Complex Biomechanics: From Atoms to Patients

Complex systems are characterized by an overall behavior which is different from that of the components making up the systems - hence, (nonlinear) interactions between the components play a very important role. Taking an interdisciplinary approach rooted in theoretical and applied mechanics and engineering mechanics, we report on two types of recently studied systems where individual system components (atoms and patients) interact in a way which unfolds very interesting emerging patterns that can be mathematically quantified through concepts arising from (bio-)mechanics: (i) the interaction of atoms within a short thread of DNA, which, as a compound, result in a family of a highly nonlinear beam structures with varying, but always coupled torsion-stretching modes [1]; (ii) the compliance of sets of patients to the lethal effect of SARS-COV-2 [2,3], which follows integro-differential equations reminiscent of those introduced by Boltzmann in the context of creep (or hereditary) mechanics [4]. We conclude that smart classical concepts of applied mechanics and physics continue to show an unparalleled potential for solving pressing global problems in the context of computational modelling of living systems.<br/>References:<br/>J. Kalliauer, G. Kahl, S. Scheiner, Ch. Hellmich, A new approach to the mechanics of DNA, <i>J Mech Phys Sol</i> 143, 104040, 2020.<br/>S. Scheiner, N. Ukaj, Ch. Hellmich, Mathematical modeling of COVID-19 fatality trends: death kinetics law versus infection-to-death delay rule, <i>Chaos, Solitons & Fractals</i> 136, 109891, 2020.<br/>N. Ukaj, S. Scheiner, Ch. Hellmich, Toward "hereditary epidemiology": a temporal Boltzmann approach to COVID-19 fatality trends, <i>Applied Physics Reviews</i>, 8, 041417, 2021.<br/>H. Markovits, Boltzmann and the Beginnings of Linear Viscoelasticity, <i>Transactions of the Society of Rheology</i> 21, 381-398, 1977.