Presence Of Geometric Uncertainties Research Articles

Modeling and Reducing the Effect of Geometric Uncertainties in Intracranial Aneurysms with Polynomial Chaos Expansion, Data Decomposition, and 4D-Flow MRI.

Variations in the vessel radius of segmented surfaces of intracranial aneurysms significantly influence the fluid velocities given by computer simulations. It is important to generate models that capture the effect of these variations in order to have a better interpretation of the numerically predicted hemodynamics. Also, it is highly relevant to develop methods that combine experimental observations with uncertainty modeling to get a closer approximation to the blood flow behavior. This work applies polynomial chaos expansion to model the effect of geometric uncertainties on the simulated fluid velocities of intracranial aneurysms. The radius of the vessel is defined as the uncertainty variable. Proper orthogonal decomposition is applied to characterize the solution space of fluid velocities. Next, a process of projecting the 4D-Flow MRI velocities on the basis vectors followed by coefficient mapping using generalized dynamic mode decomposition enables the merging of 4D-Flow MRI with the uncertainty propagated fluid velocities. Polynomial chaos expansion propagates the fluid velocities with an error of 2% in velocity magnitude relative to computer simulations. Also, the bifurcation region (or impingement location) shows a standard deviation of 0.17 m/s (since an available reported variance in the vessel radius is adopted to model the uncertainty, the expected standard deviation may be different). Numerical phantom experiments indicate that the proposed approach reconstructs the fluid velocities with 0.3% relative error in presence of geometric uncertainties. Polynomial chaos expansion is an effective approach to propagate the effect of the uncertainty variable in the blood flow velocities of intracranial aneurysms. Merging 4D-Flow MRI and uncertainty propagated fluid velocities leads to more realistic flow trends relative to ignoring the uncertainty in the vessel radius.

Geometric uncertainty propagation in laminar flows solved by RBF-FD meshless technique

The Non-Intrusive Polynomial Chaos method is employed to analyze incompressible and laminar fluid flows in presence of geometric uncertainties on the boundaries, which are described by stochastic variables with known probability distribution. Non-Intrusive methods allow the use of existing deterministic solvers, which are treated as black boxes. Therefore the quantification of the fluid flow uncertainties is based on a set of deterministic response evaluations. The required thermo-fluid dynamics solutions over the deterministic geometries are obtained through a Radial Basis Function-generated Finite Differences (RBF-FD) meshless method. The validation of the presented approach is carried out through analytical test cases (isothermal flow between non-parallel walls) with one geometric uncertainty. The applicability of the presented approach to practical problems is then presented through the prediction of geometric uncertainty effects on the non-isothermal flow over a heated backward-facing step.

Analysis of geometric uncertainties in CFD problems solved by RBF-FD meshless method

In order to analyze incompressible and laminar fluid flows in presence of geometric uncertainties on the boundaries, the Non-Intrusive Polynomial Chaos method is employed, which allows the use of a deterministic fluid dynamic solver. The quantification of the fluid flow uncertainties is based on a set of deterministic response evaluations, which are obtained through a Radial Basis Function-generated Finite Differences meshless method. The use of such deterministic solver represents the key point of the analysis, thanks to the computational efficiency and similar accuracy over the traditional mesh-based numerical methods. The validation of the proposed approach is carried out through the solution of the flow past a 2D spinning cylinder near a moving wall and the flow over a backward-facing step, in presence of stochastic geometries. The applicability to practical problems is demonstrated through the investigation of geometric uncertainty effects on the forced convection of Al2O3-water nanofluid laminar flow in a grooved microchannel.

Optimal design of trusses with geometric imperfections: Accounting for global instability

A topology optimization method is proposed for the design of trusses with random geometric imperfections due to fabrication errors. This method is a generalization of a previously developed perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is that the objective function includes the nonlinear effects of potential buckling due to misaligned structural members. Solutions are therefore dependent on the magnitude of applied loads and the direction of resulting internal member forces (whether they are compression or tension). Direct differentiation is used in the sensitivity analysis, and analytical expressions for the associated derivatives are derived in a form that is computationally efficient. A series of examples illustrate how the effects of geometric imperfections and buckling may have substantial influence on truss design. Monte Carlo simulation together with second-order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties.

Consequences of Geometric Imperfections for the Control of Redundantly Actuated Parallel Manipulators

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Actuation redundancy increases and homogenizes the kinematic dexterity and stiffness as well as the force distribution among the actuators of parallel-kinematics machines (PKMs). It also allows for internal prestresses within the PKM without affecting the environment that can potentially be used to account for secondary tasks, such as active stiffness and backlash-avoiding control. However, in the presence of geometric uncertainties, this feature can become a serious problem, since then, control forces may be annihilated, or even some of the intentional prestress components may interfere with the environment. While model uncertainties can generally be tackled with robust-control concepts, actuation redundancy of PKM impedes the use of established robust-control schemes. The effect of such uncertainties and the applicability of standard model-based control schemes are analyzed in this paper. It is shown that geometric uncertainties lead to parasitic perturbation forces that cannot be compensated by adjustment of the controls. An amended version of the augmented PD and computed torque-control scheme is proposed that does not suffer from such effects. </para>

Coverage optimized planning: Probabilistic treatment planning based on dose coverage histogram criteria

This work (i) proposes a probabilistic treatment planning framework, termed coverage optimized planning (COP), based on dose coverage histogram (DCH) criteria; (ii) describes a concrete proof-of-concept implementation of COP within the PINNACLE treatment planning system; and (iii) for a set of 28 prostate anatomies, compares COP plans generated with this implementation to traditional PTV-based plans generated with planning criteria approximating those in the high dose arm of the Radiation Therapy Oncology Group 0126 protocol. Let Dv denote the dose delivered to fractional volume v of a structure. In conventional intensity modulated radiation therapy planning, Dv has a unique value derived from the static (planned) dose distribution. In the presence of geometric uncertainties (e.g., setup errors) Dv assumes a range of values. The DCH is the complementary cumulative distribution function of D(v+). DCHs are similar to dose volume histograms (DVHs). Whereas a DVH plots volume v versus dose D, a DCH plots coverage probability Q versus D. For a given patient, Q is the probability (i.e., percentage of geometric uncertainties) for which the realized value of Dv exceeds D. PTV-based treatment plans can be converted to COP plans by replacing DVH optimization criteria with corresponding DCH criteria. In this approach, PTVs and planning organ at risk volumes are discarded, and DCH criteria are instead applied directly to clinical target volumes (CTVs) or organs at risk (OARs). Plans are optimized using a similar strategy as for DVH criteria. The specific implementation is described. COP was found to produce better plans than standard PTV-based plans, in the following sense. While target OAR dose tradeoff curves were equivalent to those for PTV-based plans, COP plans were able to exploit slack in OAR doses, i.e., cases where OAR doses were below their optimization limits, to increase target coverage. Specifically, because COP plans were not constrained by a predefined PTV, they were able to provide wider dosimetric margins around the CTV, by pushing OAR doses up to, but not beyond, their optimization limits. COP plans demonstrated improved target coverage when averaged over all 28 prostate anatomies, indicating that the COP approach can provide benefits for many patients. However, the degree to which slack OAR doses can be exploited to increase target coverage will vary according to the individual patient anatomy. The proof-of-concept COP implementation investigated here utilized a probabilistic DCH criteria only for the CTV minimum dose criterion. All other optimization criteria were conventional DVH criteria. In a mature COP implementation, all optimization criteria will be DCH criteria, enabling direct planning control over probabilistic dose distributions. Further research is necessary to determine the benefits of COP planning, in terms of tumor control probability and/or normal tissue complication probabilities.

Comparison of Several Optimization Strategies for Robust Turbine Blade Design

This paper addresses the problem of turbine blade shape optimization in the presence of geometric uncertainties. Several strategies are tested and compared on a two-dimensional compressor blade optimization process for which performance is assessed using a commercial Reynolds-averaged Navier―Stokes computational fluid dynamics code. In each case, a range of shape errors are considered that attempt to simulate foreign object damage, erosion damage, and manufacturing errors. These lead to stochastic performance measures that, in turn, are considered in a multi-objective optimization framework. Because of the long run times associated with Reynolds-averaged Navier―Stokes codes, use is also made of surrogate or response-surface-based optimization methods to speed up the search processes. The paper shows that a range of techniques can be used to tackle this problem, but that no one method is clearly best overall. The practitioner is therefore cautioned against favoring a single approach for such design problems. Further research may help clarify these issues.

WE‐C‐BRB‐08: Sensitivity of Dosimetric Margin Distribution and Coverage Estimates to Sampling Parameters

Purpose: The dosimetric margin distribution (DMD) is a planning tool for evaluating target and normal tissue dose coverage probabilities in the presence of geometric uncertainties. This work evaluates sensitivity of coverage estimates derived from the DMD to the angular increment w at which the DMD is sampled, and the distance search increment d. Method and Materials: The study utilized three plans for localized prostate cancer, with prescribed dose of 79.2Gy and 1cm clinical target volume to planning target volume (CTV‐to‐PTV) margins, planned according to the high dose arm of RTOG0126. Dose was first recalculated with beam fluences convolved with a normal probability density function to simulate the effect of random uncertainties. Dosimetric margins were then calculated between the CTV and the 79.2Gy isodose surface at elevations f from −90° to +90°, and azimuthal angles q from −180° to +180°. In each direction (f,q) the CTV was moved relative to the dose distribution in steps of d until its minimum dose fell below 79.2Gy. Estimated coverage Qest was calculated from the DMD assuming systematic uncertainties (rigid body translations) were normally distributed with standard deviation S along each axis. Minimum and maximum deviations DQest were obtained over a range of S values for w = 5°, 10°, 20° relative to w = 2°, and for d = 0.2, 0.5, 1mm relative to d = 0.1mm. Results: Coverage uncertainty due to finite angular sampling interval w is approximately 0.5% at w = 10° and 1.5% at w = 20°. Uncertainty due to finite step size d is negligible for d £ 0.2 mm, and is approximately 0.6% for d = 1mm. Conclusion: Coverage estimates accurate to ±0.5% will be obtained if the DMD is sampled with w = 10° and d = 0.2 mm. Coverage estimates accurate to this level are desirable for target and normal tissue coverage evaluation in current treatment plans, and to support future treatment planning based on probabilistic coverage criteria.(Supported by NIH P01CA116602).

WE‐A‐BRD‐02: 4D Treatment Planning: Rationale, Methods and Significance

The breathing‐induced motion adversely affects the radiotherapy process for pulmonary tumors at all stages. During the conventional 3D imaging, motion causes artifacts that lead to erroneous anatomical information that propagates as a systematic error during planning and delivery. For planning, the standard approach to insure tumor coverage in the presence of geometrical uncertainties is to surround the target with a safety region. The pitfall of the margin expansion approach is that additional high doses are delivered to the normal tissue adjacent to the target, thus increasing the chances of radiation‐induced disease, while also limiting tumor dose escalation and, subsequently, the potential for better tumor control. The advent of 4D computed tomography (4D CT) represented a significant step forward toward improved imaging accuracy for regions affected by the respiratory motion due to the ability of reconstructing multiple image sets corresponding to various points during the breathing cycle. The information from the 4D CT is first used to better identify the target region at various stages over the breathing cycle and the extent of motion. Next, the more complete imaging data has to be factored into the planning process. To this end, depending on the treatment delivery strategy, one or more treatment plans are designed for each breathing instance for which data is available. Dose computations are performed on multiple datasets (usually termed as 4D dose calculations), and the cumulative dose is then used to assess the plan quality similar to the conventional 3D planning. The accumulation of doses on a reference image dataset is accomplished by using deformable image registration, which maps corresponding image voxels from one dataset to the reference dataset. To date, several approaches have been developed to fulfill this task. The amount of data available from 4D scans increases significantly the amount of time and effort needed for treatment planning. However, studies have suggested that the dose accumulation process could be reduced to planning on certain datasets only, while preserving at an acceptable level the accuracy that would otherwise be achieved through a full 4D dose computation. Multiple centers have employed the 4D planning approach to study the changes in doses as a result of 4D treatment planning and addressed the clinical significance of the changes observed.In this presentation, we will discuss the rationale for 4D treatment planning, review the methods available for cumulative dose computation, identify potential sources of error specific to the 4D planning approach, and discuss the clinical importance of the dosimetric changes resulting from 4D‐based treatment planning.Learning Objectives:1. Understand the rationale for accounting for respiratory motion during treatment planning.2. Understand the principles of cumulative dose computation.3. Learn about the clinical importance of the changes induced by the respiratory motion.

Coverage‐based treatment planning: Optimizing the IMRT PTV to meet a CTV coverage criterion

This work demonstrates an iterative approach-referred to as coverage-based treatment planning-designed to produce treatment plans that ensure target coverage for a specified percentage of setup errors. In this approach the clinical target volume to planning target volume (CTV-to-PTV) margin is iteratively adjusted until the specified CTV coverage is achieved. The advantage of this approach is that it automatically compensates for the dosimetric margin around the CTV, i.e., the extra margin that is created when the dose distribution extends beyond the PTV. When applied to 27 prostate plans, this approach reduced the average CTV-to-PTV margin from 5 to 2.8 mm. This reduction in PTV size produced a corresponding decrease in the volume of normal tissue receiving high dose. The total volume of tissue receiving > or =65 Gy was reduced on average by 19.3% or about 48 cc. Individual reductions varied from 8.7% to 28.6%. The volume of bladder receiving > or =60 Gy was reduced on average by 5.6% (reductions for individuals varied from 1.7% to 10.6%), and the volume of periprostatic rectum receiving > or =65 Gy was reduced on average by 4.9% (reductions for individuals varied from 0.9% to 12.3%). The iterative method proposed here represents a step toward a probabilistic treatment planning algorithm which can generate dose distributions (i.e., treated volumes) that closely approximate a specified level of coverage in the presence of geometric uncertainties. The general principles of coverage-based treatment planning are applicable to arbitrary treatment sites and delivery techniques. Importantly, observed deviations between coverage implied by specified CTV-to-PTV margins and coverage achieved by a given treatment plan imply a generic need to perform coverage probability analysis on a per-plan basis to ensure that the desired level of coverage is achieved.

Image-guided adaptive radiation therapy (IGART): Radiobiological and dose escalation considerations for localized carcinoma of the prostate

The goal of this work was to evaluate the efficacy of various image-guided adaptive radiation therapy (IGART) techniques to deliver and escalate dose to the prostate in the presence of geometric uncertainties. Five prostate patients with 15-16 treatment CT studies each were retrospectively analyzed. All patients were planned with an 18 MV, six-field conformal technique with a 10 mm margin size and an initial prescription of 70 Gy in 35 fractions. The adaptive strategy employed in this work for patient-specific dose escalation was to increase the prescription dose in 2 Gy-per-fraction increments until the rectum normal tissue complication probability (NTCP) reached a level equal to that of the nominal plan NTCP (i.e., iso-NTCP dose escalation). The various target localization techniques simulated were: (1) daily laser-guided alignment to skin tattoo marks that represents treatment without image-guidance, (2) alignment to bony landmarks with daily portal images, and (3) alignment to the clinical target volume (CTV) with daily CT images. Techniques (1) and (3) were resimulated with a reduced margin size of 5 mm to investigate further dose escalation. When delivering the original clinical prescription dose of 70 Gy in 35 fractions, the "CTV registration" technique yielded the highest tumor control probability (TCP) most frequently, followed by the "bone registration" and "tattoo registration" techniques. However, the differences in TCP among the three techniques were minor when the margin size was 10 mm (⩽1.1%). Reducing the margin size to 5 mm significantly degraded the TCP values of the "tattoo registration" technique in two of the five patients, where a large difference was found compared to the other techniques (⩽11.8%). The "CTV registration" technique, however, did maintain similar TCP values compared to their 10 mm margin counterpart. In terms of normal tissue sparing, the technique producing the lowest NTCP varied from patient to patient. Reducing the margin size seemed the only sure way to reduce the NTCP significantly, irrespective of the IGART technique employed. In escalating the dose with the iso-NTCP constraint, the largest average gain in dose was observed with the "tattoo registration" technique, followed by the "CTV registration" and "bone registration" techniques. This is attributed to the fact that in three of the five patients, the "tattoo registration" technique yielded the lowest NTCP, hence a greater window of opportunity to escalate the dose was possible with this technique. However, the variation among the five patients was also largest with the "tattoo registration" technique where, in the case of one patient, the required dose actually needed to be below the original prescription dose of 70 Gy to satisfy the iso-NTCP constraint. This was not the case with the "CTV registration" technique where positive and similar dose escalation was allowed on all five patients. Based on these data, an attractive dose escalation strategy may be to implement the "CTV registration" technique (for consistent dosimetric coverage) for daily target localization in combination with a margin reduction (for increased normal tissue sparing).

SU‐FF‐J‐66: Iso‐NTCP Dose Escalation with Image‐Guided Adaptive Radiation Therapy (IGART) for Localized Carcinoma of the Prostate

Purpose: To evaluate the efficacy of various image‐guided target localization techniques to assist in the safe dose escalation for prostate cancer radiation therapy in the presence of geometric uncertainties. Method and Materials: Five prostate cancer patients were analyzed, retrospectively. All patients were planned with an 18MV six‐field conformal technique with a 10 mm margin and an initial prescription dose of 70 Gy in 35 fractions. For the dose escalation study, the prescription dose was increased from 50 Gy in 2 Gy increments until the rectum normal tissue complication probability (NTCP) reached the level equal to that of the plan NTCP (i.e., iso‐NTCP). The target localization techniques simulated were (1) laser alignment to external tattoo marks, (2) alignment to bony landmarks with daily portal images, and (3) alignment to the clinical target volume (CTV) with daily CT imaging. Techniques (1) and (3) were re‐simulated with a reduced margin of 5 mm to investigate further dose escalation. Results: The selection of the target localization technique was less critical on the treatment outcome when 10 mm margin was used. Reducing the margin size from 10 to 5 mm effectively decreased the NTCP by ∼60 % for all patients. For iso‐NTCP dose escalation, to our surprise, the average dose and TCP gain for the five patients were largest with the external tattoo technique (6.4 Gy and 7.5 %, respectively) followed by the daily CTV and the bony landmarks. The variability in gain across the five patients, however, was also largest with the tattoo registration technique and smallest with the daily CTV technique. Conclusion: Based on these data, the best dose escalation strategy is to combine margin reduction (for increased normal tissue sparing) with the use of the daily CTV technique to localize the target volume (for consistent dosimetric coverage and escalation).