Measurement of total body water (TBW) and total energy expenditure (TEE) using stable isotopes

Understanding the relationship between diet, physical activity and health in humans requires accurate measurement of body composition and daily energy expenditure. Stable isotopes provide a means of measuring total body water and daily energy expenditure under free-living conditions. While the use of isotope ratio mass spectrometry (IRMS) for the analysis of 2H (Deuterium) and 18O (Oxygen-18) is well established in the field of human energy metabolism research, numerous questions remain regarding the factors which influence analytical and measurement error using this methodology. This thesis was comprised of four studies with the following emphases. The aim of Study 1 was to determine the analytical and measurement error of the IRMS with regard to sample handling under certain conditions. Study 2 involved the comparison of TEE (Total daily energy expenditure) using two commonly employed equations. Further, saliva and urine samples, collected at different times, were used to determine if clinically significant differences would occur. Study 3 was undertaken to determine the appropriate collection times for TBW estimates and derived body composition values. Finally, Study 4, a single case study to investigate if TEE measures are affected when the human condition changes due to altered exercise and water intake. The aim of Study 1 was to validate laboratory approaches to measure isotopic enrichment to ensure accurate (to international standards), precise (reproducibility of three replicate samples) and linear (isotope ratio was constant over the expected concentration range) results. This established the machine variability for the IRMS equipment in use at Queensland University for both TBW and TEE. Using either 0.4mL or 0.5mL sample volumes for both oxygen-18 and deuterium were statistically acceptable (p>0.05) and showed a within analytical variance of 5.8 Delta VSOW units for deuterium, 0.41 Delta VSOW units for oxygen-18. This variance was used as “within analytical noise” to determine sample deviations. It was also found that there was no influence of equilibration time on oxygen-18 or deuterium values when comparing the minimum (oxygen-18: 24hr; deuterium: 3 days) and maximum (oxygen-18: and deuterium: 14 days) equilibration times. With regard to preparation using the vacuum line, any order of preparation is suitable as the TEE values fall within 8% of each other regardless of preparation order. An 8% variation is acceptable for the TEE values due to biological and technical errors (Schoeller, 1988). However, for the automated line, deuterium must be assessed first followed by oxygen-18 as the automated machine line does not evacuate tubes but merely refills them with an injection of gas for a predetermined time. Any fractionation (which may occur for both isotopes), would cause a slight elevation in the values and hence a lower TEE. The purpose of the second and third study was to investigate the use of IRMS to measure the TEE and TBW of and to validate the current IRMS practices in use with regard to sample collection times of urine and saliva, the use of two TEE equations from different research centers and the body composition values derived from these TEE and TBW values. Following the collection of a fasting baseline urine and saliva sample, 10 people (8 women, 2 men) were dosed with a doubly labeled water does comprised of 1.25g 10% oxygen-18 and 0.1 g 100% deuterium/kg body weight. The samples were collected hourly for 12 hrs on the first day and then morning, midday, and evening samples were collected for the next 14 days. The samples were analyzed using an isotope ratio mass spectrometer. For the TBW, time to equilibration was determined using three commonly employed data analysis approaches. Isotopic equilibration was reached in 90% of the sample by hour 6, and in 100% of the sample by hour 7. With regard to the TBW estimations, the optimal time for urine collection was found to be between hours 4 and 10 as to where there was no significant difference between values. In contrast, statistically significant differences in TBW estimations were found between hours 1-3 and from 11-12 when compared with hours 4-10. Most of the individuals in this study were in equilibrium after 7 hours. The TEE equations of Prof Dale Scholler (Chicago, USA, IAEA) and Prof K.Westerterp were compared with that of Prof. Andrew Coward (Dunn Nutrition Centre). When comparing values derived from samples collected in the morning and evening there was no effect of time or equation on resulting TEE values. The fourth study was a pilot study (n=1) to test the variability in TEE as a result of manipulations in fluid consumption and level of physical activity; the magnitude of change which may be expected in a sedentary adult. Physical activity levels were manipulated by increasing the number of steps per day to mimic the increases that may result when a sedentary individual commences an activity program. The study was comprised of three sub-studies completed on the same individual over a period of 8 months. There were no significant changes in TBW across all studies, even though the elimination rates changed with the supplemented water intake and additional physical activity. The extra activity may not have sufficiently strenuous enough and the water intake high enough to cause a significant change in the TBW and hence the CO2 production and TEE values. The TEE values measured show good agreement based on the estimated values calculated on an RMR of 1455 kcal/day, a DIT of 10% of TEE and activity based on measured steps. The covariance values tracked when plotting the residuals were found to be representative of “well-behaved” data and are indicative of the analytical accuracy. The ratio and product plots were found to reflect the water turnover and CO2 production and thus could, with further investigation, be employed to identify the changes in physical activity.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Analysis of efficiency and optimization of plasmon energy coupling into nanofocusing metal wedges

In this paper, we investigate theoretically and numerically the efficiency of energy coupling from a plasmon generated by a grating coupler at one of the interfaces of a metal wedge into the plasmonic eigenmode (i.e., symmetric or quasisymmetric plasmon) experiencing nanofocusing in the wedge. Thus the energy efficiency of energy coupling into metallic nanofocusing structure is analyzed. Two different nanofocusing structures with the metal wedge surrounded by a uniform dielectric (symmetric structure) and with the metal wedge enclosed between a substrate and a cladding with different dielectricpermittivities (asymmetric structure) are considered by means of the geometrical optics (adiabatic) approximation. It is demonstrated that the efficiency of the energy coupling from the plasmon generated by the grating into the symmetric or quasisymmetric plasmon experiencing nanofocusing may vary between ∼50% to ∼100%. In particular, even a very small difference (of ∼1%–2%) between the permittivities of the substrate and the cladding may result in a significant increase in the efficiency of the energy coupling (from ∼50% up to ∼100%) into the plasmon experiencing nanofocusing. Distinct beat patterns produced by the interference of the symmetric (quasisymmetric) and antisymmetric (quasiantisymmetric) plasmons are predicted and analyzed with significant oscillations of the magnetic and electric field amplitudes at both the metal wedge interfaces. Physical interpretations of the predicted effects are based upon the behavior, dispersion, and dissipation of the symmetric (quasisymmetric) and antisymmetric (quasiantisymmetric) filmplasmons in the nanofocusing metal wedge. The obtained results will be important for optimizing metallic nanofocusing structures and minimizing coupling and dissipative losses.