The concept of equivalent uniform dose (EUD) was introduced to provide a method of reporting radiotherapy dose distributions which takes account of the nonlinearity of tissue dose-response, whilst not attempting to make predictions of absolute outcome. The purpose of this investigation was to determine the level of sensitivity of EUD to model parameters for significant variations in dose distribution and consequently the reliability of the factor as a dose-indicator, and to compare EUD with the more familiar index, tumour control probability (TCP). EUD and TCP, derived from the linear-quadratic formalism, were investigated for a test tissue being irradiated non-uniformly. Variations in the parameters of the model (tissue cell characteristics, dose heterogeneity, fractionation parameters) indicated the sensitivity of EUD and TCP to them. For time independent factors--cell density, cell radiosensitivity, radiosensitivity heterogeneity (population averaged) and ratio alpha/beta--EUD was found to vary insignificantly in comparison with TCP, though this is a function of the actual form of the dose distribution under consideration. For fractionated treatments where the mean dose per fraction is varying (due to dosimetric/positioning errors for example), both EUD and TCP showed little variation with the degree of dose non-uniformity. For other time dependent factors, fractionation rate and cell repopulation times, TCP again showed significant variation relative to EUD. The relative insensitivity of EUD implies that this index will be useful for dose evaluation when parameters are not known with accuracy, for the intercomparison of dose control studies and as a radiobiologically based optimization objective. However, given confidence in model parameters, the sensitivity of TCP would make it a more reliable tool for indicating potentially successful and unsuccessful irradiation strategies. It is suggested that both parameters be used in conjunction, with EUD and TCP results viewed with an appreciation of the characteristics of each model.

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Recent breakthroughs in photonics-based quantum, neuromorphic and analogue processing have pointed out the need for new schemes for fully programmable nanophotonic devices. Universal optical elements based on interferometer meshes are large compared to the limited chip real estate, restricting the scalability of the approach. Here, we propose an ultracompact platform for low-loss programmable elements using the complex transmission matrix of a multi-port multimode waveguide. Our approach allows the design of arbitrary transmission matrices using patterns of weakly scattering perturbations, which is successfully achieved by means of a deep learning inverse network. The demonstrated platform allows full control over both the intensity and phase of all outputs in a 3x3 multiport device using a footprint of 33x6 µm 2 and for typical perturbations achievable in experiments.

Some mathematical characteristics of tumour control probability (TCP) have been examined in the light of potential intra-tumour variations in clonogenic cell characteristics. In particular, an explicit expression for the relationship between the dose distribution and the probability of local clonogen eradication is obtained which maximizes the TCP using both general and specific TCP models, for the case of fixed energy deposition into the tumour volume. Characteristics of this expression are considered for the cases of varying clonogen cell density (uniform radiosensitivity) and uniform cell density (uniform radiosensitivity), yielding the 'uniform TCP' and 'uniform dose' results respectively for TCP maximization. These situations are examined graphically to highlight the possible consequences of neglecting intra-tumour heterogeneity in dose prescription.