A multiphase multiscale model for nutrient-limited tissue growth, Part II: a simplified description

In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions. doi:10.1017/S1446181119000130

A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT-LIMITED TISSUE GROWTH, PART II: A SIMPLIFIED DESCRIPTION

In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.

A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT LIMITED TISSUE GROWTH

We derive an effective macroscale description for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics. In particular, the resulting description admits both interstitial growth and active cell motion. This model comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled with Stokes-type cell problems on the microscale, incorporating dependence on active cell motion and pore scale structure. The cell problems provide the permeability tensors with which the macroscale flow is parameterised. A subset of solutions is illustrated by numerical simulations.

Heterogeneity is key to hydrogel-based cartilage tissue regeneration

A combined computational-experimental approach showing the importance of heterogeneity in hydrogel properties and cell distribution, for the interstitial growth of cartilage.

TINJAUAN HISTOLOGIK TULANG RAWAN

Cartilage belongs to the suppportive tissue which is relatively dense. In an adult, this tissue is only found in two areas: extraskeletal cartilage and joints. During chondrogenesis in an embryo, messenchymal cells round up, retract their extensions, multiply rapidly, and form cellular condensation, cartilage formation area. The development of this ares occurs in two mechanisms: interstitial growth and apppositional growth. Injured cartilage will be repaired by the perichondrium. Its cells tend to fill spaces or deffects meanwhile chondrogenic cells of the perichondrium will undergone proliferation and differentiation to become chondroblast which produces new matrix.Keywords: cartilage, types of cartilageAbstrak: Tulang rawan merupakan jaringan ikat penahan berat yang relatif padat, tetapi tidak sekuat tulang. Dalam kehidupan pasca lahir, jaringan ini hanya ditemukan pada dua jenis tempat sesudah tidak tumbuh lagi, yaitu pada sejumlah bangunan tulang rawan ekstra-skeletal yang terdapat dalam tubuh dan pada persendian. Pada tempat pembentukan tulang rawan embrio, sel-sel mesenkim menyusutkan cabang-cabangnya dan mengumpul dalam agregasi padat yang dikenal sebagai pusat kondrifikasi. Pertumbuhan dalam perluasan pusat kondrifikasi terjadi melalui dua mekanisme berbeda, yaitu: pertumbuhan interstitial dan pertumbuhan aposisional. Cedera tulang rawan akibat trauma akan diperbaiki oleh perikondrium. Sel-sel perikondrium cenderung untuk mengisi kekosongan atau defek, sedangkan sel-sel kondrogenik dalam perikondrium akan berproliferasi dan berdiferensiasi menjadi kondroblas yang menghasilkan matriks baru.Kata kunci: kartilago, jenis kartilago