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.

Subjective blur limits for cylinder

Purpose: To compare subjective blur limits for cylinder and defocus. ---------- Method: Blur was induced with a deformable, adaptive-optics mirror when either the subjects’ own astigmatisms were corrected or when both astigmatisms and higher-order aberrations were corrected. Subjects were cyclopleged and had 5 mm artificial pupils. Black letter targets (0.1, 0.35 and 0.6 logMAR) were presented on white backgrounds. Results: For ten subjects, blur limits were approximately 50% greater for cylinder than for defocus (in diopters). While there were considerable effects of axis for individuals, overall this was not strong, with the 0° (or 180°) axis having about 20% greater limits than oblique axes. In a second experiment with text (equivalent in angle to N10 print at 40 cm distance), cylinder blur limits for 6 subjects were approximately 30% greater than those for defocus; this percentage was slightly smaller than for the three letters. Blur limits of the text were intermediate between those of 0.35 logMAR and 0.6 logMAR letters. Extensive blur limit measurements for one subject with single letters did not show expected interactions between target detail orientation and cylinder axis. ---------- Conclusion: Subjective blur limits for cylinder are 30%-50% greater than those for defocus, with the overall influence of cylinder axis being 20%.

Subjective blur limits for higher order aberrations

Purpose: We compared subjective blur limits for defocus and the higher-order aberrations of coma, trefoil, and spherical aberration. ---------- Methods: Spherical aberration was presented in both Zernike and Seidel forms. Black letter targets (0.1, 0.35, and 0.6 logMAR) on white backgrounds were blurred using an adaptive optics system for six subjects under cycloplegia with 5 mm artificial pupils. Three blur criteria of just noticeable, just troublesome, and just objectionable were used.---------- Results: When expressed as wave aberration coefficients, the just noticeable blur limits for coma and trefoil were similar to those for defocus, whereas the just noticeable limits for Zernike spherical aberration and Seidel spherical aberration (the latter given as an “rms equivalent”) were considerably smaller and larger, respectively, than defocus limits.---------- Conclusions: Blur limits increased more quickly for the higher order aberrations than for defocus as the criterion changed from just noticeable to just troublesome and then to just objectionable.

Multiple indicators of ambient and personal ultraviolet radiation exposure and risk of non-Hodgkin lymphoma (United States)

Recent epidemiologic studies have suggested that ultraviolet radiation (UV) may protect against non-Hodgkin lymphoma (NHL), but few, if any, have assessed multiple indicators of ambient and personal UV exposure. Using the US Radiologic Technologists study, we examined the association between NHL and self-reported time outdoors in summer, as well as average year-round and seasonal ambient exposures based on satellite estimates for different age periods, and sun susceptibility in participants who had responded to two questionnaires (1994–1998, 2003–2005) and who were cancer-free as of the earlier questionnaire. Using unconditional logistic regression, we estimated the odds ratio (OR) and 95% confidence intervals for 64,103 participants with 137 NHL cases. Self-reported time outdoors in summer was unrelated to risk. Lower risk was somewhat related to higher average year-round and winter ambient exposure for the period closest in time, and prior to, diagnosis (ages 20–39). Relative to 1.0 for the lowest quartile of average year-round ambient UV, the estimated OR for successively higher quartiles was 0.68 (0.42–1.10); 0.82 (0.52–1.29); and 0.64 (0.40–1.03), p-trend = 0.06), for this age period. The lower NHL risk associated with higher year-round average and winter ambient UV provides modest additional support for a protective relationship between UV and NHL.

Vitamin D intake needed to maintain target serum 25-Hydroxyvitamin D concentrations in participants with low sun exposure and dark skin pigmentation is substantially higher than current recommendations

Cutaneous cholecalciferol synthesis has not been considered in making recommendations for vitamin D intake. Our objective was to model the effects of sun exposure, vitamin D intake, and skin reflectance (pigmentation) on serum 25-hydroxyvitamin D (25[OH]D) in young adults with a wide range of skin reflectance and sun exposure. Four cohorts of participants (n = 72 total) were studied for 7-8 wk in the fall, winter, spring, and summer in Davis, CA [38.5° N, 121.7° W, Elev. 49 ft (15 m)]. Skin reflectance was measured using a spectrophotometer, vitamin D intake using food records, and sun exposure using polysulfone dosimeter badges. A multiple regression model (R^sup 2^ = 0.55; P < 0.0001) was developed and used to predict the serum 25(OH)D concentration for participants with low [median for African ancestry (AA)] and high [median for European ancestry (EA)] skin reflectance and with low [20th percentile, ~20 min/d, ~18% body surface area (BSA) exposed] and high (80th percentile, ~90 min/d, ~35% BSA exposed) sun exposure, assuming an intake of 200 IU/d (5 ug/d). Predicted serum 25(OH)D concentrations for AA individuals with low and high sun exposure in the winter were 24 and 42 nmol/L and in the summer were 40 and 60 nmol/L. Corresponding values for EA individuals were 35 and 60 nmol/L in the winter and in the summer were 58 and 85 nmol/L. To achieve 25(OH)D ≥75 nmol/L, we estimate that EA individuals with high sun exposure need 1300 IU/d vitamin D intake in the winter and AA individuals with low sun exposure need 2100-3100 IU/d year-round.

Workers’ UV exposure and the subsequent impact on skin

Introduction: Excessive exposure to ultraviolet (UV) radiation from sunlight is a causative factor in the development of skin damage and skin cancer. Little research has been undertaken into assessing the sun exposure linking to skin damage inside buildings or behind window glass. This project directly addressed this issue by aiming to assess the role that UV exposure has on skin damage for indoor workers and drivers. Methods: Measurements of personal UV exposure using UV sensitive polymer dosimeters were undertaken of 41 indoor workers and 3 professional drivers. Physical measurements of skin characteristics including skin pigmentation and UV induced skin photoaging were also determined. In addition, demographic information along with phenotypic characteristics, sun exposure and sun protection practice history, and history of skin damage were assessed through a questionnaire. Results: Indoor workers typically received low doses of UV radiation. However, one driver received a high dose (13J/cm2 UVA and 4.99 MED UVB on the arm). Age and years residing in Australia had a positive correlation with UV induced skin pigmentation. The number of major sunburns before 18 years was a risk factor for skin damage in adults. Those participants with fair skin, non-black hair and blue/green /blue-grey eye were more likely to have skin damage related to sun exposure. Conclusions: A person’s age, years residing in Australia, numbers of major sunburn, skin colour, hair colour and eye colour are important factors associated with the development of sun-related skin damage in workers. ‘Real World’ implications: 1. The number of major sunburns before 18 years was a risk factor for skin damage in adults. This clearly confirms the importance of early prevention. To protect the skin from extensive sun exposure for your generation should have significance for further prevention of skin damage. 2. It is unsurprising that age and years residing in Australia were associated with skin damage related UV radiation. Therefore, the general public should reinforce their sun protective measures and check skin regularly. 3. Drivers should take sun protective measures during their working hours between sunrise and sunset.

Effect of cabin ventilation rate on ultrafine particle exposure inside automobiles

We alternately measured on-road and in-vehicle ultrafine (<100 nm) particle (UFP) concentration for 5 passenger vehicles that comprised an age range of 18 years. A range of cabin ventilation settings were assessed during 301 trips through a 4 km road tunnel in Sydney, Australia. Outdoor airflow(ventilation) rates under these settings were quantified on open roads using tracer gas techniques. Significant variability in tunnel trip average median in-cabin/on-road (I/O) UFP ratios was observed (0.08 to ∼1.0). Based on data spanning all test automobiles and ventilation settings, a positive linear relationship was found between outdoor air flow rate and I/O ratio, with the former accounting for a substantial proportion of variation in the latter (R2 ) 0.81). UFP concentrations recorded in cabin during tunnel travel were significantly higher than those reported by comparable studies performed on open roadways. A simple mathematical model afforded the ability to predict tunnel trip average in-cabin UFP concentrations with good accuracy. Our data indicate that under certain conditions, in-cabin UFP exposures incurred during tunnel travel may contribute significantly to daily exposure. The UFP exposure of automobile occupants appears strongly related to their choice of ventilation setting and vehicle.

Exposure to particle number, surface area and PM concentrations in pizzerias

The aim of this work was to quantify exposure to particles emitted by wood-fired ovens in pizzerias. Overall, 15 microenvironments were chosen and analyzed in a 14-month experimental campaign. Particle number concentration and distribution were measured simultaneously using a Condensation Particle Counter (CPC), a Scanning Mobility Particle Sizer (SMPS), an Aerodynamic Particle Sizer (APS). The surface area and mass distributions and concentrations, as well as the estimation of lung deposition surface area and PM1 were evaluated using the SMPS-APS system with dosimetric models, by taking into account the presence of aggregates on the basis of the Idealized Aggregate (IA) theory. The fraction of inhaled particles deposited in the respiratory system and different fractions of particulate matter were also measured by means of a Nanoparticle Surface Area Monitor (NSAM) and a photometer (DustTrak DRX), respectively. In this way, supplementary data were obtained during the monitoring of trends inside the pizzerias. We found that surface area and PM1 particle concentrations in pizzerias can be very high, especially when compared to other critical microenvironments, such as the transport hubs. During pizza cooking under normal ventilation conditions, concentrations were found up to 74, 70 and 23 times higher than background levels for number, surface area and PM1, respectively. A key parameter is the oven shape factor, defined as the ratio between the size of the face opening in respect