Analysis Of Hierarchical Storage Of Radiological Images Based On The Morse Model

AbstractOne of the persistent problems facing radiology departments is storage and timely re­ trieval of images. Usually prudence and the law require that old studies be kept for yearsf which can often be difficult and costly. Digital storage of images poses even more diffi­ cult problems. The cost of rapid access storage is likely to force the development of hierarchical storage of images. This paper examines the problem of which images to migrate to secondary or tertiary storage and the cost of different approaches both in terms of dollars and probability of delayed access. The model used is based on P. M. Morse's model of library book circulation. The Morse model attempts to determine the probability distri­ bution of future use based the past use. It assumes that usage is a Markov process and that the probability that usage will be any particular value is dependent on the previous year's use. Each year's probability distribution is Poisson with the mean governed by a constant decay factor and by a factor which is a multiple of the actual use in the preceeding year. This model will be used as a basis for theoretical analysis to determine the cost of dif­ ferent methods of assigning images to secondary storage.IntroductionOne of the recurrent questions in radiology departments is what to do with images after they are taken. Many schemes have been developed to organize film libraries, to determine when to discard old images, and to decide when and how frequently to make duplicate copies of images. These questions are not unique to radiology departments' film libraries but also apply to libraries of patient records and still more generally books other materials. The advent of computer storeable data changes the problem in several ways. First, usage patterns of images may change as clinicians become familiar with the new technologies and availabilities of information. Second the cost differential between dif­ fering storage methods is different than the present choices and more likely to change rapidly over time. Third, the availability of temporarily creating and storing duplicate copies of images is increased and the cost is reduced. Fourth, the cost of communicating the images to different sites and the cost of viewing equipment at those sites become more important parts of the total cost picture.In this paper we will discuss a method of analyzing the economies of various storage algorithms and hierarchies. The purpose is to provide a means of determining the most appropriate and cost-effective structures for image storage given the relevant costs and some information about the usage patterns for the images. The intent is to model the usage of images in such a way as to allow the computation of system cost to be done more easily. We would desire to describe the usage patterns with a relatively small number of parameters which could then be input into the model as usage patterns change and the model could then be easily rerun with the new data. Also changing cost data could be plugged into the model and the library system structure changed as appropriate.The Morse ModelThe model of image usage proposed here was originally developed by Phillip Morse of MIT^ to model the usage of books in the science libraries there. The model was then used by Morse to describe the optimal policies for collection development, storage and circulation for these libraries. We shall attempt some of the equivalent analyses here for a library of radiological images and more particularly for libraries of digital images.The basic model assumes that usage is measured over a series of equal-length time periods. The amount of use in each time period is considered to be the state a Markov process. A Markov process is a theoretical construct used to describe the state of a system that changes stochastically. The system described is presumed to occupy a sequence of states - one state per time period. The Markovian assumption the assumption which dif­ ferentiates a Markov process from other stochastic models is that the state of the system in a random function only of the previous state of the system.The most commonly given example of a Markov process is a pond with lily pads and a frog. At any point in time the frog is on a particular lily pad. The lily pad occupied by the frog is considered the state of the system. In the next time period the frog will either remain on the lily pad or jump to another pad. From our point of view the behavior may well