Using mortuary and burial data to place COVID-19 in Lusaka, Zambia within a global context

Reported COVID-19 cases and associated mortality remain low in many sub-Saharan countries relative to global averages, but true impact is difficult to estimate given limitations around surveillance and mortality registration. In Lusaka, Zambia, burial registration and SARS-CoV-2 prevalence data during 2020 allow estimation of excess mortality and transmission. Relative to pre-pandemic patterns, we estimate age-dependent mortality increases, totalling 3212 excess deaths (95% CrI: 2104-4591), representing an 18.5% (95% CrI: 13.0-25.2%) increase relative to pre-pandemic levels. Using a dynamical model-based inferential framework, we find that these mortality patterns and SARS-CoV-2 prevalence data are in agreement with established COVID-19 severity estimates. Our results support hypotheses that COVID-19 impact in Lusaka during 2020 was consistent with COVID-19 epidemics elsewhere, without requiring exceptional explanations for low reported figures. For more equitable decision-making during future pandemics, barriers to ascertaining attributable mortality in low-income settings must be addressed and factored into discourse around reported impact differences.

Alternative epidemic indicators for COVID-19 in three settings with incomplete death registration systems

Not all COVID-19 deaths are officially reported, and particularly in low-income and humanitarian settings, the magnitude of reporting gaps remains sparsely characterized. Alternative data sources, including burial site worker reports, satellite imagery of cemeteries, and social media-conducted surveys of infection may offer solutions. By merging these data with independently conducted, representative serological studies within a mathematical modeling framework, we aim to better understand the range of underreporting using examples from three major cities: Addis Ababa (Ethiopia), Aden (Yemen), and Khartoum (Sudan) during 2020. We estimate that 69 to 100%, 0.8 to 8.0%, and 3.0 to 6.0% of COVID-19 deaths were reported in each setting, respectively. In future epidemics, and in settings where vital registration systems are limited, using multiple alternative data sources could provide critically needed, improved estimates of epidemic impact. However, ultimately, these systems are needed to ensure that, in contrast to COVID-19, the impact of future pandemics or other drivers of mortality is reported and understood worldwide.

The Evolution of Plasmid Transfer Rate in Bacteria and Its Effect on Plasmid Persistence

AbstractPlasmids are extrachromosomal segments of DNA that can transfer genes between bacterial cells. Many plasmid genes benefit bacteria but cause harm to human health by granting antibiotic resistance to pathogens. Transfer rate is a key parameter for predicting plasmid dynamics, but observed rates are highly variable, and the effects of selective forces on their evolution are unclear. We apply evolutionary analysis to plasmid conjugation models to investigate selective pressures affecting plasmid transfer rate, emphasizing host versus plasmid control, the costs of plasmid transfer, and the role of recipient cells. Our analyses show that plasmid-determined transfer rates can be predicted with three parameters (host growth rate, plasmid loss rate, and the cost of plasmid transfer on growth) under some conditions. We also show that low-frequency genetic variation in transfer rate can accumulate, facilitating rapid adaptation to changing conditions. Furthermore, reduced transfer rates due to host control have limited effects on plasmid prevalence until low enough to prevent plasmid persistence. These results provide a framework to predict plasmid transfer rate evolution in different environments and demonstrate the limited impact of host mechanisms to control the costs incurred when plasmids are present.

Inhibition of the renin-angiotensin system for lowering coronary artery disease risk

The renin-angiotensin system when activated exerts proliferative and pro-inflammatory actions and thereby contributes to progression of atherosclerosis, including that occurring in the coronary arteries. It thus contributes as well to coronary artery disease (CAD). Several clinical trials have examined effects of renin-angiotensin system inhibition for primary and secondary prevention of coronary heart disease. These include important trials such as HOPE, EUROPA and PEACE using angiotensin converting enzyme inhibitors, VALIANT, OPTIMAAL and TRANSCEND using angiotensin receptor blockers, and the ongoing TOPCAT study in patients with preserved ejection fraction heart failure, many of who also have coronary artery disease. Data are unavailable as yet of effects of either direct renin inhibitors or the new angiotensin receptor/neprilysin inhibitor agents. Today, inhibition of the renin-angiotensin system is standard-of-care therapy for lowering cardiovascular risk in secondary prevention in high cardiovascular risk subjects.

Cardiotoxicity of cancer therapeutics: current issues in screening, prevention, and therapy

In the context of modern cancer chemotherapeutics, cancer survivors are living longer and being exposed to potential comorbidities related to non-cancer side effects of such treatments. With close monitoring of cancer patients receiving potentially cardiotoxic medical therapies, oncologists, and cardiologists alike are identifying patients in both clinical and subclinical phases of cardiovascular disease related to such chemotherapies. Specifically, cardiotoxicity at the level of the myocardium and potential for the development of heart failure are becoming a growing concern with increasing survival of cancer patients. Traditional chemotherapeutic agents used commonly in the treatment of breast cancer and hematologic malignancies, such as anthracyclines and HER-2 antagonists, are well known to be associated with cardiovascular sequelae. Patients often present without symptoms and an abnormal cardiac imaging study performed as part of routine evaluation of patients receiving cardiotoxic therapies. Additionally, patients can present with signs and symptoms of cardiovascular disease months to years after receiving the chemotherapies. As the understanding of the physiology underlying the various cancers has grown, therapies have been developed that target specific molecules that represent key aspects of physiologic pathways responsible for cancer growth. Inhibition of these pathways, such as those involving tyrosine kinases, has lead to the potential for cardiotoxicity as well. In view of the potential cardiotoxicity of specific chemotherapies, there is a growing interest in identifying patients who are at risk of cardiotoxicity prior to becoming symptomatic or developing cardiotoxicity that may limit the use of potentially life-saving chemotherapy agents. Serological markers and novel cardiac imaging techniques have become the source of many investigations with the goal of screening patients for pre-clinical cardiotoxicity. Additionally, studies have been performed.

Heart rate recovery--a potential marker of clinical outcomes in heart failure patients receiving beta-blocker therapy

BACKGROUND

Heart rate recovery (HRR) within the first few minutes of graded exercise has been associated with impaired clinical outcomes in patients being evaluated for coronary artery disease. HRR is abnormal in patients with heart failure (HF), but has not been associated with clinical outcomes in these patients. The objective of the present study was to determine whether HRR following cardiopulmonary exercise testing (CPET) correlates with peak oxygen consumption (VO(2)), and whether it impacts clinical outcomes, including HF hospitalizations and total mortality, or the need for cardiac transplantation.

METHODS

CPET was performed in 78 patients referred to the Montreal Heart Institute (Montreal, Quebec) with congestive HF between January 2000 and December 2002. All patients had New York Heart Association class II or III HF with a left ventricular ejection fraction of 45% or lower. Mean (+/- SD) age was 53+/-11 years and left ventricular ejection fraction was 27+/-9%. Forty-four per cent had ischemic cardiomyopathy, 88% received beta-blockers and 79% received angiotensin-converting enzyme inhibitors. HRR was defined as the difference from peak exercise HR to HR measured at specific time intervals. HRR was calculated 30 s, 60 s, 90 s and 120 s after exercise.

RESULTS

Mean peak VO(2) was 18.0+/-5.3 mL/kg/min, resting HR was 74+/-13 beats/min and peak HR was 119+/-22 beats/min. HRR measured was 10+/-9 beats/min after 30 s, 20+/-12 beats/min after 60 s, 25+/-15 beats/min after 90 s and 30+/-13 beats/min after 120 s. At 90 s, patients with an HRR below 24 beats/min were more likely to have an HF hospitalization at five-year follow-up (eight hospitalizations [22.2%] versus two hospitalizations [2.7%]; P=0.0134). There was a correlation between peak VO(2) and HRR 90 s and 120 s after completion of the exercise test (r=0.40 after 90 s, P=0.001, and r=0.41 after 120 s, P=0.008).

CONCLUSIONS

In patients with HF, blunted HRR 90 s and 120 s after CPET correlate with peak VO(2) and are associated with increased risk of worsening HF. HRR is easily measured and a useful marker for morbidity in patients with HF.

Aminoalkyl adenylate and aminoacyl sulfamate intermediate analogues differing greatly in affinity for their cognate Staphylococcus aureus aminoacyl tRNA synthetases

Aminoalkyl adenylates and aminoacyl sulfamates derived from arginine, histidine and threonine, have been prepared and tested as inhibitors of their cognate Staphylococcus aureus aminoacyl tRNA synthetases. The arginyl derivatives were both potent nanomolar inhibitors of the Class I arginyl tRNA synthetase whereas for the Class II histidyl and threonyl tRNA synthetases, the acyl sulfamates were potent inhibitors but the adenylates had very little affinity.

Mechanistic insights into the inhibition of serine proteases by monocyclic lactams

Although originally discovered as inhibitors of pencillin-binding proteins, beta-lactams have more recently found utility as serine protease inhibitors. Indeed through their ability to react irreversibly with nucleophilic serine residues they have proved extraordinarily successful as enzyme inhibitors. Consequently there has been much speculation as to the reason for the general effectiveness of beta-lactams as antibacterials or inhibitors of hydrolytic enzymes. The interaction of analogous beta- and gamma-lactams with a serine protease was investigated. Three series of gamma-lactams based upon monocyclic beta-lactam inhibitors of elastase [Firestone, R. A. et al. (1990) Tetrahedron 46, 2255-2262.] but with an extra methylene group inserted between three of the bonds in the ring were synthesized. Their interaction with porcine pancreatic elastase and their efficacy as inhibitors were evaluated through the use of kinetic, NMR, mass spectrometric, and X-ray crystallographic analyses. The first series, with the methylene group inserted between C-3 and C-4 of the beta-lactam template, were readily hydrolyzed but were inactive or very weakly active as inhibitors. The second series, with the methylene group between C-4 and the nitrogen of the beta-lactam template, were inhibitory and reacted reversibly with PPE to form acyl-enzyme complexes, which were stable with respect to hydrolysis. The third series, with the methylene group inserted between C-2 and C-3, were not hydrolyzed and were not inhibitors consistent with lack of binding to PPE. Comparison of the crystal structure of the acyl-enzyme complex formed between PPE and a second series gamma-lactam and that formed between PPE and a peptide [Wilmouth, R. C., et al. (1997) Nat. Struct. Biol. 4, 456-462.] reveals why the complexes formed with this series were resistant to hydrolysis and suggests ways in which stable acyl-enzyme complexes might be obtained from monocyclic gamma-lactam-based inhibitors.

The accuracy of a new system for estimating organ volume using ultrasound

A new system is described for estimating volume from a series of multiplanar 2D ultrasound images. Ultrasound images are captured using a personal computer video digitizing card and an electromagnetic localization system is used to record the pose of the ultrasound images. The accuracy of the system was assessed by scanning four groups of ten cadaveric kidneys on four different ultrasound machines. Scan image planes were oriented either radially, in parallel or slanted at 30 degrees to the vertical. The cross-sectional images of the kidneys were traced using a mouse and the outline points transformed to 3D space using the Fastrak position and orientation data. Points on adjacent region of interest outlines were connected to form a triangle mesh and the volume of the kidneys estimated using the ellipsoid, planimetry, tetrahedral and ray tracing methods. There was little difference between the results for the different scan techniques or volume estimation alogorithms, although, perhaps as expected, the ellipsoid results were the least precise. For radial scanning and ray tracing, the mean and standard deviation of the percentage errors for the four different machines were as follows: Hitachi EUB-240, -3.0 +/- 2.7%; Tosbee RM3, -0.1 +/- 2.3%; Hitachi EUB-415, 0.2 +/- 2.3%; Acuson, 2.7 +/- 2.3%.

Application of a new discreet form of Gauss' theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss' theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference +/- one standard deviation were 1.2 +/- 2.3, 5.5 +/- 4.7, 3.0 +/- 3.2 and -1.2 +/- 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

Volume estimation from multiplanar 2D ultrasound images using a remote electromagnetic position and orientation sensor

A system is described for calculating volume from a sequence of multiplanar 2D ultrasound images. Ultrasound images are captured using a video digitising card (Hauppauge Win/TV card) installed in a personal computer, and regions of interest transformed into 3D space using position and orientation data obtained from an electromagnetic device (Polhemus, Fastrak). The accuracy of the system was assessed by scanning 10 water filled balloons (13-141 mL), 10 kidneys (147-200 mL) and 16 fetal livers (8-37 mL) in water using an Acuson 128XP/10 (5 MHz curvilinear probe). Volume was calculated using the ellipsoid, planimetry, tetrahedral and ray tracing methods and compared with the actual volume measured by weighing (balloons) and water displacement (kidneys and livers). The mean percentage error for the ray tracing method was 0.9 +/- 2.4%, 2.7 +/- 2.3%, 6.6 +/- 5.4% for balloons, kidneys and livers, respectively. So far the system has been used clinically to scan fetal livers and lungs, neonate brain ventricles and adult prostate glands.

Dielectric properties of human blood at microwave frequencies

Waveguides systems have been used to obtain measurements for the complex permittivity of human blood in the frequent range 29-90 GHz. The data are reported and analysed in conjunction with lower frequency work, in particular that of Wei. There are two distinct regimes of behaviour in the spectra obtained: a high-frequency relaxation process in parallel with a lower frequency fractional power-law response.

The dielectric properties of rabbit tissue, pure water and various liquids suitable for tissue phantoms at 35 GHz

Newly developed microwave apparatus was used to measure the complex permittivity of some rabbit tissues and water over the temperature range 20-37 degrees C. Various liquid mixtures which might be suitable as phantom tissue equivalents at 35 GHz were also considered. Some of the measured tissue data were compared with previous lower frequency data and it was concluded that the observed behaviour was not anomalous.

The modelling of biological systems in three dimensions using the time domain finite-difference method: II. The application and experimental evaluation of the method in hyperthermia applicator design

The three-dimensional time domain finite-difference (TDFD) method was used to design a 433 MHz circular waveguide applicator for electromagnetic hyperthermia. This applicator has a water-filled lens at one end, providing surface cooling as well as some shaping of the emergent electromagnetic field. An experimental system for scanning the EM field in three dimensions is described. The experimental data were compared with those calculated from the TDFD program and good agreement was found. A realistic three-dimensional model based on an ultrasound scan of a surface tumour was built. Both the EM field and the specific absorption rate (SAR) within the model when irradiated by the applicator were calculated.

The modelling of biological systems in three dimensions using the time domain finite-difference method: I. The implementation of the model

A computer method has been developed which uses the time domain finite-difference (TDFD) algorithm to calculate the deposition of the electromagnetic (EM) field in three-dimensional biological models. This, the first of two papers, describes the algorithm and the computer programs developed. The method is demonstrated by calculating the penetration of the EM field from a rectangular waveguide radiating into a homogeneous model, the calculation being carried out in two dimensions for simplicity in this paper.

Dielectric behavior of water in biological solutions: studies on myoglobin, human low-density lipoprotein, and polyvinylpyrrolidone

The dielectric behavior of the aqueous solutions of three widely differing macromolecules has been investigated: myoglobin, polyvinylpyrrolidone (PVP), and human serum low-density lipoprotein (LDL). It was not possible to interpret unambiguously the dielectric properties of the PVP solution in terms of water structure. The best interpretation of the dielectric data on the myoglobin and LDL solutions was that, in both cases, the macromolecule attracts a layer of water of hydration one or two water molecules in width. For LDL, this corresponds to a hydration factor of only 0.05 g/g, whereas for myoglobin the figure is nearer 0.6 g/g. With myoglobin, part of the water of hydration exhibits its dispersion at frequencies of a few GHz, and the rest disperses at lower frequencies, perhaps as low as 10-12 MHz. The approximate constancy of the width of the hydration shell for two molecules as dissimilar in size as LDL and myoglobin confirms that the proportion of water existing as water of hydration in a biological solution depends critically on the size of the macromolecules as well as on their concentration.

Dielectric properties of lens tissue at microwave frequencies

The relative permittivity and conductivity of rabbit eye lens were measured in the frequency domain between 2 and 18 GHz at temperatures of 37 and 20 degrees C. An analysis of the data suggested that a significant proportion of the bulk water in nuclear and cortical lens tissue may behave differently to pure water. In addition, the Maxwell-Fricke mixture theory was used to estimate the amount of hydrated water that relaxes far below 1 GHz.

Dielectric properties of mammalian brain tissue between 1 and 18 GHz

A newly developed frequency domain technique was used to measure the dielectric properties of white matter, grey matter and macerated rabbit brain at 20 and 37 degrees C. An analysis of the data showed that between 1 and 4 GHz there were substantial contributions from processes other than the gamma dispersion. However, above 7.5 GHz it appeared that mainly free water was relaxing although evidence of a small spread of relaxation times was found for the bulk water in the white matter. Mouse and rat brain were also measured but no significant differences were found between the species. The quantity of bound water was estimated but there was no evidence of a difference in the amount between either the tissues or the temperatures.

Dielectric properties of developing rabbit brain at 37 degrees C

The dielectric properties of developing rabbit brain were measured at 37 degrees C between 10 MHz and 18 GHz using time domain and frequency domain systems. The results show a variation with age of the dielectric properties of brain. An analysis of the data suggests that the water dispersion in the brain of newly born animals can be represented by a Debye equation. This dispersion increases in complexity with age, and there is evidence of a smaller additional relaxation process centered around 1 GHz. It is concluded that the principal contribution to this subsidiary dispersion region arises from water of hydration.

Microwave dielectric measurements (0.8-70 GHz) on Artemia cysts at variable water content

Dielectric permittivity measurements are reported for cysts of Artemia, a crustacean known as the brine shrimp. Using coaxial and waveguide techniques we examined the frequency range from 0.8 to 70 GHz. Taking advantage of the ability of this system to reversibly lose essentially all intracellular water, we determined the permittivity over the entire range of cyst water contents. Although experimental errors prevent a rigorous treatment of the data, we advance the general conclusion that little of the water in this system behaves dielectrically like pure water, regardless of water content. This conclusion is supported by, and is consistent with, the results of previously published studies that probe the motional properties of water in this system using nuclear magnetic resonance spectroscopy and quasi-elastic neutron scattering.

Dielectric behavior of DNA solution at radio and microwave frequencies (at 20 degrees C)

The dielectric constant and conductivity of calf thymus DNA were investigated at frequencies between 0.1 MHz and 70 GHz. This work is to investigate the dielectric properties of DNA in low gigahertz region and also to study whether the dielectric behavior of the water is affected by the presence of highly charged DNA. The results of these measurements indicate the presence of two anomalous dispersions, the one between 1 MHz and 1 GHz and the second one above 1 GHZ. The dispersion at low frequencies is likely to arise from polar groups in the DNA molecule. The relaxation behavior of unbound water in DNA solution is only slightly affected by the presence of DNA at concentrations below 1%.

Dielectric properties of insulin in solution

Values of the relative permittivity of a 5% solution of despentapeptide insulin (DPI) are given at six temperatures over a frequency range 0.2-50 MHz. The solvent was a mixture of water and ethylene glycol at pH = 3. From the dispersion curves a dipole moment of 72 +/- 1 was obtained for the insulin molecule at 25 degrees C. By combining the dielectric measurements with values of solvent viscosity the volume of the insulin molecule in solution was found to be only slightly larger than that in the crystal. This indicates that insulin possesses a markedly lower quantity of water of hydration than has been observed for globular proteins containing a higher proportion of hydrophilic groups on the surface of the molecule.

The dielectric properties of the cerebellum, cerebrum and brain stem of mouse brain at radiowave and microwave frequencies

The relative permittivity and conductivity of the cerebellum, cerebrum and brain stem of mouse brain were measured at a temperature of 37 degrees C over a frequency range of 72 MHz to over 5 GHz using time-domain spectroscopy. An analysis of the data suggests that the water exists in various forms of binding with an average relaxation frequency less than free water.

The dielectric properties of normal and tumour mouse tissue between 50 MHz and 10 GHz

Microwaves are currently being investigated as a method of inducing hyperthermia. Values of the relative permittivity and conductivity of mouse muscle and tumour tissues over the frequency range 50 MHz to 10 GHz at a temperature of 37 degrees C are reported. The data were obtained by using an on-line computer-based time-domain spectrometer. The tumour tissues were the RIF/1 and KHT fibrosarcomas sited in the hind leg muscle of C3H mice. A significant difference in the relative permittivity between the normal and tumour tissue was shown to exist at frequencies up to 200 MHz.

Dielectric properties of ocular tissues at 37 degrees C

Values of the relative permittivity, dielectric loss and conductivity are given for various rabbit ocular tissues at frequencies in the range 10 MHz-10 GHz. The tissues measured were cornea, retina, choroid, iris, and the cortical and nuclear zones of the lens. The dielectric parameters were determined using the technique of multiple response time domain spectroscopy. For all tissues the water relaxation could be characterised by a Debye dispersion with a relaxation time longer than that of pure water, indicating that its dielectric behaviour was affected by the presence of the biological macromolecules.

A generalized model for the interaction of microwave radiation with bound water in biological material

Calculations have been performed concerning the deposition of microwave energy in bound water surrounding a biological macromolecule immersed in a continuum consisting of free water and dissolved ions. In particular a previous model of a hydrated macromolecule has been generalised to one where the relaxation frequency of the bound water varies across the layer, and the calculations have been carried out for three combinations of values of ionic conductivity of the bound water and the continuum. When these conductivities are equal, but low, the average energy deposition per unit volume in the bound water is greater, sometimes by at least an order of magnitude, than that in the continuum at frequencies in the region of hundreds of MHz to a few GHz. As the ionic conductivity increases this effect decreases and at conductivities equal to that of physiological saline the specific energy deposition in the bound water is not more than around twice that in the surrounding electrolyte continuum over this frequency range. Therefore, for tissues of high bound water content exposed to microwaves of a given power density the biological effect produced is enhanced. For a biological tissue of high ionic conductivity with 20% of its water in the bound state the overall energy absorption would be 25% greater at certain frequencies than if all the water were in the free state. For materials of low ionic conductivity the increase would be more than one order of magnitude.

Electrical properties of lens material at microwave frequencies

Values of the complex permittivity of human and rabbit lens material in the frequency range 100--6000 MHz are reported. The data were obtained by using an on-line computer-based time-domain spectrometer. The lenses were divided into an outer (cortical) zone and an inner (nuclear) zone and the dielectric properties of each zone were measured separately for both species of lens. The results are analysed in terms of the aqueous and protein constituents, assuming a molecular model whereby the hydrated protein molecule is represented by a spherical particle embedded in an aqueous continuum. It is shown that for lens material taken from the nuclear zone the particle can be separated into protein and bound water (water of hydration). For the cortical zone the amount of water of hydration is smaller and, within the limitations of the model and uncertainties due to experimental error, cannot be distinguished from zero.

The anomalous behaviour of the permittivity of human serum low density lipoprotein around 37 degrees C

The structure of human serum low density lipoprotein has been investigated, as a function of temperature, by measurement of permittivity. Statistical analysis of the dielectric data reveals a transition at around the temperature of the human body. This may be associated with a structural change in the interior of the molecule.

A comparative dielectric study of human serum low density lipoprotein before and after partial digestion by trypsin

The relative permittivity of aqueous solutions of human serum low density lipoprotein (LDL) and partially trypsin digested lipoprotein (T-LDL) has been determined for various concentrations at 20 degrees C over the frequency range 0.15-100 MHz. Comparison of the dielectric dispersion curves for the digested lipoprotein with those for the native preparation revealed a larger low-frequency dielectric increment, which may be attributed to an increase in the number of counterions moving over the surface of the molecule. An explanation of this observation is an elevation of 70% in the net negative charge on the surface of the trypsin-treated particle as compared to its native counterpart.

The role of water in microwave absorption by biological material with particular reference to microwave hazards

The problem of the absorption of the energy of plane electromagnetic radiation by an aqueous solution of macromolecules is considered. A simplified model for the hydrated molecule is employed, consisting of a spherical shell of bound water surrounding a spherical core. The power deposition per unit volume of the shell is calculated in the frequency range 100 MHz-100 GHz for several bound water relaxation frequencies. In each case the corresponding values are also calculated for free water for comparison. The values obtained for the bound water are shown to be significantly higher than those for the free water up to frequencies of at least 1 GHz. The maximum difference between these two sets of values is of the order of a factor of five and occurs roughly at the bound water relaxation frequency. Because of the strong coupling between the bound water molecules and the macromolecules present in biological material this result could be a significant factor in the explanation of the biological effects of microwaves at a molecular level.