Optimization theories and algorithms are used to efficiently find optimal solutions under constraints. In the era of “Big Data”, the amount of data is skyrocketing,and this overwhelms conventional techniques used to solve large scale and distributed optimization problems. By taking advantage of structural information in data representations, this thesis offers convex and non-convex optimization solutions to various large scale optimization problems such as super-resolution, sparse signal processing,hypothesis testing, machine learning, and treatment planning for brachytherapy. Super-resolution: Super-resolution aims to recover a signal expressed as a sum of a few Dirac delta functions in the time domain from measurements in the frequency domain. The challenge is that the possible locations of the delta functions are in the continuous domain [0,1). To enhance recovery performance, we considered deterministic and probabilistic prior information for the locations of the delta functions and provided novel semidefinite programming formulations under the information. We also proposed block iterative reweighted methods to improve recovery performance without prior information. We further considered phaseless measurements, motivated by applications in optic microscopy and x-ray crystallography. By using the lifting method and introducing the squared atomic norm minimization, we can achieve super-resolution using only low frequency magnitude information. Finally, we proposed non-convex algorithms using structured matrix completion. Sparse signal processing: L1 minimization is well known for promoting sparse structures in recovered signals. The Null Space Condition (NSC) for L1 minimization is a necessary and sufficient condition on sensing matrices such that a sparse signal can be uniquely recovered via L1 minimization. However, verifying NSC is a non-convex problem and known to be NP-hard. We proposed enumeration-based polynomial-time algorithms to provide performance bounds on NSC, and efficient algorithms to verify NSC precisely by using the branch and bound method. Hypothesis testing: Recovering statistical structures of random variables is important in some applications such as cognitive radio. Our goal is distinguishing two different types of random variables among n>>1 random variables. Distinguishing them via experiments for each random variable one by one takes lots of time and efforts. Hence, we proposed hypothesis testing using mixed measurements to reduce sample complexity. We also designed efficient algorithms to solve large scale problems. Machine learning: When feature data are stored in a tree structured network having time delay in communication, quickly finding an optimal solution to the regularized loss minimization is challenging. In this scenario, we studied a communication-efficient stochastic dual coordinate ascent and its convergence analysis. Treatment planning: In the Rotating-Shield Brachytherapy (RSBT) for cancer treatment, there is a compelling need to quickly obtain optimal treatment plans to enable clinical usage. However, due to the degree of freedom in RSBT, finding optimal treatment planning is difficult. For this, we designed a first order dose optimization method based on the alternating direction method of multipliers, and reduced the execution time around 18 times compared to the previous research.

Intensity-modulated brachytherapy techniques, compensator-based intensity modulated brachytherapy (CBT) and interstitial rotating shield brachytherapy (I-RSBT), are two novel conceptual radiation therapies for treating cervical and prostate cancer, respectively. Compared to conventional brachytherapy techniques for treating cervical cancer, CBT can potentially improve the dose conformity to the high-risk clinical target volume (CTV) of the cervix in a less invasive approach. I-RSBT can reduce the dose delivered to the prostate organ at risks (OARs) with the same radiation dose delivered to the prostate CTV. In this work, concepts and prototypes for CBT and I-RSBT were introduced and developed. Preliminary dosimetric measurements were performed for CBT and I-RSBT, respectively. A CBT prototype system was constructed and experimentally validated. A prototype cylindrical compensator with eight octants, each with different thicknesses, was designed. Direct metal laser sintering (DMLS) was used to construct CoCr and Ti compensator prototypes, and a 4-D milling technique was used to construct a Ti compensator prototype. Gafchromic EBT2 films, held by an acrylic quality assurance (QA) phantom, were irradiated to approximately 125 cGy with an electronic brachytherapy (eBT) source for both shielded and unshielded cases. The dose at each point on the films were calculated using a TG-43 calculation model that was modified to account for the presence of a compensator prototype by ray-tracing. With I-RSBT, a multi-pass dose delivery mechanism with prototypes was developed. Dosimetric measurements for a Gd-153 radioisotope was performed to demonstrate that using multiple partially shielded Gd-153 sources for I-RSBT is feasible. A treatment planning model was developed for applying I-RSBT clinically. A custom-built, stainless steel encapsulated 150 mCi Gd-153 capsule with an outer length of 12.8 mm, outer diameter of 2.10 mm, active length of 9.98 mm, and active diameter of 1.53 mm was used. A partially shielded catheter was constructed with a 500 micron platinum shield and a 500 micron aluminum emission window, both with 180° azimuthal coverage. An acrylic phantom was constructed to measure the dose distributions from the shielded catheter in the transverse plane using Gafchromic EBT3 films. Film calibration curves were generated from 50, 70, and 100 kVp x-ray beams with NIST-traceable air kerma values to account for energy variation. In conclusion, CBT, which is a non-invasive alternative to supplementary interstitial brachytherapy, is expected to improve dose conformity to bulky cervical tumors relative to conventional intracavitary brachytherapy. However, at the current stage, it would be time-consuming to construct a patient-specific compensator using DMLS, and the quality assurance of the compensator would be difficult. I-RSBT is a promising approach to reducing radiation dose delivered to prostate OARs. The next step in making Gd-153 based I-RSBT feasible in clinic is developing a Gd-153 source that is small enough such that the source, shield, and catheter all fit within a 16 guage needle, which has a 1.65 mm diameter.

The construction of phantoms for testing imaging parameters has been well documented in the literature. As computers have been introduced into the different areas of medicine, they have become more and more relied upon to replace conventional technologies. One specific example is that of plane film X-rays. Digitally Reconstructed Radiographs (DRR's) are computer generated images that are generated from a 3 D volume of data, such as CT or MRI axial scans, and can be used in place of conventional X rays. The computer can generate a DRR image for any position, orientation and magnification, and geometries not physically possible in the real world. In this work a technique is developed to generate phantoms that can be used for testing the accuracy of DRR's. A computer generated phantom can produce multiple test cases that can be used to test specific variables of the DRR's. A series of 12 different standard phantoms were used to test the ability of three different commercially available treatment planning or virtual simulation systems to generate DRR's. A virtual simulation system under development by the author and collaborators and seeking approval from the Food and Drug Administration (FDA), was used as a development platform for this work. Initial evaluation of the usefulness of the digital phantoms for testing showed immediate results. The first virtual simulation system tested with the phantoms revealed a major error in its ability to generate accurate DRR's. Subsequently tests of the three commercially available systems further demonstrated the usefulness of the work. The tests revealed errors in two of the three systems evaluated but it was determined that they were not clinically significant. In conclusion, the digital phantoms developed in this work are a fast, accurate method for testing digitally reconstructed radiographs. It is an extremely versatile testing method, as the phantoms can be generated with ease for any geometry without needing access to a CT scanner. This method of testing can be used to test a number of different DRR image parameters. Should an error be found, it can be used to isolate errors that might exist in the imaging device. It is an extremely versatile testing method, as the phantoms can be generated with ease for any geometry without needing access to a CT scanner. This method of testing can be used to test a number of different DRR image parameters. Should an error be found, it can be used to isolate errors that might exist in the imaging device.

<p>Biological treatment optimization aim at improving radiation therapy by accounting for the radiobiological tumour and normal tissues response properties when optimizing the dose delivery. Generally traditional methods, using only dosimetrical measures, disregard the nonlinear radiation response of different tumours and normal tissues. The accumulated knowledge on tissue response to radiation, in the form of more accurate dose response relations, cell survival models and their associated biological parameters, alongside with the tools for biological treatment plan optimization, has allowed the present investigation on the potential merits of biologically based treatment optimization in radiation therapy.</p><p>With a more widespread implementation of intensity modulated radiation therapy in the clinic, there is an increasing demand for faster and safer treatment delivery techniques. In this thesis biological treatment plan optimization, using the probability to achieve complication free tumour control as the quantifier for treatment outcome, was applied to radiation therapy of early breast cancer and advanced cervix cancer. It is shown that very conformal dose distributions can generally be produced with 3 or 4 optimally orientated coplanar intensity modulated beams, without having clinically significant losses in treatment outcome from the optimal dose distribution.</p><p>By using exhaustive search methods, the optimal coplanar beam directions for intensity modulated photon beams for early breast cancer and the optimal non-coplanar directions for an advanced cervix cancer were investigated. Although time consuming, exhaustive search methods have the advantage of revealing most features involving interactions between a small number of beams and how this may influence the treatment outcome. Thus phase spaces may serve as a general database for selecting an almost optimal treatment configuration for similar patients. Previous knowledge acquired with physically optimized uniform beam radiation therapy may not apply when intensity modulated biological optimization is used. Thus unconventional treatment directions were sometimes found.</p>

<p>The major aim was to explore perceived daily occupations in mentally disordered offenders (MDO) through occupational performance (OP) and social participation (SP) with descriptive, comparative and longitudinal designs. The 74 consecutively included MDOs were visited onsite for data collection. The following assessments were used: Capability to Perform Daily Occupation, Self-efficacy Scale, Importance scale, Allen Cognitive Level Screen, Interview Schedule for Social Interaction, Manchester Short Assessment of Quality of Life, Psycho/social and Environmental Problems, Global Assessment of Functioning Scale, assessment of Support and Service for Persons with Certain Functional Impairments and Karolinska Scales of Personality. Background factors were assembled from the individual forensic psychiatric investigation. The results indicate that MDOs had contradictive problems in OP, SP and lack of disability awareness. The MDOs and professionals had different appraisals of the MDOs’ OP and SP. Schizophrenic MDOs need substantial support for community dwelling. MDOs with psychopathic personality traits had more problems during upbringing, however, no perceived problems in OP and SP compared to the remaining group. Low Socialization, high Anxiety and psychopathy personality traits partially influenced perceived OP and SP. After one year of forensic psychiatric care, 60 % were still hospitalized and 32 % were community dwelling. Changes after one year of care consisted of higher satisfaction of OP and SP, 1/36 subject valued daily occupations higher and 5/36 subjects reported better social interaction. Although, there are some methodological weaknesses in this thesis (e.g. high attrition rate), the unique results should be taken into consideration. It is concluded that MDOs’ appraisal of their own capability has to be taken seriously in treatment and care. Also long treatment periods, targeting daily occupations from start and providing substantial individual support are necessary for successful transition into community dwelling for MDOs. This thesis contributes to extended knowledge of the MDOs’ daily occupations.</p>

Biological treatment optimization aim at improving radiation therapy by accounting for the radiobiological tumour and normal tissues response properties when optimizing the dose delivery. Generally traditional methods, using only dosimetrical measures, disregard the nonlinear radiation response of different tumours and normal tissues. The accumulated knowledge on tissue response to radiation, in the form of more accurate dose response relations, cell survival models and their associated biological parameters, alongside with the tools for biological treatment plan optimization, has allowed the present investigation on the potential merits of biologically based treatment optimization in radiation therapy. With a more widespread implementation of intensity modulated radiation therapy in the clinic, there is an increasing demand for faster and safer treatment delivery techniques. In this thesis biological treatment plan optimization, using the probability to achieve complication free tumour control as the quantifier for treatment outcome, was applied to radiation therapy of early breast cancer and advanced cervix cancer. It is shown that very conformal dose distributions can generally be produced with 3 or 4 optimally orientated coplanar intensity modulated beams, without having clinically significant losses in treatment outcome from the optimal dose distribution. By using exhaustive search methods, the optimal coplanar beam directions for intensity modulated photon beams for early breast cancer and the optimal non-coplanar directions for an advanced cervix cancer were investigated. Although time consuming, exhaustive search methods have the advantage of revealing most features involving interactions between a small number of beams and how this may influence the treatment outcome. Thus phase spaces may serve as a general database for selecting an almost optimal treatment configuration for similar patients. Previous knowledge acquired with physically optimized uniform beam radiation therapy may not apply when intensity modulated biological optimization is used. Thus unconventional treatment directions were sometimes found.

The major aim was to explore perceived daily occupations in mentally disordered offenders (MDO) through occupational performance (OP) and social participation (SP) with descriptive, comparative and longitudinal designs. The 74 consecutively included MDOs were visited onsite for data collection. The following assessments were used: Capability to Perform Daily Occupation, Self-efficacy Scale, Importance scale, Allen Cognitive Level Screen, Interview Schedule for Social Interaction, Manchester Short Assessment of Quality of Life, Psycho/social and Environmental Problems, Global Assessment of Functioning Scale, assessment of Support and Service for Persons with Certain Functional Impairments and Karolinska Scales of Personality. Background factors were assembled from the individual forensic psychiatric investigation. The results indicate that MDOs had contradictive problems in OP, SP and lack of disability awareness. The MDOs and professionals had different appraisals of the MDOs’ OP and SP. Schizophrenic MDOs need substantial support for community dwelling. MDOs with psychopathic personality traits had more problems during upbringing, however, no perceived problems in OP and SP compared to the remaining group. Low Socialization, high Anxiety and psychopathy personality traits partially influenced perceived OP and SP. After one year of forensic psychiatric care, 60 % were still hospitalized and 32 % were community dwelling. Changes after one year of care consisted of higher satisfaction of OP and SP, 1/36 subject valued daily occupations higher and 5/36 subjects reported better social interaction. Although, there are some methodological weaknesses in this thesis (e.g. high attrition rate), the unique results should be taken into consideration. It is concluded that MDOs’ appraisal of their own capability has to be taken seriously in treatment and care. Also long treatment periods, targeting daily occupations from start and providing substantial individual support are necessary for successful transition into community dwelling for MDOs. This thesis contributes to extended knowledge of the MDOs’ daily occupations.

Scanned proton beams offer the possibility to take full advantage of the dose deposition properties of proton beams, i.e. the limited range and sharp peak at the end of the range, the Bragg peak. By actively scanning the proton beam, laterally by scanning magnets and longitudinally by shifting the energy, the position of the Bragg peak can be controlled in all three dimensions, thereby enabling high dose delivery to the target volume only. A typical scanned proton beam line consists of a pair of scanning magnets to perform the lateral beam scanning and possibly a range shifter and a multi-leaf collimator (MLC). Part of this thesis deals with the development of control, supervision and verification methods for the scanned proton beam line at the The Svedberg laboratory in Uppsala, Sweden. Radiotherapy is preceded by treatment planning, where one of the main objectives is predicting the dose to the patient. The dose is calculated by a dose calculation engine and the accuracy of the results is of course dependent on the accuracy and sophistication of the transport and interaction models of the dose engine itself. But, for the dose distribution calculation to have any bearing on the reality, it needs to be started with relevant input in accordance with the beam that is emitted from the treatment machine. This input is provided by the beam model. As such, the beam model is the link between the reality (the treatment machine) and the treatment planning system. The beam model contains methods to characterise the treatment machine and provides the dose calculation with the reconstructed beam phase space, in some convenient representation. In order for a beam model to be applicable in a treatment planning system, its methods have to be general. In this thesis, a beam model for a scanned proton beam is developed. The beam model contains models and descriptions of the beam modifying elements of a scanned proton beam line. Based on a well-defined set of generally applicable characterisation measurements, ten beam model parameters are extracted, describing the basic properties of the beam, i.e. the energy spectrum, the radial and the angular distributions and the nominal direction. Optional beam modifying elements such as a range shifter and an MLC are modelled by dedicated Monte Carlo calculation algorithms. The algorithm that describes the MLC contains a parameterisation of collimator scatter, in which the rather complex phase space of collimator scattered protons has been parameterised by a set of analytical functions. Dose calculations based on the phase space reconstructed by the beam model are in good agreement with experimental data. This holds both for the dose distribution of the elementary pencil beam, reflecting the modelling of the basic properties of the scanned beam, as well as for complete calculations of collimated scanned fields.

Περιλαμβάνονται όλες οι διαδικασίες ποιοτικού ελεγχου σε ένα σύγχρονο σύστημα πλάνου θεραπείας (treatment planning) τρισδιάστατης σύμμορφης ακτινοθεραπείας (3D-CRT). Θα αναφερθούμε στην χρησιμότητα του ποιοτικού ελέγχου των συστημάτων απεικόνισης που σχετίζονται με την ακτινοθεραπεία και έπειτα θα κατηγοριοποιήσουμε και αναλύσουμε τις κατηγορίες ελέγχου ενός σύγχρονου συστήματος πλάνου θεραπείας. Στο τέλος θα αναφερθούμε στις τακτικές δοκιμές ποιοτικού ελέγχου, ώστε να διασφαλιστεί ο συνεχής έλεγχος πιθανών σφαλμάτων και η σωστή λειτουργία όλου του συστήματος. Προτού συνεχίσουμε, θα πρέπει να αναφέρουμε την χρησιμότητα ύπαρξης ενός πρωτοκόλλου μεταφοράς ιατρικών εικόνων, καθώς η μεταφορά ιατρικών εικόνων έχει άμεση συνάφεια με το QA των σύγχρονων συστημάτων πλάνου θεραπείας. / The procedures that are involved in quality assurance for a 3D conformal radiotherapy treatment planning system.

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