Practical IMRT treatment-plan optimization is based on the creation of a joint objective function that promotes dose to the target volume and penalizes dose delivery elsewhere, paying special attention to certain volumes-at-risk. In practice, the planner must guess the values of certain starting parameters (the volume-objective relative weights) and achieve overall plan optimization via repeated iterations. Unfortunately, such parameters appear to be specific to patient anatomy peculiarities, with no universally applicable set of "golden" starting parameters available.
Evolving thinking in the area of IMRT optimization suggests that the treatment-planning task is an optimization-under-constraints Pareto problem (based on the Pareto principle in which 20% of the input creates 80% of the results). Such cases are found in other fields of applied science and can be addressed mathematically via multi-objective optimization programming (MOP), in which conflicting objectives are optimized simultaneously subject to certain constraints. In the case of IMRT, the MOP method starts with the generation of a database of radiotherapy plans, created using parameters that span the reasonable clinical phase-space.
In this paradigm, radiotherapy planning can be thought as a transformation that maps discreet points of the clinical parameter phase-space into a more restrictive volume: the dose-deliverable phase-space. MOP appears to be a promising technique, especially since it reveals to the planner the landscape of options available in the vicinity of the plan of choice. There's a downside, however: the severe computational cost of generating hundreds of individual plans in order to densely cover the parameter phase-space.
To address the issue of generating such a large number of radiotherapy plans in a clinically reasonable time, we have introduced a technique that was initially developed for the needs of the high-energy physics community: the computational grid.
Shared resource
A computational grid, as defined by Ian Foster and Carl Kesselman (arguably the pioneers of the concept more than a decade ago1) is "a hardware/software infrastructure that provides dependable, consistent, pervasive and inexpensive access to high-end computational capabilities." In other words, it's a means of simultaneously applying the resources of many networked computers to a single problem.
Take, for instance, the idea of a web site designed for advanced algebra applications, in which the user enters the values of a large square matrix that needs to be inverted. Transparently to the user, the inverse matrix is computed by feeding discreet calculations to many processors, the results are collected, final values stored and a text message sent upon completion of the task. Such a scheme would effectively allow inverse matrix calculations for anyone with a modern cell phone.
For an example closer to clinical radiotherapy planning, consider a similar computer interface in which the user submits a DICOM-RT file including delineated target volume and organs-at-risk, a set of dose-coverage requirements (say, in some form of dose-volume histogram or a reasonable objective function value), a specific radiotherapy delivery hardware option (say, a Varian Trilogy or a Siemens Artiste linac) and a specific planning package (say, DKFZ KonRad or BrainLab iPlan).
Shortly after submission, the user receives the clinical phase-space coordinates of 200 radiotherapy plans in the neighbourhood of the desired initial conditions. These options can then be "navigated" to arrive at a Pareto-optimal, clinically relevant and realistically deliverable radiotherapy plan.
Clinical case
Commercial radiotherapy planning systems don't generally allow for facile generation of treatment plans with starting parameters covering the planning phase-space. One notable exception is BrainLab's BrainScan/iPlan that, in its IMRT-mode, automatically generates four "nearby" plans for every set of starting parameters, with different degrees of target coverage/organ-at-risk sparing.
Using the computational engine of Pinnacle (version 7.6, Philips) we built a computational grid designed to generate a large number of radiotherapy plans for a challenging base-of-the-tongue case. The organs-at-risk were defined as the left parotid, right parotid and spinal cord. Using a plausible set of initial conditions, the grid created 150 individual plans in around three hours. We estimate that execution of this task on a Sun Blade 2000 workstation would have taken in excess of 60 CPU-hrs.
Our computational grid comprises around 55 commodity workstations (HP dc7600, Pentium4 2.8 GHz) running ScientificLinux 4.4 (CERN/Fermilab) and gLite, a next-generation middleware for grid computing developed within the Enabling Grids for E-Science project. For convenience and for data security, our grid was physically under our control. The grid was computationally activated after-hours or during weekends.
At the end of the computation, all of the integral dose-volume histograms (DVH) for the completed plans were saved for analysis. The resulting integral DVH plots from all plans were then examined by at least three experienced radiotherapy planners, who graded them as "good" or "no good" and awarded them 1 or 0 points respectively.
We used the equivalent uniform dose (EUD) as our organ objective function (a means to represent the global information contained in a DVH by a single number). For visualization simplicity, plotting the objective functions of just two organs-at-risk (the spinal cord and the right parotid) reveals a clear Pareto boundary. In addition, when highlighting the subjective subset of better plans, it is intriguing to see their preferential clustering at the edge of the Pareto bound of optimality (see figure).
Multi-objective optimized radiotherapy planning attempts to offer an intriguing solution to our current inability to produce certified optimal IMRT plans. We have demonstrated that computational grids are both feasible and - as the only existing realistic generators of large number of quasi-optimal plans - essential to the success of such a programme. We envision the deployment of geographically dispersed, load-balanced, time-shifted computational grids for our clinical needs, following the infrastructure lessons from the high-energy physics labs.
Unfortunately, the utility of such computational grids is not yet widely known to the IMRT practitioners. However, the radiotherapy community commands ample resources that, if harnessed as a focused computational grid virtual organization, could produce true personalized medicine for the immediate benefit of our patients.