Francesco Mollica

On the mechanics of a growing tumor

In this paper we study tumor growth within the framework of Continuum Mechanics, considering a tumor as a specific case of a growing soft tissue. Using the notion of multiple natural configurations we introduce a mechanical description that splits volumetric growth and mechanical response into two separate contributions. Growth is described as an increase of the mass of the particles of the body and not as an increase of their number. As tumor growth strongly depends upon the availability of nutrients and on the presence of chemical signals, such as growth factors, their diffusion through the growing material is introduced in the description. The model is then applied to describe the homogeneous growth inside a rigid cylinder, a model mimicking the growth of a ductal carcinoma, and to the growth of a multicell spheroid fed by a non-homogeneous diffusion of nutrients. In the latter case residual stresses are generated because the non-uniform distribution of nutrients leads to inhomogeneous growth.

Dynamic Co-Seeding of Osteoblast and Endothelial Cells on 3D Polycaprolactone Scaffolds for Enhanced Bone Tissue Engineering

Tissue engineered scaffolds must have an organized and repeatable microstructure which enables cells to assemble in an ordered matrix that allows adequate nutriental perfusion. In this work, to evaluate the reciprocal cell interactions of endothelial and osteoblast-like cells, human osteoblast-like cells (MG63) and Human Umbilical Vein Endothelial Cells (HUVEC) were co-seeded onto 3D geometrically controlled porous poly(ε-caprolactone) (PCL) and cultured by means of a rotary cell culture system (RCCS-4DQ). In our dynamic co-culture system, the lack of significant enhancement of osteoblast ALP activity and ECM production indicated that the microgravity conditions of the rotary system affected the cells by favoring their proliferation and cellular cross-talk. These results emphasize how osteoblasts increase endothelial cell proliferate and endothelial cells amplify the growth of osteoblasts but decrease their differentiation. This dynamic seeding of osteoblasts and endothelial cells onto a 3D polymeric scaffold may represent a unique approach for studying the mechanisms of interaction of endothelial and osteoblast cells as well as achieve a functional hybrid in which angiogenesis, furnished by neo-vascular organization of endothelial cells may further support osteoblasts growth. Furthermore, this in vitro model may be useful in examining the applicability of novel material structures for tissue engineering.

A model for temporal heterogeneities of tumor blood flow.

Tumor blood flow (TBF) plays a fundamental role in tumor growth and treatment, and is characterized by spatial and temporal heterogeneities. Here we show that the interstitial fluid pressure (IFP), which is higher in tumoral tissue than in normal tissue, coupled with the tumor microvascular pressure (MVP) and the higher permeability of tumoral vessels, can explain the sustained oscillatory behavior of TBF, observed in vivo.

The inelastic behavior of metals subject to loading reversal

Abstract One of the consequences of memory effects in the plastic deformation of metals is the Bauschinger effect (Civilingenieur 27 (1881) 289–348), which manifests itself as a difference in the values of the yield stress in tension and compression for a material that has undergone plastic deformation. The Bauschinger effect has been modeled with the kinematic hardening rules e.g., Ziegler (Quart. Appl. Math. 17 (1959) 55) and Chaboche (Int. J. Plasticity 2 (1986) 149). These models, though, are not able to reproduce the stress-strain response accurately at points of loading reversal: it has been observed (Acta Metall. 34 (1986) 1553; Mater. Sci. Engineering A113 (1989) 441) that, for some materials, the stress has a plateau after the loading is reversed. This is not reflected by the kinematic hardening rule nor by its modifications. In this paper we will develop a general three dimensional model that is able to reproduce the stress–strain response at loading reversals and can be applied also to more general changes of loading direction. The central idea of our model is to link the hardening behavior of the material to thermodynamical quantities such as the stored energy due to cold work and the rate of dissipation. The predictions of the theory show good agreement with the stress–strain curve and also with the manner in which the stored energy varies with the inelastic strain, as obtained from experiments (Progress in Materials Science (1973) Vol. 17. Pergamon, Oxford; Trans. Met. Soc. AIME 224 (1962) 719).

Load deflection characteristics and force level of nickel titanium initial archwires

OBJECTIVES To investigate and compare the characteristics of commonly used types of traditional and heat-activated initial archwire by plotting their load/deflection graphs and quantifying three suitable parameters describing the discharge plateau phase. MATERIALS AND METHODS Forty-eight archwires (22 nickel titanium [NiTi] and 26 heat-activated) of cross-sectional diameter ranging from 0.010 to 0.016 inch were obtained from seven different manufacturers. A modified three-point wire-bending test was performed on three analogous samples of each type of archwire at a constant temperature (37.0°C). For each resulting load/deflection curve, the plateau section was isolated, along with the mean value of the average plateau force, the plateau length, and the plateau slope for each type of wire obtained. RESULTS Statistically significant differences were found between almost all wires for the three parameters considered. Statistically significant differences were also found between traditional and heat-activated archwires, the latter of which generated longer plateaus and lighter average forces. The increase in average force seen with increasing diameter tended to be rather stable, although some differences were noted between traditional and heat-activated wires. CONCLUSIONS Although great variation was seen in the plateau behavior, heat-activated versions appear to generate lighter forces over greater deflection plateaus. On average, the increase in plateau force was roughly 50% when the diameter was increased by 0.002 inch (from 0.012 to 0.014 and from 0.014 to 0.016 inch) and about 150% when the diameter was increased by 0.004 inch (from 0.012 to 0.016), with differences between traditional and heat-activated wires noted in this case.

Dynamic mechanical behavior of PMMA based bone cements in wet environment

The mechanical properties of three wet commercial bone cements, namely Braxel (from Bioland®), Simplex-P (from Howmedica®) and CMW1-G (from DePuy®) are investigated by means of stress relaxation and dynamic mechanical analysis (DMA). The geometry of loading that was used is the three point bending method (ASTM D790); all the tests were performed in a water chamber by means of temperature sweeps between 17 and 57 °C and spanning four frequency decades. The results show that viscoelastic properties are strongly dependent on specimen conditioning (i.e. water uptake and heat treatment). The results also show that all the cements that were analyzed show mechanical properties which are intermediate between the ones of the cancellous bone and of the metals of which prostheses are normally made. As a consequence, the cement is able to reduce the stress concentrations due to the interfacing of materials which have very different stiffnesses. Moreover, the results of the DMA, particularly the ones concerning the damping factor (tan δ), indicate that at body temperature the bone cements tested show an increased capacity of dissipation, the higher is the loading frequency, thus displaying shock absorbing properties.

Secondary flows due to axial shearing of a third grade fluid between two eccentrically placed cylinders

Abstract In general, purely axial flows of non-Newtonian fluids are not possible in straight pipes of non-circular cross section. The secondary flow pattern for the flow of various non-Newtonian fluids in pipes of non-circular cross section has been studied by many authors. The method which is used is invariably a perturbation technique using either the driving force for the problem or one of the material constants as the parameter for the expansion. The former implies that the solution is a perturbation of the state of rest, while the latter implies that the null solution corresponds to the Newtonian solution. However, in many problems of practical relevance, flows of a particular non-Newtonian fluid, with specific values for the non-Newtonian parameters (not necessarily small), take place under a finite driving force, making such approaches of dubious value. For instance, as a consequence of perturbing in the driving force, the secondary flows appear only at the fourth order. In this paper we use a perturbation technique in which the perturbation parameter is a geometric measure of the departure from the geometry in which rectilinear flow is possible. Such an approach allows one to study perturbation of flows which are not the null state, and this, in turn, leads to secondary flows at first order.

Optimal Palatal Configuration for Miniscrew Applications

OBJECTIVE To test the hypothesis that palatal bone is not able to support titanium miniscrews (11 mm in length and 2 mm in diameter) when subjected to forces normally generated during orthodontic treatment. MATERIALS AND METHODS The miniscrew-palatal bone system was modeled and analyzed using the commercial finite element method software ANSYS Multiphysics 10.0; tests were done in both a state of total osseointegration and in the absence of it. Calculations were carried out in both cases in configurations where the miniscrew was inserted into two different palatal regions: in the first it was anchored in one layer of cortical bone and in the underlying trabecular bone; in the second, two layers of cortical bone and the trabecular bone in between were involved. Two different loads were taken into account, 240 gf and 480 gf, both of which are within the normal range for orthodontic treatment, and applied to the miniscrew heads. RESULTS The results demonstrated that the miniscrew inserted into the palate can be anchored to bone and loaded within normal orthodontic force range without exceeding the stress levels that lead to bone fracture. The osseointegrated system was characterized by a lower level of stress than the nonosseointegrated one, but anchorage within the second layer of cortical bone markedly reduced the stress on the trabecular bone, thereby improving the stability of the implant, also in the absence of osseointegration. CONCLUSIONS The hypothesis is rejected. Miniscrews loaded within the normal orthodontic force range do not exceed the stress levels that lead to bone fracture.

The effect of temperature on the mechanical behavior of nickel-titanium orthodontic initial archwires

OBJECTIVES To investigate and compare the characteristics of commonly used types of traditional and heat-activated initial archwires at different temperatures by plotting their load/deflection graphs and quantifying three parameters describing the discharge plateau phase. MATERIALS AND METHODS Forty-eight archwires of cross-sectional diameters ranging from 0.010 inches to 0.016 inches were obtained from seven different manufacturers. A modified three-point wire-bending test was performed on three analogous samples of each type of archwire at 55°C and 5°C, simulating an inserted archwire that is subjected to cold or hot drinks during a meal. For each resulting load/deflection curve the plateau section was isolated and the mean value of each parameter for each type of wire was obtained. RESULTS Permanent strain was exhibited by all wires tested at 55°C. Statistically significant differences were found between almost all wires for the three considered parameters when tested at 55°C and 5°C. Loads were greater at 55°C than at 5°C. Differences were also found between traditional and heat-activated archwires, the latter of which generated longer plateaus at 55°C, shorter plateaus at 5°C, and lighter mean forces at both temperatures. The increase in average force seen with increasing diameter tended to be rather stable at both temperatures. CONCLUSIONS All nickel-titanium wires tested showed a significant change related to temperature in terms of behavior and force for both traditional and heat-activated wires. Stress under high temperatures can induce permanent strain, whereas the residual strain detected at low temperatures can be recovered from as temperature increases.

Mechanical Properties of Human Mineralized Connective Tissues

Experimental work has to be tightly linked with modeling. In fact, successful modeling requires firstly comparison with experiments in order to verify its predictions or to set its range of validity. Secondly, experiments measuring the mechanical properties of tissues are needed as input to calibrate mechanical models of organs that can be used to run simulations in silico. In this chapter we wish to provide a comprehensive literature review covering the mechanical characterization of hard tissues, in particular compact bone, trabecular bone and dentine