A review on design of scaffold for osteoinduction: Toward the unification of independent design variables

摘要

Abstract Biophysical stimulus quantifies the osteoinductivity of the scaffold concerning the mechanoregulatory mathematical models of scaffold-assisted cellular differentiation. Consider a set of independent structural variables ($) that comprises bulk porosity levels (φdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$varphi$$end{document}) and a set of morphological features of the micro-structure (Fdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal{F}$$end{document}) associated with scaffolds, i.e., $=φ∪Fdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$$ = left( {varphi cup mathcal{F}} right)$$end{document}. The literature suggests that biophysical stimulus (Sdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S$$end{document}) is a function of independent structural variables ($). Limited understanding of the functional correlation between biophysical stimulus and structural features results in the lack of the desired osteoinductivity in a scaffold. Consequently, it limits their broad applicability to assist bone tissue regeneration for treating critical-sized bone fractures. The literature indicates the existence of multi-dimensional independent design variable space as a probable reason for the general lack of osteoinductivity in scaffolds. For instance, known morphological features are the size, shape, orientation, continuity, and connectivity of the porous regions in the scaffold. It implies that the number of independent variables (ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document}) is more than two, i.e., n≥2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n ge 2$$end{document}, which interact and influence the magnitude of Sdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S$$end{document} in a unified manner. The efficiency of standard engineering design procedures to analyze the correlation between dependent variable (Sdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S$$end{document}) and independent variables ($) in 3D mutually orthogonal Cartesian coordinate system diminishes proportionally with the increase in the number of independent variables (ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document}) (Deb in Optimization for engineering design—algorithms and examples, PHI Learning Private Limited, New Delhi, 2012). Therefore, there is an immediate need to devise a fr