John M. Dowden

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A time dependent mathematical model of optical energy transfer and heat conduction in tissue with strong anisotropic scattering is used to analyse the results of experiments (1) in which the livers of rats were treated by local laser hyperthermia. Good qualitative agreement to the temperature distribution is possible, but satisfactory quantitative agreement(More)
A mathematical model of ablation of tissue by an incident laser beam is formulated in terms of a series of layers in which laser power is absorbed and water and tissue vaporized. Thermal energy is also deposited and removed by conduction. Time dependent mathematical equations are set up for these processes; they are solved numerically. The model assumes(More)
A mathematical model is employed to discuss the region treated by local hyperthermia, when the source of heat is a laser whose energy is directed into the treatment region through four optical fibres ending at the corners of a square. If treatment is over a period that is substantially longer than the time for the temperature distribution to reach(More)
A mathematical model for laser treatment of tumours is proposed, and is based on a diffusion approximation to the distribution of laser energy in tissue. Spherically symmetrical solutions are possible, and they give some insight into the character of the solution. The full set of equations has been solved numerically for blood thrombus, and the solution is(More)
The interpolation of a discrete set of data, on the interval [a, b], representing the functiong(x) is obtained using a local piecewise polynomial of order 3. This piecewise cubic interpolant has the following properties: monotonicity and/or convexity or turning points that are present in the data are preserved and no extraneous turning points are created.(More)
A mathematical model is described for the temperature distribution produced when the optical fibre used in laser treatment of tumours has an etched cylindrical tip. Exact solutions are quoted for the equilibrium temperature distribution, of a form easily evaluated with minimal computing facilities. A number of special cases are worked out to illustrate the(More)
This paper suggests a novel way for measuring the similarity between sequences of symbols from alphabets of small cardinality such as DNA and RNA sequences. The approach relies on finding one-to-one mappings between these sequences and a subset of the real numbers. Gaps in nonidentical sequences are easily detected. Computational illustrations on DNA(More)
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