Mathematical Methods in Medical Physics


Department of Radiation Oncology
Regensburg University Medical Center
93053 Regensburg, Germany

wolfgang.hoegele {at} hs-regensburg.de


Research projects:     

»  Stochastic Modeling for Patient Positioning (Doctoral Studies)
»  Inverse Planning Optimization for VMAT  

»  Publications  
»  Talks  





Focus of Research for Doctoral Studies


Determination of Setup-Errors in Patient Positioning for Radiotherapy
Utilizing Cone-Beam CT Projections
—
Working with Non-negligible Geometrical Uncertainties in Poor Data Acquisition Scenarios
Utilizing Prior Knowledge in a Bayesian Framework - with and w/o Time Dependency


This research project takes place in the field of Medical Physics and image processing with its applications to radiotherapy.
The objective of this work is to find a clinically useful approach for the determination of setup-errors in patient positioning prior to the radiotherapy treatment. The primary source of data are Cone-Beam CT (CBCT) projections.

Linear accelerators with on-board X-ray imaging devices are commercially available in the last few years. Their use is to detect the patient position prior to the actual treatment in the framework of image guided radiotherapy (IGRT). Once the patient position is determined the patient is shifted and (sometimes) slightly rotated to fit optimally to the treatment plan. This is performed to achieve an effective treatment (accurately irradiating the target and sparing the surrounding normal tissue as much as possible).

Up to now commercially available systems (such as at the University Hospital Regensburg) utilize a full CBCT scan, meaning all projections in a range of about 200 degrees for a small imaging area and 360 degrees for larger imaging areas. With this full set of projections a Cone-Beam CT volume is reconstructed (typically by filtered backprojection techniques) and easily detectable structures (such as bones) between the full planning CT and the CBCT image are matched automatically. After that a manual interaction of the user has to take place to verify or change the computer assisted registration. Since nonlinear geometrical deformations might occur inside the body of the patient, a current field of research is non-rigid image registration, what is up to now not broadly applied in the clinical routine.

In the standard approaches the only prior knowledge utilized for patient positioning is derived from the planning CT. In this research project the focus is on the development of a new technique that utilizes planning CT as well as additional prior knowledge derived from clinical experience (such as the expectation of the range of shifts and/or formerly registered CBCT images in the course of fractionation, or the delineation of organs, etc.). In such an approach not a full CBCT scan might be necessary anymore and a partial or sparse set of CBCT projections might be sufficient for patient positioning. This would have advantages, such as dose reduction (following the general principle of dose reduction: As Low As Reasonably Possible (ALARP)), a reliable positioning of patients when only sparse or partial beams are possible (because of the patient setup) and better time efficiency of the scanning (less motion artifacts). Additionally a main problem in image reconstruction, metal artifacts (also occuring for similary dense material), is naturally avoided with this approach since there are no artifacts in the projections. Moreover the investigation of which CBCT data is actually useful for a robust determination of setup-errors in patient positioning is of a more fundamental interest.

The direct approach focused on is based on a combination of estimation theory (stochastics) utilizing a Bayesian framework and the underlying geometrical situation of the measurement. It includes prior knowledge in a transparent way, models the non-negligible uncertainties of the measurement situation and also regards non-rigid (nonlinear) transformations inside the body, such as deformations of organs and their relative interfractional shifts. Moreover, estimation theory provides good possibilities to investigate such situations in a rather general way with fundamental bounds for accuracy and theoretical properties of estimation, such as efficiency or consistency. The practical focus lies on a computationally efficient, robust and intuitive approach, that allows direct interpretations of the algorithm and the results in the clinical application.

This project is a cooperation of the University Hospital Regensburg, the Dana Farber / Brigham and Women’s Cancer Center, HMS (Boston, USA), and the University of Applied Sciences Regensburg (Department of Computer Science and Mathematics).





Research on VMAT Optimization


Inverse Planning Optimization for Volumetric Modulated Arc Therapy (VMAT)
Utilizing the Projection Theorem


This project takes place in the field of inverse planning optimization, as it is typically performed in radiation therapy based on intensity modulation by dynamic multi-leaf collimators (dMLCs) in a treatment planning system (TPS). The results of this optimization is the way the linear accelerator (linac) with the corresponding dMLC system has to move for the treatment of a given patient. This includes the individual dose prescriptions, geometries of the planning target volume (PTV), in which the applied dose has to be focussed, next to organs at risk (OARs), which have to be spared due to dose sensitivity. This optimization has also to take care about the physical constraints, such as a realistic X-Ray-Beam model and the physical constraints of the treatment machine (maximal leaf and gantry speed).

This complex optimization is typically solved with rather general iterative optimization methods, such as gradient methods and its modifications (essentially based on the Banach fixed point theorem) or the more physically interpretable simulated annealing methods. Iterative methods have the disadvantage to represent local optimizers, since they essentially can get stuck in local minimas. Additionally, they depend strongly on a well chosen starting value and tend to lead to rather extensive optimizations.

The idea of this project is to model the inverse problem for the special application of volumetric arc therapy (VMAT - including simultaneous motion of the leaves, the gantry and change of the dose rate) in such a way that global optimization can be performed, applying the Projection Theorem in inner product spaces of Functional Analysis. Therefore we call this method straightforwardly the Projection Method. This new way of stating the inverse problem includes a simple, but very general motion model of the multi-leaf collimator that leaves just a few degrees of freedom left compared to the classical modeling (representing also a direct aperture approach optimization (DAO)). For these few degrees of freedom optimization can be performed by just solving a single small-to-medium sized system of linear equations, the so called normal equations.

This global optimization leads eventually to unique, always existing solutions, that depend intuitively (continuously) on the geometry and the dose prescription. This means, if for example a minor redefinition of the PTV is necessary - as it may be necessary in adaptive planning - the resulting motions of the machine will also be just slightly different. This cannot be guaranteed by the broadly applied optimization methods up to now. In total, these properties are rather unusual for this field of research and may simplify the optimization process, making it reproducible and eventually more transparent.

Leaf motion patterns and their corresponding solutions for concave PTVs surrounding a single OAR (typical for prostate-rectum geometry) and for convex PTVs close to several OARs (typical for spine or breast geometry) are investigated. The results are comparable to current clinically applied software, but have advantages due to the strong theoretical properties. Focus of future work is to further test the clinical applicability of this type of optimization by more adaptive leaf motion patterns and, implicitly, to state and solve the inverse problem of treatment planning optimization in a more general way.





Original Research Articles / Forschungsartikel


An Efficient Inverse Radiotherapy Planning Method for VMAT using
Quadratic Programming Optimization (PubMed)
W. Hoegele, R. Loeschel, N. Merkle and P. Zygmanski
Medical Physics, 39:444-454, 2012

Stochastic Formulation of Patient Positioning Using Linac-Mounted
Cone Beam Imaging with Prior Knowledge (PubMed)
W. Hoegele, R. Loeschel, B. Dobler, J. Hesser, O. Koelbl and P. Zygmanski
Medical Physics, 38:668-681, 2011

Clinical Application of Varian OBI CBCT System and Dose Reduction Techniques
in Breast Cancer Patients Set-up (PubMed)
S. Ueltzhöffer, P. Zygmanski, J. Hesser, W. Högele, J. Wong, J. R. Bellon and Y. Lyatskaya
Medical Physics, 37:2985-2998, 2010

An Alternative VMAT with Prior Knowledge about the Type of Leaf Motion
Utilizing Projection Method for Concave Targets (PubMed)
W. Hoegele, R. Loeschel. and P. Zygmanski
Medical Physics, 36:3764-3774, 2009

A volumetric-modulated arc therapy using sub-conformal dynamic arc
with a monotonic dynamic multileaf collimator modulation (PubMed)
Zygmanski P, Högele W, Cormack R, Chin L, Löschel R
Physics in Medicine and Biology, 53:6395-6417, 2008


Further Publications / Weitere Veröffentlichungen


A Bayesian Framework for Marker-Based Patient Positioning with a Few Projections in Very Short Arcs
W. Hoegele, R. Loeschel, B. Dobler, M. Kroiss, O. Koelbl and P. Zygmanski
ESTRO 31, Volume 103, Supplement 1, 165-166, 2012

Introducing A Stochastic Model in Order to Deal with Marker Displacements due to Non-Rigid Deformations in Feature Based Image Registration for Patient Positioning with Multiple Radiographs
W. Hoegele, P. Zygmanski, B. Dobler, O. Koelbl and R. Loeschel
3 Ländertagung der ÖGMP, DGMP und SGSMP, Conference Proceedings, 100-101, 2011

An Alternative Approach to Inverse Planning Optimization:
Applying the Projection Theorem to Concave and Convex PTVs for VMAT Delivery
W. Hoegele, R. Loeschel. and P. Zygmanski
World Congress on Medical Physics and Biomedical Engineering, Munich, Germany
IFMBE Proceedings, 25/I:848–851, 2009


Master's Thesis:

 Inverse Planning Optimization for Arc Therapy by Projection Method
Medizinische Fakultät Mannheim, Ruprecht-Karls-Universität Heidelberg, 2009


Diploma Thesis / Diplomarbeit:

 IMAT with dMLCs - Modeling, Analysis, Optimization
Fakultät Informatik und Mathematik, Hochschule Regensburg, 2007




Conferences / Konferenzen


A Bayesian Framework for Marker-Based Patient Positioning with a Few Projections in Very Short Arcs
Talk for the Award, ESTRO 31, Barcelona, Spain, May 2012

Introducing A Stochastic Model in Order to Deal with Marker Displacements due to Non-Rigid Deformations
in Feature Based Image Registration for Patient Positioning with Multiple Radiographs
Poster, 3 Ländertagung der ÖGMP, DGMP und SGSMP, Vienna, Austria, September/October 2011

An Alternative Approach to Inverse Planning Optimization:
Applying the Projection Theorem to Concave and Convex PTVs for VMAT Delivery
Talk, World Congress on Medical Physics and Biomedical Engineering, Munich, Germany, September 2009

A new VMAT - delivery scheme, solution of inverse problem and main properties
Talk, New England AAPM Young Investigators Symposium, Boston, USA, May 2008


Internal Talks in Research Groups / Arbeitsgruppenvorträge


Marker-Basierte Patientenpositionierung mit wenigen Radiographen
in kleinwinkligen Aufnahmen unter der Verwendung von Bayes'scher Schätzung
2. Kolloquium
Department of Radiation Oncology, University Hospital Regensburg, Germany, November 2011

Bayesian Inference for Patient Positioning
Current Developments of the Collaboration for Ph.D.
Dana-Farber / Brigham and Women's Cancer Center, Boston, USA, September 2011

Monte-Carlo Algorithmen: Idee und Anwendungen
Medical Physics Seminar, Department of Radiation Oncology, University Hospital Regensburg, Germany, May 2011

Aktuelle Techniken zur Patientenpositionierung
Department of Radiation Oncology, University Hospital Regensburg, Germany, April 2011

Gauß'sche Prozesse und ihre Anwendung in der Regression
Einführung in die Nichtparametrische Regression
Medical Physics Seminar, Department of Radiation Oncology, University Hospital Regensburg, Germany, December 2010

Stochastische Formulierung der Patientenpositionierung mithilfe in Radiographen detektierter Features
1. Kolloquium
Department of Radiation Oncology, University Hospital Regensburg, Germany, November 2010

Application of Parameter Estimation to Patient Positioning
Current Developments of the Collaboration for Ph.D.
Dana-Farber / Brigham and Women's Cancer Center, Boston, USA, September 2010

Parameter Estimation Theory - An Intuitive Introduction for Everyone
Dana-Farber / Brigham and Women's Cancer Center, Boston, USA, September 2010

Estimation Theory for Patient Positioning - Maximum A Posteriori Estimation
Department of Radiation Oncology, University Hospital Regensburg, Germany, August 2010

Patient Setup-Error Modeled with Probabilities
Medical Physics Seminar, Department of Radiation Oncology, University Hospital Regensburg, Germany, June 2010

VMAT Optimization by Projection Method
Department of Radiation Oncology, University Hospital Regensburg, Germany, May 2010

Inverse Planning Optimization for Arc Therapy by Projection Method
Dana-Farber / Brigham and Women's Cancer Center, Boston, USA, August 2009

Mathematiker in der Medizinphysik - Beispiel eines Quereinstiegs
Alumni-Vortrag, Hochschule Regensburg, Germany, December 2008

The VMAT Technique - The goals achieved and future directions
Dana-Farber / Brigham and Women's Cancer Center, Boston, USA, June 2008

VMAT inverse planning algorithm - an intuitive solution, basic properties and future directions
Dana-Farber / Brigham and Women's Cancer Center, Boston, USA, February 2008