Optimal modality selection in external beam radiotherapy.

The goal in external beam radiotherapy (EBRT) for cancer is to maximize damage to the tumour while limiting toxic effects on the organs-at-risk. EBRT can be delivered via different modalities such as photons, protons and neutrons. The choice of an optimal modality depends on the anatomy of the irradiated area and the relative physical and biological properties of the modalities under consideration. There is no single universally dominant modality. We present the first-ever mathematical formulation of the optimal modality selection problem. We show that this problem can be tackled by solving the Karush-Kuhn-Tucker conditions of optimality, which reduce to an analytically tractable quartic equation. We perform numerical experiments to gain insights into the effect of biological and physical properties on the choice of an optimal modality or combination of modalities.

A passive cold storage device economic model to evaluate selected immunization location scenarios.

BACKGROUND: The challenge of keeping vaccines cold at health posts given the unreliability of power sources in many low- and middle-income countries and the expense and maintenance requirements of solar refrigerators has motivated the development of passive cold storage devices (PCDs), containers that keep vaccines cold without using an active energy source. With different PCDs under development, manufacturers, policymakers and funders need guidance on how varying different PCD characteristics may affect the devices' cost and utility. METHODS: We developed an economic spreadsheet model representing the lowest two levels of a typical Expanded Program on Immunization (EPI) vaccine supply chain: a district store, the immunization locations that the district store serves, and the transport vehicles that operate between the district store and the immunization locations. The model compares the use of three vaccine storage device options [(1) portable PCDs, (2) stationary PCDs, or (3) solar refrigerators] and allows the user to vary different device (e.g., size and cost) and scenario characteristics (e.g., catchment area population size and vaccine schedule). RESULTS: For a sample set of select scenarios and equipment specification, we found the portable PCD to generally be better suited to populations of 5,000 or less. The stationary PCD replenished once per month can be a robust design especially with a 35L capacity and a cost of $2,500 or less. The solar device was generally a reasonable alternative for most of the scenarios explored if the cost was $2,100 or less (including installation). No one device type dominated over all explored circumstances. Therefore, the best device may vary from country-to-country and location-to-location within a country. CONCLUSIONS: This study introduces a quantitative model to help guide PCD development. Although our selected set of explored scenarios and device designs was not exhaustive, future explorations can further alter model input values to represent additional scenarios and device designs.