Contributed Session Mon.3.H 2033

Monday, 15:15 - 16:45 h, Room: H 2033

Cluster 12: Life sciences & healthcare [...]

Therapy planning


Chair: Laurenz Göllmann



Monday, 15:15 - 15:40 h, Room: H 2033, Talk 1

Åsa Holm
A new optimization model for brachytherapy dose plans

Coauthors: Åsa Carlsson Tedgren, Torbjörn Larsson


There are many types of radiotherapy, brachytherapy is one such. As a part of treatment planning, a dose plan needs to be constructed, this decides where and for how long to irradiate. Optimization of dose plans for brachytherapy is still an area that is relatively unexplored, and since the treatment is quite different, models used for external radiotherapy are not directly applicable. In this talk I will highlight the most important differences and then present the model we have formulated and some results from our tests. Our model differs from others used in the brachytherapy field by more directly including dosimetric indices.



Monday, 15:45 - 16:10 h, Room: H 2033, Talk 2

Rasmus Bokrantz
Multi-criteria optimization for volumetric-modulated arc therapy by convex decompositions


Volumetric-modulated arc therapy (VMAT) is a technique for rotational radiation therapy that has gained widespread clinical use due to its ability of improving delivery efficiency without compromising treatment quality. Treatment planning for VMAT is a challenging multi-criteria decision problem due to a high-dimensional trade-off between tumor coverage and sparing of healthy structures in the vicinity of the target volume. Here, an approach to multi-criteria VMAT optimization is presented that relies on two convex decompositions of an initially nonconvex problem formulation. An infeasible relaxation with the elements of the energy fluence vector as variables is first used to define a global trade-off between conflicting objectives. The solution to the relaxed problem is subsequently converted into a deliverable VMAT plan. A feasible restriction with segment weights as variables is finally used to evaluate deliverable solutions in its neighborhood. The practical value of the presented method is discussed in view of comparative results with a commercially available single-objective method.



Monday, 16:15 - 16:40 h, Room: H 2033, Talk 3

Laurenz Göllmann
Combination therapy considered as a multiple delayed optimal control problem

Coauthor: Helmut Maurer


We consider optimal control problems with multiple time
delays in state and control and present an enhanced form of Pontryagin's
minimum principle as well as a numerical discretization method.
Let x(t) ∈ Rn denote the state and
u(t) ∈ Rm denote the control of a system at time t.
Time delays for x and u are
given by a vector (r1, … ,rd).
The problem for two delays has been investigated earlier in
[GöllmannKernMaurer09]. We now present
a generalization in form of necessary conditions for the problem with multiple
We finally optimize
a combination therapy by a model of the innate immune response
with a delayed antibody production and a retarded drug action.


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