Governing equations of tissue modelling and remodelling: A unified generalised description of surface and bulk balance

Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old tissue material properties with newly formed, immature tissue properties. As a result, tissues are made up of different "patches", i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries. In this paper, generalised equations governing the spatio-temporal evolution of such tissues are developed within the continuum model. These equations take into account nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces, and bulk balance due to tissue maturation. These equations make it possible to model patchy tissue states and their evolution without explicitly maintaining a record of when/where resorption and formation processes occurred. The time evolution of spatially averaged tissue properties is derived systematically by integration. These spatially-averaged equations cannot be written in closed form as they retain traces that tissue destruction is localised at tissue boundaries. The formalism developed in this paper is applied to bone tissues, which exhibit strong material heterogeneities due to their slow mineralisation and remodelling processes. Evolution equations are proposed in particular for osteocyte density and bone mineral density. Effective average equations for bone mineral density (BMD) and tissue mineral density (TMD) are derived using a mean-field approximation. The error made by this approximation when remodelling patchy tissue is investigated. The specific time signatures of BMD or TMD during remodelling events may provide a way to detect these events occurring at lower, unseen spatial resolutions from microCT scans.Comment: 14 pages, 8 figures. V2: minor stylistic changes, more detailed derivation of Eqs (30)-(31), additional comments on implication of BMD and TMD signatures for microCT scan

Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix

The formation of new bone involves both the deposition of bone matrix, and the formation of a network of cells embedded within the bone matrix, called osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that become buried in bone matrix during bone deposition. The generation of osteocytes is a complex process that remains incompletely understood. Whilst osteoblast burial determines the density of osteocytes, the expanding network of osteocytes regulates in turn osteoblast activity and osteoblast burial. In this paper, a spatiotemporal continuous model is proposed to investigate the osteoblast-to-osteocyte transition. The aims of the model are (i) to link dynamic properties of osteocyte generation with properties of the osteocyte network imprinted in bone, and (ii) to investigate Marotti's hypothesis that osteocytes prompt the burial of osteoblasts when they become covered with sufficient bone matrix. Osteocyte density is assumed in the model to be generated at the moving bone surface by a combination of osteoblast density, matrix secretory rate, rate of entrapment, and curvature of the bone substrate, but is found to be determined solely by the ratio of the instantaneous burial rate and matrix secretory rate. Osteocyte density does not explicitly depend on osteoblast density nor curvature. Osteocyte apoptosis is also included to distinguish between the density of osteocyte lacuna and the density of live osteocytes. Experimental measurements of osteocyte lacuna densities are used to estimate the rate of burial of osteoblasts in bone matrix. These results suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the control of osteoblast burial by osteocytes is likely to emanate as a collective signal from a large group of osteocytes, rather than from the osteocytes closest to the bone deposition front.Comment: 11 pages, 6 figures. V2: substantially augmented version. Addition of Section 4 (osteocyte apoptosis

Lessons Learned from a 10-Year Collaboration between Engineering and Industrial Design Students in Capstone Design Projects

Engineers and industrial designers have different approaches to problem solving. Both place heavy emphasis on identification of customer needs, manufacturing methods, and prototyping. Industrial designers focus on aesthetics, ergonomics, ease of use, and the user’s experience. They tend to be more visual and more concerned with the interaction between users and products. Engineers focus on functionality, performance requirements, analytical modeling, and design verification and validation. They tend to be more analytical and more concerned with the design of internal components and product performance. Engineers and industrial designers often work together on project teams in industry. Collaboration between the two groups on senior capstone design projects can teach each to respect and value the unique contributions each brings to the project team, result in improved design solutions, and help prepare students for future collaboration in industry. Student feedback and lessons learned by faculty and students from a ten-year collaboration between engineering and industrial design students from Marquette University and the Milwaukee Institute of Art and Design, respectively, are presented. Students learned to communicate with people in other disciplines, appreciate the complementary skills of each discipline, and value different approaches to problem solving

Lessons Learned from a 10-Year Collaboration Between Biomedical Engineering and Industrial Design Students in Capstone Design Projects

Engineers and industrial designers have different approaches to problem solving. Both place heavy emphasis on identification of customer needs, manufacturing methods, and prototyping. Industrial designers focus on aesthetics, ergonomics, ease of use, manufacturing methods, and the user’s experience. They tend to be more visual and more concerned with the interaction between users and products. Engineers focus on functionality, performance requirements, analytical modeling, and design verification and validation. They tend to be more analytical and more concerned with the design of internal components and product performance. Engineers and industrial designers often work together on project teams in industry. Collaboration between the two groups on senior capstone design projects can teach each to respect and value the unique contributions each brings to the project team, result in improved design solutions, and help prepare students for future collaboration in industry. Student feedback and lessons learned by faculty and students from a ten-year collaboration between engineering and industrial design students from Marquette University and the Milwaukee Institute of Art and Design, respectively, are presented. Students learned to communicate with people in other disciplines, appreciate the complementary skills of each discipline, and value different approaches to problem solving

Relaxation of hole spins in quantum dots via two-phonon processes

We investigate theoretically spin relaxation in heavy hole quantum dots in low external magnetic fields. We demonstrate that two-phonon processes and spin-orbit interaction are experimentally relevant and provide an explanation for the recently observed saturation of the spin relaxation rate in heavy hole quantum dots with vanishing magnetic fields. We propose further experiments to identify the relevant spin relaxation mechanisms in low magnetic fields.Comment: 5 pages, 2 figure

THE EFFECTS OF ALTERNATIVE SEASONAL PRICE DIFFERENTIALS ON MILK PRODUCTION IN NEW YORK

Uneven monthly milk production (seasonality) is a major problem in the New York dairy industry. This article estimates expected monthly milk production response to a set of hypothetical seasonal price differentials designed to reduce the degree of seasonality. The analysis is based on a random mail survey and farm record data. The results indicate that a seasonal price differential of $1.12 per cwt. (over three times the current differential) would be necessary to completely balance spring and fall production in New York, based on the perceptions of farmers surveyed. Also, producers with better managerial skills are shown to be able to reduce their seasonality at a significantly lower price differential than less skilled farm managers.Livestock Production/Industries,

Osteoblasts infill irregular pores under curvature and porosity controls: A hypothesis-testing analysis of cell behaviours

The geometric control of bone tissue growth plays a significant role in bone remodelling, age-related bone loss, and tissue engineering. However, how exactly geometry influences the behaviour of bone-forming cells remains elusive. Geometry modulates cell populations collectively through the evolving space available to the cells, but it may also modulate the individual behaviours of cells. To factor out the collective influence of geometry and gain access to the geometric regulation of individual cell behaviours, we develop a mathematical model of the infilling of cortical bone pores and use it with available experimental data on cortical infilling rates. Testing different possible modes of geometric controls of individual cell behaviours consistent with the experimental data, we find that efficient smoothing of irregular pores only occurs when cell secretory rate is controlled by porosity rather than curvature. This porosity control suggests the convergence of a large scale of intercellular signalling to single bone-forming cells, consistent with that provided by the osteocyte network in response to mechanical stimulus. After validating the mathematical model with the histological record of a real cortical pore infilling, we explore the infilling of a population of randomly generated initial pore shapes. We find that amongst all the geometric regulations considered, the collective influence of curvature on cell crowding is a dominant factor for how fast cortical bone pores infill, and we suggest that the irregularity of cement lines thereby explains some of the variability in double labelling data as well as the overall speed of osteon infilling.Comment: 14 pages, 11 figures, Appendi