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Biomedical subjects

G K Aldis

Publications and source records attributed to G K Aldis.

13 recordsLinked to original sources
PubMed2005

An integral equation model for the control of a smallpox outbreak.

An integral equation model of a smallpox epidemic is proposed. The model structures the incidence of infection among the household, the workplace, the wider community and a health-care facility; and incorporates a finite incubation period and plausible infectivity functions. Linearisation of the model is appropriate for small epidemics, and enables analytic expressions to be derived for the basic reproduction number and the size of the epidemic. The effects of control interventions (vaccination, isolation, quarantine and public education) are explored for a smallpox epidemic following an imported case. It is found that the rapid identification and isolation of cases, the quarantine of affected households and a public education campaign to reduce contact would be capable of bringing an epidemic under control. This could be used in conjunction with the vaccination of healthcare workers and contacts. Our results suggest that prior mass vaccination would be an inefficient method of containing an outbreak.

Algorithms↗
PubMed2002

Flow spectra from spectral power density calculations for pulsed Doppler.

Range gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. Both the transducer and the sample volume are of finite size, and this prohibits the measurement of velocity at a point. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen of a vessel. However no such set of spectra will correspond directly to the true velocity profile. In this study we developed a systematic theoretical treatment which allows Doppler spectral power density (SPD) functions to be calculated under a very wide range of conditions. Simulated flow spectra were created from sets of these spectra. The model is based on the beam intensity weighted volume method and incorporates, through the idea of a spread function, Guidi's individual flow line spectrum. Our method can be applied for different spread functions; with beam profiles which are uniform, Gaussian or arbitrarily narrow (needle beam); with range gated sample volumes which can be maximal (CW-type) or minimal (PW-type); and for beams which intersect the flow tube axis, or are off centre. Under all conditions we find the spread function parameter k, equal to the ratio of the central Doppler shift to half the bandwidth, plays a key role. After formulating the model analytically, we sought simplifications to allow results to be obtained from simple, practical formulae. Spread and unspread SPD functions are in most cases given as single integrals which contain measurable physical parameters and can be easily evaluated numerically. Model results are presented for flow spectra of parabolic flow, illustrating the interplay between different factors in determining the appearance of spectral flow profiles.

Blood Flow Velocity↗
PubMed2002

Spectral power density calculations for pulsed Doppler.

Range-gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen, but no set of spectra will correspond directly to the true velocity profile. Spectral flow profiles are affected by a complex interplay between different sources of spectral broadening. In this study we developed a systematic theoretical method which allows spectral power density functions to be calculated under a very wide range of conditions, and used it to obtain simulated flow spectra. The model was formulated analytically. It is based on the weighted-volume approach and incorporates, through the concept of a spread function, the intrinsic spectral broadening associated with a focused transducer. It can be applied for arbitrary values of the spread parameter; for non-uniform beam profiles; with maximal (continuous wave-type) or minimal (pulse wave-type) range-gated sample volumes; and for beams that intersect the flow tube axis, or are off centre. Results are presented for a Gaussian beam and parabolic flow. Simulated spectral flow profiles are given which illustrate how a profile's appearance can be altered by the different sources of spectral broadening.

Blood Flow Velocity↗
PubMed2000

Selective transmission of a focused Doppler ultrasound beam through a plastic layer.

Laboratory test objects are widely used in Doppler ultrasound (US). Although the acoustic properties of in vitro materials are usually known, they are unlikely to match each other, or their in vivo counterparts, exactly. We conducted theoretical and experimental studies of a focused ultrasound beam as it passes from one fluid, through an intervening plastic layer at an oblique angle, and then into a different fluid. Dual mode propagation may occur (i.e., both longitudinal and shear waves can propagate in the plastic layer). Our calculations show that the power transmitted by either mode drops very rapidly to zero at certain critical angles. A range of angles of incidence exists within a focused beam and this, combined with the highly angle-dependent power transmission behaviour, can produce major distortions of Doppler data. These may persist even when the beam axis is not oriented exactly at the critical angle. The total power transmitted depends on all the wave speeds, may involve mode conversion, and is a very complicated function of the angle of incidence. This study reports a practical method for the calculation of power transmission though a plastic layer, and shows how the resulting power vs. angle graph can be used to avoid artefacts in in vitro Doppler studies.

Phantoms, Imaging↗
PubMed1996

Effect of a cylindrical refracting interface on ultrasound intensity and the CW Doppler spectrum.

The insonation of axisymmetric flow in a tube by an ultrasound beam which is refracted at the tube surface is considered. A three-dimensional (3-D) model for refraction at a cylindrical interface is developed. The incident beam, which is planar but otherwise arbitrary, is refracted at a single acoustic impedance interface between the medium within the tube and the surrounding medium. A ray approximation is used as the ultrasonic wavelength is small compared to the radius of curvature of the tube. A parametric form for the ray paths is obtained and used to derive an expression for the intensity. The intensity depends on the specific position within the tube, as well as the ratio of sound speeds, N, and the Doppler angle thetaD. A diverging (N = 1.2, thetaD = 45 degrees) and a converging (N = 0.8, thetaD = 45 degrees) case are presented in detail. The converging interface results in more extreme intensity distortion. The regions of maximum and minimum intensity over a tube slice are immediately adjacent in both diverging and converging cases. Once the intensity distribution across a tube slice is known, the previously reported volume integral method for the calculation of continuous wave (CW) Doppler spectral power density (spd) functions may be used. The effect of refraction of the incident beam on the spd function is shown for both an infinite beam and a circular beam with radius equal to the tube radius. A curved acoustic impedance interface, as may be encountered in vitro in flow phantoms or in vivo in vascular disease, leads to nonuniform insonation and spectral distortion which depends on transducer orientation.

Animals↗
PubMed1995

Ion induced deformation of soft tissue.

In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Lai et al. (1990, Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myers et al. (1984, ASME J. biomech. Engng, 106, 151-158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to account for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility of approximate analytic solutions in certain cases.

Animals↗
PubMed1992

Flow-induced deformation from pressurized cavities in absorbing porous tissues.

The behaviour of a cavity during an injection of fluid into biological tissue is considered. High cavity pressure drives fluid into the neighbouring tissue where it is absorbed by capillaries and lymphatics. The tissue is modelled as a nonlinear deformable porous medium with the injected fluid absorbed by the tissue at a rate proportional to the local pressure. A model with a spherical cavity in an infinite medium is used to find the pressure and displacement of the tissue as a function of time and radial distance. Analytical and numerical solutions for a step change in cavity pressure show that the flow induces a radial compression in the medium together with an annular expansion, the net result being an overall expansion of the medium. Thus any flow induced deformation of the material will aid in the absorption of fluid.

Absorption↗
PubMed1992

Calculation of Doppler spectral power density functions.

A volume integral method for the calculation of Doppler ultrasound spectral power density (spd) functions is described. Axisymmetric flow in a circular tube with a power law velocity profile is assumed. The spd function is regarded as a probability density function for scatterer velocity, and the assumptions under which this is justified are considered. It is shown that the spd function is independent of Doppler angle except in the presence of wall reflection effects. A coordinate system centered on the beam is used and this enables the integrals to be easily formulated for arbitrary beams. Irregularly shaped and nonuniform beams can be treated. For the common flow and beam patterns, which exhibit symmetry, the volume integrals can often be reduced to a single integral and evaluated directly. The method is applied and the spectra are calculated for various different cases. Results are obtained for uniform rectangular and circular insonating beams, and for nonuniform beams with Gaussian, jinc, and sinc profiles. The effects of narrow beams and wall reflection are shown. The method may be readily applied to other beam and flow patterns, and extension to more complicated situations is also discussed.

Blood Flow Velocity↗
PubMed1990

Comparison of models for flow induced deformation of soft biological tissue.

The behaviour of a deformable porous medium during the flow of fluid under a pressure difference is examined for both infinitesimal and finite deformations. Models for both cases are solved for the problem of steady one-dimensional compression and compared with experimental data from Parker et al. (J. appl. Mech. 54, 794-800, 1987) for a polyurethane sponge. The purpose of this study is to identify a simple model which agrees qualitatively with these published results. To relate the stress relations for biological tissues to the data for polymer sponges (Parker et al., 1987) a translation of 1.1 kPa was introduced. This allows for some structural differences between the two media. It was found that the infinitesimal models were adequate up to 20% strain, but significant divergence occurred for higher strains. A finite deformation model with the permeability depending exponentially on the strain gave the most consistent results and required the fitting of only two parameters.

Connective Tissue↗