Transcatheter Aortic Valve Replacement (TAVR) Versus Surgical Aortic Valve Replacement (SAVR): A Review on the Length of Stay, Cost, Comorbidities, and Procedural Complications.

This review provides an in-depth analysis of the effect of length of stay (LOS), comorbidities, and procedural complications on the cost-effectiveness of transcatheter aortic valve replacement (TAVR) in comparison to surgical aortic valve replacement (SAVR). We found that the average LOS was shorter for patients undergoing TAVR, contributing to lower average costs associated with the procedure, although the LOS varied between patients due to the severity of illness and comorbidities present. TAVR has also been found to improve the quality of life for patients receiving aortic valve replacement compared to SAVR. Although TAVR has a lower rate of most post-operative complications caused by SAVR, such as bleeding and cardiac complications, TAVR shows an increased rate of permanent pacemaker (PPM) implantation due to mechanical trauma on the heart's conduction system. In addition, our findings suggest that the cost-effectiveness of each procedure varies based on the types of valve, the patient history of other medical conditions, and the procedural methods. Our findings show that TAVR is preferred over SAVR in terms of cost-effectiveness across a variety of patients with other coexisting medical conditions, including cancer, advanced kidney disease, cirrhosis, diabetes mellitus, and bundle branch block. TAVR also appears to be superior to SAVR with fewer post-operative complications. However, TAVR appears to have a higher rate of PPM implantation rates as compared to SAVR. The comorbidities of the valve recipient must be considered when deciding whether to use TAVR or SAVR as cost-effectiveness varies with the patient background.

A Review of the Cost Effectiveness of Transcatheter Aortic Valve Replacement (TAVR) Versus Surgical Aortic Valve Replacement (SAVR).

The cost of transcatheter aortic valve replacement (TAVR) has been studied in the context of high-risk or specific comorbidity populations; this paper provides a comprehensive overview of broader patient populations' outcomes and costs with TAVR in comparison to surgical aortic valve replacement (SAVR). In the past, SAVR had been the more cost-effective option than TAVR, but in recent years, TAVR has been becoming more cost-effective.Though the cost of TAVR can vary due to several factors the major focus of this review will focus on the surgical technique, medicare reimbursements, insertion point, and varying risk populations. In conclusion, the price of TAVR is declining as more cost-efficient valves arrive on the market. Climbing healthcare costs play a significant role in clinical decisions when deciding on which procedures are most cost-effective for the patient and healthcare system. The declining price of TAVR could lead to the preference of TAVR over SAVR for both low-risk and high-risk aortic stenosis patients.

Assessment of Toxic Effects and Survival in Treatment Deescalation With Radiotherapy vs Transoral Surgery for HPV-Associated Oropharyngeal Squamous Cell Carcinoma: The ORATOR2 Phase 2 Randomized Clinical Trial.

Importance: The optimal approach for treatment deescalation in human papillomavirus (HPV)-related oropharyngeal squamous cell carcinomas (OPSCCs) is unknown. Objective: To assess a primary radiotherapy (RT) approach vs a primary transoral surgical (TOS) approach in treatment deescalation for HPV-related OPSCC. Design, Setting, and Participants: This international, multicenter, open-label parallel-group phase 2 randomized clinical trial was conducted at 9 tertiary academic cancer centers in Canada and Australia and enrolled patients with T1-T2N0-2 p16-positive OPSCC between February 13, 2018, and November 17, 2020. Patients had up to 3 years of follow-up. Interventions: Primary RT (consisting of 60 Gy of RT with concurrent weekly cisplatin in node-positive patients) vs TOS and neck dissection (ND) (with adjuvant reduced-dose RT depending on pathologic findings). Main Outcomes and Measures: The primary end point was overall survival (OS) compared with a historical control. Secondary end points included progression-free survival (PFS), quality of life, and toxic effects. Results: Overall, 61 patients were randomized (30 [49.2%] in the RT arm and 31 [50.8%] in the TOS and ND arm; median [IQR] age, 61.9 [57.2-67.9] years; 8 women [13.6%] and 51 men [86.4%]; 31 [50.8%] never smoked). The trial began in February 2018, and accrual was halted in November 2020 because of excessive toxic effects in the TOS and ND arm. Median follow-up was 17 months (IQR, 15-20 months). For the OS end point, there were 3 death events, all in the TOS and ND arm, including the 2 treatment-related deaths (0.7 and 4.3 months after randomization, respectively) and 1 of myocardial infarction at 8.5 months. There were 4 events for the PFS end point, also all in the TOS and ND arm, which included the 3 mortality events and 1 local recurrence. Thus, the OS and PFS data remained immature. Grade 2 to 5 toxic effects occurred in 20 patients (67%) in the RT arm and 22 (71%) in the TOS and ND arm. Mean (SD) MD Anderson Dysphagia Inventory scores at 1 year were similar between arms (85.7 [15.6] and 84.7 [14.5], respectively). Conclusions and Relevance: In this randomized clinical trial, TOS was associated with an unacceptable risk of grade 5 toxic effects, but patients in both trial arms achieved good swallowing outcomes at 1 year. Long-term follow-up is required to assess OS and PFS outcomes. Trial Registration: Clinicaltrials.gov Identifier: NCT03210103.

Patient-specific calibration of cone-beam computed tomography data sets for radiotherapy dose calculations and treatment plan assessment.

PURPOSE: In this work, we propose a new method of calibrating cone beam computed tomography (CBCT) data sets for radiotherapy dose calculation and plan assessment. The motivation for this patient-specific calibration (PSC) method is to develop an efficient, robust, and accurate CBCT calibration process that is less susceptible to deformable image registration (DIR) errors. METHODS: Instead of mapping the CT numbers voxel-by-voxel with traditional DIR calibration methods, the PSC methods generates correlation plots between deformably registered planning CT and CBCT voxel values, for each image slice. A linear calibration curve specific to each slice is then obtained by least-squares fitting, and applied to the CBCT slice's voxel values. This allows each CBCT slice to be corrected using DIR without altering the patient geometry through regional DIR errors. A retrospective study was performed on 15 head-and-neck cancer patients, each having routine CBCTs and a middle-of-treatment re-planning CT (reCT). The original treatment plan was re-calculated on the patient's reCT image set (serving as the gold standard) as well as the image sets produced by voxel-to-voxel DIR, density-overriding, and the new PSC calibration methods. Dose accuracy of each calibration method was compared to the reference reCT data set using common dose-volume metrics and 3D gamma analysis. A phantom study was also performed to assess the accuracy of the DIR and PSC CBCT calibration methods compared with planning CT. RESULTS: Compared with the gold standard using reCT, the average dose metric differences were ≤ 1.1% for all three methods (PSC: -0.3%; DIR: -0.7%; density-override: -1.1%). The average gamma pass rates with thresholds 3%, 3 mm were also similar among the three techniques (PSC: 95.0%; DIR: 96.1%; density-override: 94.4%). CONCLUSIONS: An automated patient-specific calibration method was developed which yielded strong dosimetric agreement with the results obtained using a re-planning CT for head-and-neck patients.

Maier-Saupe model of polymer nematics: Comparing free energies calculated with Self Consistent Field theory and Monte Carlo simulations.

Self Consistent Field (SCF) theory serves as an efficient tool for studying mesoscale structure and thermodynamics of polymeric liquid crystals (LC). We investigate how some of the intrinsic approximations of SCF affect the description of the thermodynamics of polymeric LC, using a coarse-grained model. Polymer nematics are represented as discrete worm-like chains (WLC) where non-bonded interactions are defined combining an isotropic repulsive and an anisotropic attractive Maier-Saupe (MS) potential. The range of the potentials, σ, controls the strength of correlations due to non-bonded interactions. Increasing σ (which can be seen as an increase of coarse-graining) while preserving the integrated strength of the potentials reduces correlations. The model is studied with particle-based Monte Carlo (MC) simulations and SCF theory which uses partial enumeration to describe discrete WLC. In MC simulations the Helmholtz free energy is calculated as a function of strength of MS interactions to obtain reference thermodynamic data. To calculate the free energy of the nematic branch with respect to the disordered melt, we employ a special thermodynamic integration (TI) scheme invoking an external field to bypass the first-order isotropic-nematic transition. Methodological aspects which have not been discussed in earlier implementations of the TI to LC are considered. Special attention is given to the rotational Goldstone mode. The free-energy landscape in MC and SCF is directly compared. For moderate σ the differences highlight the importance of local non-bonded orientation correlations between segments, which SCF neglects. Simple renormalization of parameters in SCF cannot compensate the missing correlations. Increasing σ reduces correlations and SCF reproduces well the free energy in MC simulations.

Assessment of contrast enhanced respiration managed cone-beam CT for image guided radiotherapy of intrahepatic tumors.

PURPOSE: Contrast enhancement and respiration management are widely used during image acquisition for radiotherapy treatment planning of liver tumors along with respiration management at the treatment unit. However, neither respiration management nor intravenous contrast is commonly used during cone-beam CT (CBCT) image acquisition for alignment prior to radiotherapy. In this study, the authors investigate the potential gains of injecting an iodinated contrast agent in combination with respiration management during CBCT acquisition for liver tumor radiotherapy. METHODS: Five rabbits with implanted liver tumors were subjected to CBCT with and without motion management and contrast injection. The acquired CBCT images were registered to the planning CT to determine alignment accuracy and dosimetric impact. The authors developed a simulation tool for simulating contrast-enhanced CBCT images from dynamic contrast enhanced CT imaging (DCE-CT) to determine optimal contrast injection protocols. The tool was validated against contrast-enhanced CBCT of the rabbit subjects and was used for five human patients diagnosed with hepatocellular carcinoma. RESULTS: In the rabbit experiment, when neither motion management nor contrast was used, tumor centroid misalignment between planning image and CBCT was 9.2 mm. This was reduced to 2.8 mm when both techniques were employed. Tumors were not visualized in clinical CBCT images of human subjects. Simulated contrast-enhanced CBCT was found to improve tumor contrast in all subjects. Different patients were found to require different contrast injections to maximize tumor contrast. CONCLUSIONS: Based on the authors' animal study, respiration managed contrast enhanced CBCT improves IGRT significantly. Contrast enhanced CBCT benefits from patient specific tracer kinetics determined from DCE-CT.

Implementation and commissioning of an integrated micro-CT∕RT system with computerized independent jaw collimation.

PURPOSE: To design, construct, and commission a set of computer-controlled motorized jaws for a micro-CT∕RT system to perform conformal image-guided small animal radiotherapy. METHODS: The authors designed and evaluated a system of custom-built motorized orthogonal jaws, which allows the delivery of off-axis rectangular fields on a GE eXplore CT 120 preclinical imaging system. The jaws in the x direction are independently driven, while the y-direction jaws are symmetric. All motors have backup encoders, verifying jaw positions. Mechanical performance of the jaws was characterized. Square beam profiles ranging from 2×2 to 60×60 mm2 were measured using EBT2 film in the center of a 70×70×22 mm3 solid water block. Similarly, absolute depth dose was measured in a solid water and EBT2 film stack 50×50×50 mm3. A calibrated Farmer ion chamber in a 70×70×20 mm3 solid water block was used to measure the output of three field sizes: 50×50, 40×40, and 30×30 mm2. Elliptical target plans were delivered to films to assess overall system performance. Respiratory-gated treatment was implemented on the system and initially proved using a simple sinusoidal motion phantom. All films were scanned on a flatbed scanner (Epson 1000XL) and converted to dose using a fitted calibration curve. A Monte Carlo beam model of the micro-CT with the jaws has been created using BEAMnrc for comparison with the measurements. An example image-guided partial lung irradiation in a rat is demonstrated. RESULTS: The averaged random error of positioning each jaw is less than 0.1 mm. Relative output factors measured with the ion chamber agree with Monte Carlo simulations within 2%. Beam profiles and absolute depth dose curves measured from the films agree with simulations within measurement uncertainty. Respiratory-gated treatments applied to a phantom moving with a peak-to-peak amplitude of 5 mm showed improved beam penumbra (80%-20%) from 3.9 to 0.8 mm. CONCLUSIONS: A set of computer-controlled motorized jaws for a micro-CT∕RT system were constructed with position reliably better than a tenth of a millimeter. The hardware system is ready for image-guided conformal radiotherapy for small animals with capability of respiratory-gated delivery.

Pressing soft membrane on a self-avoiding polymer against a flat wall.

A polymer-membrane interacting system can produce a variety of structures. Here, we theoretically study a model system in which a membrane pushes a polymer against a hard surface; we show that a first-order structural phase transition can occur. Using a Monte Carlo simulation, we reveal that the system undergoes a transition from a confined (bump) state to a strongly confined (flattened-out) state as the pressure increases. A scaling argument is also made to understand the physical mechanism behind the phase transition and the properties of each state.

Structure of a micropipette-aspirated vesicle determined from the bending-energy model.

The structure of the system consisting of an aspirating pipette and an aspirated vesicle is investigated with fixed total vesicle volume, total vesicle surface area, and aspirated volume fraction, based on the bending-energy model. Through an energetic consideration, the usage of an aspirated volume fraction can be converted to the aspirating pressure for the determination of a phase diagram; the procedure identifies a first-order transition, between a weakly aspirated state and the strongly aspirated state, as the pressure increases. The physical properties of the system are obtained from minimization of the bending energy by an implementation of the simulated annealing Monte Carlo procedure, which searches for a minimum in a multivariable space. An analysis of the hysteresis effects indicates that the experimentally observed aspirating and releasing critical pressures are related to the location of the spinodal points.

Study of the IMRT interplay effect using a 4DCT Monte Carlo dose calculation.

Respiratory motion may lead to dose errors when treating thoracic and abdominal tumours with radiotherapy. The interplay between complex multileaf collimator patterns and patient respiratory motion could result in unintuitive dose changes. We have developed a treatment reconstruction simulation computer code that accounts for interplay effects by combining multileaf collimator controller log files, respiratory trace log files, 4DCT images and a Monte Carlo dose calculator. Two three-dimensional (3D) IMRT step-and-shoot plans, a concave target and integrated boost were delivered to a 1D rigid motion phantom. Three sets of experiments were performed with 100%, 50% and 25% duty cycle gating. The log files were collected, and five simulation types were performed on each data set: continuous isocentre shift, discrete isocentre shift, 4DCT, 4DCT delivery average and 4DCT plan average. Analysis was performed using 3D gamma analysis with passing criteria of 2%, 2 mm. The simulation framework was able to demonstrate that a single fraction of the integrated boost plan was more sensitive to interplay effects than the concave target. Gating was shown to reduce the interplay effects. We have developed a 4DCT Monte Carlo simulation method that accounts for IMRT interplay effects with respiratory motion by utilizing delivery log files.

Coil-bridge transition and Monte Carlo simulation of a stretched polymer.

The structure of the system consisting of a grafted self-avoiding polymer chain attracted to the surface layer of a flat wall at a distance away by a short-ranged force is investigated. A first-order transition is determined between the coil state at a low attraction energy and the bridge state at a high attraction energy. The transition properties of the system are obtained by a Monte Carlo simulation, which uses the inverse density of states as the transition weight and is reweighted back to a canonical ensemble. The determination of the density of states follows a revised Wang-Landau procedure in which the center-of-mass distance from the grafted site is used as the variable. Scaling arguments are also given for the observed numerical results.

Model of a polymer chain adsorbed to a soft membrane surface.

The structure of the system consisting of a self-avoiding polymer chain attracted to the surface of a freely supported soft membrane surface by a short-ranged force is investigated. The adhesion of the polymer to the deformed surface can produce distinctive states such as pancake, pinch, and bud, dependent on the phenomenological parameters in the Helfrich model describing the membrane as well as an adsorption energy describing the attraction between a monomer and a membrane surface.

Comparison of predicted native structures of Met-enkephalin based on various accessible-surface-area solvent models.

We examine the variation and similarity of the native structures predicted from various accessible-surface-area solvent models for peptide Met-enkephalin. Both ECEPP/2 and ECEPP/3 force fields have been used in conjunction with ten different sets of accessible-surface-area parameterization. The native structures were determined by an implementation of the basin hopping Monte Carlo technique. The results suggest that the implicit solvent models examined in this study should be employed in computer simulations with extreme caution. In addition, the effect of fixing or not fixing the peptide angles omega has been examined. We conclude that fixing omega generally gives rise to a poor prediction.

Experimental measurements and Monte Carlo simulations for dosimetric evaluations of intrafraction motion for gated and ungated intensity modulated arc therapy deliveries.

Respiratory gated radiation therapy allows for a smaller margin expansion for the planning target volume (PTV) to account for respiratory induced motion and is emerging as a common method to treat lung and liver tumors. We investigated the dosimetric effect of free motion and gated delivery for intensity modulated arc therapy (IMAT) with experimental measurements and Monte Carlo simulations. The impact of PTV margin and duty cycle for gated delivery is studied with Monte Carlo simulations. A motion phantom is used for this study. Two sets of contours were drawn on the mid-inspiration CT scan of this motion phantom. For each set of contours, an IMAT plan to be delivered with constant dose rate was created. The plans were generated on a CT scan of the phantom in the static condition with 3 mm PTV margin and applied to the motion phantom under four conditions: static, full superior-inferior (SI) motion (A = 1 cm, T = 4 s) and gating conditions (25% and 50% duty cycles) with full SI motion. A 6 by 15 cm piece of radiographic film was placed in the sagittal plane of the phantom and then irradiated under all measurement conditions. Film calibration was performed with a step-wedge method to convert optical density to dose. Gated IMAT delivery was first validated in 2D by comparing static film with that from gating and full motion. A previously verified simulation tool for IMRT that takes the log files from the multileaf collimator (MLC) controller and the gating system were adapted to simulate the delivered IMAT treatment for full 3D dosimetric analysis. The IMAT simulations were validated against the 2D film measurements. The resultant IMAT simulations were evaluated with dose criteria, dose-volume histograms and 3D gamma analysis. We validated gated IMAT deliveries when we compared the static film with the one from gating using 25% duty cycle using 2D gamma analysis. Within experimental and setup uncertainties, film measurements agreed with their corresponding simulated plans using 2D gamma analysis. Finally, when planning with margins designed for gating with 25% duty cycle and applying 50% or no gating during treatment, the dose differences in D(min,) D(99%) and D(95%) of the clinical target volume can be up to 27 cGy, 20 cGy and 18 cGy, respectively, for a plan with 200 cGy prescription dose. We have experimentally delivered gated IMAT with constant dose rate to a motion phantom and assessed their accuracies with film dosimetry and Monte Carlo simulations. Film dosimetry demonstrated that 25% gating and static plans are within 2%, 2 mm. The Monte Carlo simulation method was employed to generate dose delivered in 3D to a motion phantom, and the dosimetric results were reported. Since our film measurements agreed well with Monte Carlo simulations, we can reliably use this simulation tool to further study the dosimetric effects of target motion and effectiveness of gating for IMAT deliveries.

Incorporating geometric ray tracing to generate initial conditions for intensity modulated arc therapy optimization.

PURPOSE AND BACKGROUND: Intensity modulated arc therapy (IMAT) is a rotational variant of Intensity modulated radiation therapy (IMRT) that is achieved by allowing the multileaf collimator (MLC) positions to vary as the gantry rotates around the patient. This work describes a method to generate an IMAT plan through the use of a fast ray tracing technique based on dosimetric and geometric information for setting initial MLC leaf positions prior to final IMAT optimization. METHODS AND MATERIALS: Three steps were used to generate an IMAT plan. The first step was to generate arcs based on anatomical contours. The second step was to generate ray importance factor (RIF) maps by ray tracing the dose distribution inside the planning target volume (PTV) to modify the MLC leaf positions of the anatomical arcs to reduce the maximum dose inside the PTV. The RIF maps were also segmented to create a new set of arcs to improve the dose to low dose voxels within the PTV. In the third step, the MLC leaf positions from all arcs were put through a leaf position optimization (LPO) algorithm and brought into a fast Monte Carlo dose calculation engine for a final dose calculation. The method was applied to two phantom cases, a clinical prostate case and the Radiological Physics Center (RPC)'s head and neck phantom. The authors assessed the plan improvements achieved by each step and compared plans with and without using RIF. They also compared the IMAT plan with an IMRT plan for the RPC phantom. RESULTS: All plans that incorporated RIF and LPO had lower objective function values than those that incorporated LPO only. The objective function value was reduced by about 15% after the generation of RIF arcs and 52% after generation of RIF arcs and leaf position optimization. The IMAT plan for the RPC phantom had similar dose coverage for PTV1 and PTV2 (the same dose volume histogram curves), however, slightly lower dose to the normal tissues compared to a six-field IMRT plan. CONCLUSION: The use of a ray importance factor can generate initial IMAT arcs efficiently for further MLC leaf position optimization to obtain more favorable IMAT plan.

Commissioning a fast Monte Carlo dose calculation algorithm for lung cancer treatment planning.

A commercial Monte Carlo simulation package, NXEGS 1.12 (NumeriX LLC, New York, NY), was commissioned for photon-beam dose calculations. The same sets of measured data from 6-MV and 18-MV beams were used to commission NXEGS and Pinnacle 6.2b (Philips Medical Systems, Andover, MA). Accuracy and efficiency were compared against the collapsed cone convolution algorithm implemented in Pinnacle 6.2b, together with BEAM simulation (BEAMnrc 2001: National Research Council of Canada, Ottawa, ON). We investigated a number of options in NXEGS: the accuracy of fast Monte Carlo, the re-implementation of EGS4, post-processing technique (dose de-noising algorithm), and dose calculation time. Dose distributions were calculated with NXEGS, Pinnacle, and BEAM in water, lung-slab, and air-cylinder phantoms and in a lung patient plan. We compared the dose distributions calculated by NXEGS, Pinnacle, and BEAM. In a selected region of interest (7725 voxels) in the lung phantom, all but 1 voxel had a gamma (3% and 3 mm thresholds) of 1 or less for the dose difference between the NXEGS re-implementation of EGS4 and BEAM, and 99% of the voxels had a gamma of 1 or less for the dose difference between NXEGS fast Monte Carlo and BEAM. Fast Monte Carlo with post-processing was up to 100 times faster than the NXEGS re-implementation of EGS4, while maintaining +/- 2% statistical uncertainty. With air inhomogeneities larger than 1 cm, post-processing preserves the dose perturbations from the air cylinder. When 3 or more beams were used, fast Monte Carlo with post-processing was comparable to or faster than Pinnacle 6.2b collapsed cone convolution.

Monte Carlo dose calculation of segmental IMRT delivery to a moving phantom using dynamic MLC and gating log files.

Respiratory gating is emerging as a tool to limit the effect of motion for liver and lung tumors. In order to study the impact of target motion and gated intensity modulated radiation therapy (IMRT) delivery, a computer program was developed to simulate segmental IMRT delivery to a moving phantom. Two distinct plans were delivered to a rigid-motion phantom with a film insert in place under four conditions: static, sinusoidal motion, gated sinusoidal motion with a duty cycle of 25% and gated sinusoidal motion with duty cycle of 50% under motion conditions of a typical patient (A = 1 cm, T = 4 s). The MLC controller log files and gating log files were retained to perform a retrospective Monte Carlo dose calculation of the plans. Comparison of the 2D planar dose distributions between simulation and measurement demonstrated that our technique had at least 94% of the points passing gamma criteria of 3% for dose difference and 3 mm as the distance to agreement. This note demonstrates that the use of dynamic multi-leaf collimator and respiratory monitoring system log files together with a fast Monte Carlo dose calculation algorithm is an accurate and efficient way to study the dosimetric effect of motion for gated or non-gated IMRT delivery on a rigidly-moving body.

Minimum model for the alpha-helix-beta-hairpin transition in proteins.

We present a minimal model for proteins, which is able to capture the structural conversion between the alpha-helix and beta-hairpin. In most regimes of the parameter space, the model produces a stable structure at a low temperature; in a few limited regimes of the parameter space, the model displays an beta-hairpin transition as the physical conditions vary. These variations include a perturbation on hydrogen bonding propensity at the middle of the modeled chain, or the change of the hydrophobicity of a designated pair along the chain. Using Monte Carlo simulations, we demonstrate the structural conversion by means of state diagrams, heat capacity maps, and free energy maps.

Computational study of the Trp-cage miniprotein based on the ECEPP/3 force field.

Using a newly developed Monte Carlo global optimization method called basin paving, we have performed an ab initio computation for the structure of Trp-cage based on the ECEPP/3 force field in vacuo. The lowest energy minimum has been located. Its corresponding configuration is comparable to the native structure of Trp-cage (PDB code 1L2Y) with a backbone root mean square deviation of 2.24 A.

Monte Carlo basin paving: an improved global optimization method.

We propose a global optimization procedure, basin paving, which is based on the combination of the optimization strategies behind basin hopping and energy landscape paving. As an example, we describe its application in the protein structure prediction by examining two well-studied peptides, where we have found lower potential energy minima than previously located. We also compare the statistics of the searching trajectories produced by basin paving, basin hopping, and energy landscape paving.