Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Molecular dynamics investigation on shearing between osteopontin and hydroxyapatite in biological materials

Bone, a hard biological material, possesses a combination of high stiffness and toughness, even though the main basic building blocks of bone are simply mineral platelets and protein molecules. Bone has a very complex microstructure with at least seven hierachical levels. This unique material characteristic attracts great attention, but the deformation mechanisms in bone have not been well understood. Simulation at nano-length scale such as molecular dynamics (MD) is proven to be a powerful tool to investigate bone nanomechanics for developing new artificial biological materials. This study focuses on the ultra large and thin layer of extrafibrillar protein matrix (thickness = ~ 1 nm) located between mineralized collagen fibrils (MCF). Non-collagenous proteins such as osteopontin (OPN) can be found in this protein matrix, while MCF consists mainly of hydroxyapatite (HA) nanoplatelets (thickness = 1.5 – 4.5 nm). By using molecular dynamics method, an OPN peptide was pulled between two HA mineral platelets with water in presence. Periodic boundary condition (PBC) was applied. The results indicate that the mechanical response of OPN peptide greatly depends on the attractive electrostatics interaction between the acidic residues in OPN peptide and HA mineral surfaces. These bonds restrict the movement of OPN peptide, leading to a high energy dissipation under shear loading.

A non-resonant mass sensor to eliminate the ``missing mass'' effect during mass measurement of biological materials

Resonant sensors and crystal oscillators for mass detection need to be excited at very high natural frequencies (MHz). Use of such systems to measure mass of biological materials affects the accuracy of mass measurement due to their viscous and/or viscoelastic properties. The measurement limitation of such sensor system is the difficulty in accounting for the ``missing mass'' of the biological specimen in question. A sensor system has been developed in this work, to be operated in the stiffness controlled region at very low frequencies as compared to its fundamental natural frequency. The resulting reduction in the sensitivity due to non-resonant mode of operation of this sensor is compensated by the high resolution of the sensor. The mass of different aged drosophila melanogaster (fruit fly) is measured. The difference in its mass measurement during resonant mode of operation is also presented. That, viscosity effects do not affect the working of this non-resonant mass sensor is clearly established by direct comparison. (C) 2014 AIP Publishing LLC.

Biological materials in colorectal surgery: current applications and potential for the future.

Biological materials are increasingly used in abdominal surgery for ventral, pelvic and perineal reconstructions, especially in contaminated fields. Future applications are multi-fold and include prevention and one-step closure of infected areas. This includes prevention of abdominal, parastomal and pelvic hernia, but could also include prevention of separation of multiple anastomoses, suture- or staple-lines. Further indications could be a containment of infected and/or inflammatory areas and protection of vital implants such as vascular grafts. Reinforcement patches of high-risk anastomoses or unresectable perforation sites are possibilities at least. Current applications are based mostly on case series and better data is urgently needed. Clinical benefits need to be assessed in prospective studies to provide reliable proof of efficacy with a sufficient follow-up. Only superior results compared with standard treatment will justify the higher costs of these materials. To date, the use of biological materials is not standard and applications should be limited to case-by-case decision.

Dielectric properties of certain biological materials at microwave frequencies.

In the medical field, microwaves play a larger role for treatment than diagnosis. For the detection of diseases by microwave methods, it is essential to know the dielectric properties of biological materials. For the present study, a cavity perturbation technique was employed to determine the dielectric properties of these materials. Rectangular cavity resonators were used to measure the complex permittivity of human bile, bile stones, gastric juice and saliva. The measurements were carried out in the S and J bands. It is observed that normal and infected bile have different dielectric constant and loss tangent. Dielectric constant of infected bile and gastric juice varies from patient to patient. Detection and extraction of bile stone with possible method of treatment is also discussed.

Molecular depth profiling of organic and biological materials

Atomic depth profiling using secondary ion mass spectrometry, SIMS, is common in the field micro-electronics; however, the generation of molecular information as a function of sample depth is difficult due to the accumulation of damage both on and beneath the sample surface. The introduction of polyatomic ion beams such as SF₅ and C₆₀ have raised the possibility of overcoming this problem as they deposit the majority of their energy in the upper surface of the sample resulting in increased sputter yields but with a complimentary reduction in sub-surface damage accumulation. In this paper we report the depth profile analysis of the bio-polymer polycaprolactone, PCL, using the polyatomic ions Au₃⁺ and C₆₀⁺ and the monoatomic Au+. Results are compared to recent analysis of a similar sample using . depth profiling of cellulose is also demonstrated, an experiment that has been reported as unsuccessful when attempted with implications for biological analysis are discussed.

Solids rheology for dehydrated food and biological materials

Mechanical properties of food products and biological materials are greatly affected by the drying process and are considered one of the most important quality attributes of dehydrated products. The aim of this work was to review theoretical principles and mathematical modeling, analyzing the measurement techniques and major experimental results that exist in the literature about rheological properties of dehydrated foods and biological materials. Different methods of measuring rheological parameters (fundamental and empiric or imitative) are discussed and major experimental results, as well as the rheological models used in their analysis, published in recent years are presented.

Dielectric relaxation in biological materials

The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important in order to explain various phenomena in Solid-State Physics and in Physics of Biological Materials. Indeed, during the last two centuries, many scientists have tried to explain and model the dielectric relaxation. Starting from the Kohlrausch model and passing through the ideal Debye one, they arrived at more com- plex models that try to explain the experimentally observed distributions of relaxation times, including the classical (Cole-Cole, Davidson-Cole and Havriliak-Negami) and the more recent ones (Hilfer, Jonscher, Weron, etc.). The purpose of this thesis is to discuss a variety of models carrying out the analysis both in the frequency and in the time domain. Particular attention is devoted to the three classical models, that are studied using a transcendental function known as Mittag-Leffler function. We highlight that one of the most important properties of this function, its complete monotonicity, is an essential property for the physical acceptability and realizability of the models. Lo studio delle proprietà dielettriche riguarda l’immagazzinamento e la dissipazione di energia elettrica e magnetica nei materiali. I dielettrici sono importanti al fine di spiegare vari fenomeni nell’ambito della Fisica dello Stato Solido e della Fisica dei Materiali Biologici. Infatti, durante i due secoli passati, molti scienziati hanno tentato di spiegare e modellizzare il rilassamento dielettrico. A partire dal modello di Kohlrausch e passando attraverso quello ideale di Debye, sono giunti a modelli più complessi che tentano di spiegare la distribuzione osservata sperimentalmente di tempi di rilassamento, tra i quali modelli abbiamo quelli classici (Cole-Cole, Davidson-Cole e Havriliak-Negami) e quelli più recenti (Hilfer, Jonscher, Weron, etc.). L’obiettivo di questa tesi è discutere vari modelli, conducendo l’analisi sia nel dominio delle frequenze sia in quello dei tempi. Particolare attenzione è rivolta ai tre modelli classici, i quali sono studiati utilizzando una funzione trascendente nota come funzione di Mittag-Leffler. Evidenziamo come una delle più importanti proprietà di questa funzione, la sua completa monotonia, è una proprietà essenziale per l’accettabilità fisica e la realizzabilità dei modelli.

Biological materials : Part A. tuning LCST of raft copolymers and gold/copolymer hybrid nanoparticles and Part B. biobased nanomaterials

The research described in this dissertation is comprised of two major parts. The first part studied the effects of asymmetric amphiphilic end groups on the thermo-response of diblock copolymers of (oligo/di(ethylene glycol) methyl ether (meth)acrylates, OEGA/DEGMA) and the hybrid nanoparticles of these copolymers with a gold nanoparticle core. Placing the more hydrophilic end group on the more hydrophilic block significantly increased the cloud point compared to a similar copolymer composition with the end group placement reversed. For a given composition, the cloud point was shifted by as much as 28 °C depending on the placement of end groups. This is a much stronger effect than either changing the hydrophilic/hydrophobic block ratio or replacing the hydrophilic acrylate monomer with the equivalent methacrylate monomer. The temperature range of the coil-globule transition was also altered. Binding these diblock copolymers to a gold core decreased the cloud point by 5-15 °C and narrowed the temperature range of the coil-globule transition. The effects were more pronounced when the gold core was bound to the less hydrophilic block. Given the limited numbers of monomers that are approved safe for in vivo use, employing amphiphilic end group placement is a useful tool to tune a thermo-response without otherwise changing the copolymer composition. The second part of the dissertation investigated the production of value-added nanomaterials from two biorefinery “wastes”: lignin and peptidoglycan. Different solvents and spinning methods (melt-, wet-, and electro-spinning) were tested to make lignin/cellulose blended and carbonized fibers. Only electro-spinning yielded fibers having a small enough diameter for efficient carbonization ( Peptidoglycan (a bacterial cell wall material) was copolymerized with poly-(3-hydroxybutyrate), a common polyhydroxyalkanoate produced by bacteria with the objective of determining if a useful material could be obtained with a less rigorous work-up on harvesting polyhydroxyalkanoates. The copolyesteramide product having 25 wt.% peptidoglycan from a highly purified peptidoglycan increased thermal stability by 100-200 °C compared to the poly-(3-hydroxybutyrate) control, while a less pure peptidoglycan, harvested from B. megaterium (ATCC 11561), gave a 25-50 °C increase in thermal stability. Both copolymers absorbed more moisture than pure poly-(3-hydroxybutyrate). The results suggest that a less rigorously harvested and purified polyhydroxyalkanoate might be useful for some applications.