Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat