Beam Angle Optimization for Automated Coplanar IMRT Lung Plans

Purpose: To investigate the effect of incorporating a beam spreading parameter in a beam angle optimization algorithm and to evaluate its efficacy for creating coplanar IMRT lung plans in conjunction with machine learning generated dose objectives.

Methods: Fifteen anonymized patient cases were each re-planned with ten values over the range of the beam spreading parameter, k, and analyzed with a Wilcoxon signed-rank test to determine whether any particular value resulted in significant improvement over the initially treated plan created by a trained dosimetrist. Dose constraints were generated by a machine learning algorithm and kept constant for each case across all k values. Parameters investigated for potential improvement included mean lung dose, V20 lung, V40 heart, 80% conformity index, and 90% conformity index.

Results: With a confidence level of 5%, treatment plans created with this method resulted in significantly better conformity indices. Dose coverage to the PTV was improved by an average of 12% over the initial plans. At the same time, these treatment plans showed no significant difference in mean lung dose, V20 lung, or V40 heart when compared to the initial plans; however, it should be noted that these results could be influenced by the small sample size of patient cases.

Conclusions: The beam angle optimization algorithm, with the inclusion of the beam spreading parameter k, increases the dose conformity of the automatically generated treatment plans over that of the initial plans without adversely affecting the dose to organs at risk. This parameter can be varied according to physician preference in order to control the tradeoff between dose conformity and OAR sparing without compromising the integrity of the plan.

Learning from Geometry

Subspaces and manifolds are two powerful models for high dimensional signals. Subspaces model linear correlation and are a good fit to signals generated by physical systems, such as frontal images of human faces and multiple sources impinging at an antenna array. Manifolds model sources that are not linearly correlated, but where signals are determined by a small number of parameters. Examples are images of human faces under different poses or expressions, and handwritten digits with varying styles. However, there will always be some degree of model mismatch between the subspace or manifold model and the true statistics of the source. This dissertation exploits subspace and manifold models as prior information in various signal processing and machine learning tasks.

A near-low-rank Gaussian mixture model measures proximity to a union of linear or affine subspaces. This simple model can effectively capture the signal distribution when each class is near a subspace. This dissertation studies how the pairwise geometry between these subspaces affects classification performance. When model mismatch is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the model mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. This linear transformation, termed TRAIT, also preserves some specific features in each class, being complementary to a recently developed Low Rank Transform (LRT). Moreover, when the model mismatch is more significant, TRAIT shows superior performance compared to LRT.

The manifold model enforces a constraint on the freedom of data variation. Learning features that are robust to data variation is very important, especially when the size of the training set is small. A learning machine with large numbers of parameters, e.g., deep neural network, can well describe a very complicated data distribution. However, it is also more likely to be sensitive to small perturbations of the data, and to suffer from suffer from degraded performance when generalizing to unseen (test) data.

From the perspective of complexity of function classes, such a learning machine has a huge capacity (complexity), which tends to overfit. The manifold model provides us with a way of regularizing the learning machine, so as to reduce the generalization error, therefore mitigate overfiting. Two different overfiting-preventing approaches are proposed, one from the perspective of data variation, the other from capacity/complexity control. In the first approach, the learning machine is encouraged to make decisions that vary smoothly for data points in local neighborhoods on the manifold. In the second approach, a graph adjacency matrix is derived for the manifold, and the learned features are encouraged to be aligned with the principal components of this adjacency matrix. Experimental results on benchmark datasets are demonstrated, showing an obvious advantage of the proposed approaches when the training set is small.

Stochastic optimization makes it possible to track a slowly varying subspace underlying streaming data. By approximating local neighborhoods using affine subspaces, a slowly varying manifold can be efficiently tracked as well, even with corrupted and noisy data. The more the local neighborhoods, the better the approximation, but the higher the computational complexity. A multiscale approximation scheme is proposed, where the local approximating subspaces are organized in a tree structure. Splitting and merging of the tree nodes then allows efficient control of the number of neighbourhoods. Deviation (of each datum) from the learned model is estimated, yielding a series of statistics for anomaly detection. This framework extends the classical {\em changepoint detection} technique, which only works for one dimensional signals. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

Learning and Exploiting Camera Geometry for Computer Vision

This work explores the use of statistical methods in describing and estimating camera poses, as well as the information feedback loop between camera pose and object detection. Surging development in robotics and computer vision has pushed the need for algorithms that infer, understand, and utilize information about the position and orientation of the sensor platforms when observing and/or interacting with their environment.

The first contribution of this thesis is the development of a set of statistical tools for representing and estimating the uncertainty in object poses. A distribution for representing the joint uncertainty over multiple object positions and orientations is described, called the mirrored normal-Bingham distribution. This distribution generalizes both the normal distribution in Euclidean space, and the Bingham distribution on the unit hypersphere. It is shown to inherit many of the convenient properties of these special cases: it is the maximum-entropy distribution with fixed second moment, and there is a generalized Laplace approximation whose result is the mirrored normal-Bingham distribution. This distribution and approximation method are demonstrated by deriving the analytical approximation to the wrapped-normal distribution. Further, it is shown how these tools can be used to represent the uncertainty in the result of a bundle adjustment problem.

Another application of these methods is illustrated as part of a novel camera pose estimation algorithm based on object detections. The autocalibration task is formulated as a bundle adjustment problem using prior distributions over the 3D points to enforce the objects' structure and their relationship with the scene geometry. This framework is very flexible and enables the use of off-the-shelf computational tools to solve specialized autocalibration problems. Its performance is evaluated using a pedestrian detector to provide head and foot location observations, and it proves much faster and potentially more accurate than existing methods.

Finally, the information feedback loop between object detection and camera pose estimation is closed by utilizing camera pose information to improve object detection in scenarios with significant perspective warping. Methods are presented that allow the inverse perspective mapping traditionally applied to images to be applied instead to features computed from those images. For the special case of HOG-like features, which are used by many modern object detection systems, these methods are shown to provide substantial performance benefits over unadapted detectors while achieving real-time frame rates, orders of magnitude faster than comparable image warping methods.

The statistical tools and algorithms presented here are especially promising for mobile cameras, providing the ability to autocalibrate and adapt to the camera pose in real time. In addition, these methods have wide-ranging potential applications in diverse areas of computer vision, robotics, and imaging.

Development and Testing of An Automatic Lung IMRT Planning Algorithm

Knowledge-based radiation treatment is an emerging concept in radiotherapy. It

mainly refers to the technique that can guide or automate treatment planning in

clinic by learning from prior knowledge. Dierent models are developed to realize

it, one of which is proposed by Yuan et al. at Duke for lung IMRT planning. This

model can automatically determine both beam conguration and optimization ob-

jectives with non-coplanar beams based on patient-specic anatomical information.

Although plans automatically generated by this model demonstrate equivalent or

better dosimetric quality compared to clinical approved plans, its validity and gener-

ality are limited due to the empirical assignment to a coecient called angle spread

constraint dened in the beam eciency index used for beam ranking. To eliminate

these limitations, a systematic study on this coecient is needed to acquire evidences

for its optimal value.

To achieve this purpose, eleven lung cancer patients with complex tumor shape

with non-coplanar beams adopted in clinical approved plans were retrospectively

studied in the frame of the automatic lung IMRT treatment algorithm. The primary

and boost plans used in three patients were treated as dierent cases due to the

dierent target size and shape. A total of 14 lung cases, thus, were re-planned using

the knowledge-based automatic lung IMRT planning algorithm by varying angle

spread constraint from 0 to 1 with increment of 0.2. A modied beam angle eciency

index used for navigate the beam selection was adopted. Great eorts were made to assure the quality of plans associated to every angle spread constraint as good

as possible. Important dosimetric parameters for PTV and OARs, quantitatively

re

ecting the plan quality, were extracted from the DVHs and analyzed as a function

of angle spread constraint for each case. Comparisons of these parameters between

clinical plans and model-based plans were evaluated by two-sampled Students t-tests,

and regression analysis on a composite index built on the percentage errors between

dosimetric parameters in the model-based plans and those in the clinical plans as a

function of angle spread constraint was performed.

Results show that model-based plans generally have equivalent or better quality

than clinical approved plans, qualitatively and quantitatively. All dosimetric param-

eters except those for lungs in the automatically generated plans are statistically

better or comparable to those in the clinical plans. On average, more than 15% re-

duction on conformity index and homogeneity index for PTV and V40, V60 for heart

while an 8% and 3% increase on V5, V20 for lungs, respectively, are observed. The

intra-plan comparison among model-based plans demonstrates that plan quality does

not change much with angle spread constraint larger than 0.4. Further examination

on the variation curve of the composite index as a function of angle spread constraint

shows that 0.6 is the optimal value that can result in statistically the best achievable

plans.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.