporating more details of the invasion process.

Expression of MMP-2, -9 and -13 in cell lines and fresh biopsies of squamous cell carcinomas of the upper aerodigestive tract.

BACKGROUND: The expression patterns of the matrix metalloproteinases (MMP) 2, 9 and 13 have been examined in biopsies and cell lines of squamous cell carcinomas (SCC) of the upper aerodigestive tract to determine the association between MMP expression and the aggressiveness of the tumor. MATERIALS AND METHODS: The expression of MMP-2, -9 and -13 was analyzed by immuno-hybridization in 12 keratinocyte cell lines, 13 SCC cell lines and in 63 biopsies from SCCs of the upper aerodigestive tract. RESULTS: In biopsies a correlation was detected between T-status and the MMP expression [MMP-2 (p < 0.05), MMP-9 (p < 0.01), MMP-13 (p < 0.01)], between N-status and MMP expression [MMP-2 (p < 0.05), MMP-9 (p < 0.01)] and between UICC stage and MMP-9 expression (p < 0.01). CONCLUSION: The MMP-2, MMP-9 and MMP-13 expressions correlate strongly with pathological parameters. The determination of these tumor-biological parameters could help to identify high risk patients with increased frequency of metastatic spread.

[The value of parameters of iron metabolism in the differential diagnosis of anemias]. / Die Wertigkeit von Parametern des Eisenstoffwechsels in der Differentialdiagnose von Anämien.

As a result of investigations into the diagnostic validity of selected haematologic-morphological and clinical-chemical test factors of iron metabolism in the diagnosis of hypochromic anaemia, the examined test faktora are differently evaluated as individual parameters and in their combination. 1. Haematocrit (PCV) is equal to the determination of haemoglobin concentration as a search parameter. 2. The number of reticulocytes, copper and zinc as well as caeruloplasmin have a separating effect as individual parameters on the examined classes of iron deficiency and tumour and infect anaemia. 3. Iron has no value as a individual parameter. It is only in combination with TEBK and the haematologic test factors that is has a diagnostic value. 4. In contrast, ferritin as an individual parameter is of primary importance and should be used extensively in the laboratory diagnosis of hypochromic anaemia. 5. TEBK and transferrin may be supposed to be equal in their diagnostic value. 6. When used in combination, haemoglobin, MCV, TEBK, Transferrin, and ferritin have effective separating function. They permit hypochromic anaemia to be widely assigned to one or another kind of the examined classes.

[Optimizing the diagnosis of anemia]. / Optimierung der Diagnostik von Anämien.

The specific value of the erythrocyte parameters MCH and MCV for the differential-diagnostic arrangement of anaemias to the use of the haematological automations of analysis PHA 1/2 is represented. A prerequisite is the precise determination of haemoglobin concentration and erythrocyte number. MCHC has no sufficient discriminatory capacity.