Adjacent Control Points Research Articles

Impact of the gradient in gantry-table rotation on dynamic trajectory radiotherapy plan quality.

To improve organ at risk (OAR) sparing, dynamic trajectory radiotherapy (DTRT) extends VMAT by dynamic table and collimator rotation during beam-on. However, comprehensive investigations regarding the impact of the gantry-table (GT) rotation gradient on the DTRT plan quality have not been conducted. To investigate the impact of a user-defined GT rotation gradient on plan quality of DTRT plans in terms of dosimetric plan quality, dosimetric robustness, deliverability, and delivery time. The dynamic trajectories of DTRT are described by GT and gantry-collimator paths. The GT path is determined by minimizing the overlap of OARs with planning target volume (PTV). This approach is extended to consider a GT rotation gradient by means of a maximum gradient of the path ( ) between two adjacent control points ( ) and maximum absolute change of G ( ). Four DTRT plans are created with different maximum G&∆G: & =0.5&0.125 (DTRT-1), 1&0.125 (DTRT-2), 3&0.125 (DTRT-3) and 3&1‍(DTRT-4), including 3-4 dynamic trajectories, for three clinically motivated cases in the head and neck and brain region (A, B, and C). A reference VMAT plan for each case is created. For all plans, plan quality is assessed and compared. Dosimetric plan quality is evaluated by target coverage, conformity, and OAR sparing. Dosimetric robustness is evaluated against systematic and random patient-setup uncertainties between in the lateral, longitudinal, and vertical directions, and machine uncertainties between in the dynamically rotating machine components (gantry, table, collimator rotation). Delivery time is recorded. Deliverability and delivery accuracy on a TrueBeam are assessed by logfile analysis for all plans and additionally verified by film measurements for one case. All dose calculations are Monte Carlo based. The extension of the DTRT planning process with user-defined to investigate the impact of the GT rotation gradient on plan quality is successfully demonstrated. With increasing , slight (case C, : up to‍-1‍Gy) and substantial (case A, : up to -9.3Gy, case‍B, : up to -4.7‍Gy) improvements in OAR sparing are observed compared to VMAT, while maintaining similar target coverage. All plans are delivered on the TrueBeam. Expected and actual machine position values recorded in the logfiles deviated by <0.2° for gantry, table and collimator rotation. The film measurements agreed by >96% (2%‍global/2mm Gamma passing rate) with the dose calculation. With increasing , delivery time is prolonged by <2min/trajectory (DTRT-4) compared to VMAT and DTRT-1. The DTRT plans for case A and B and the VMAT plan for case C plan reveal the best dosimetric robustness for the considered uncertainties. The impact of the GT rotation gradient on DTRT plan quality is comprehensively investigated for three cases in the head and neck and brain region. Increasing freedom in this gradient improves dosimetric plan quality at the cost of increased delivery time for the investigated cases. No clear dependency of GT rotation gradient on dosimetric robustness is observed.

A hybrid trigger strategy based mixed impulsive control scheme on uncertain local field neural networks with leakage delay

Solved in this paper is the stabilization of uncertain local field neural networks (ULFNNs) with leakage delay by dint of a mixed impulsive control scheme. The impulsive control instants are decided by a Lyapunov functional-based event triggered scheme and a periodic impulse triggered scheme. Based on the proposed control scheme, sufficient conditions are deduced for eliminating the Zeno behavior and guaranteeing the uniform asymptotic stability (UAS) of the delayed ULFNNs in the framework of Lyapunov functional analysis method. Different from individual event triggered impulse control strategy where the triggered instants may be unexpected, the mixed impulsive control scheme can release the impulse control instants in line with the distance between any two adjacent successful control points, which improves the control performance and also achieves the goal of saving the communication resource. Furthermore, the decay behavior of impulse control signal is considered to make mathematical derivation more practical, and based on this behavior, a criterion is derived to make ensure the exponential stability of delayed ULFNNs. Finally, numerical examples are given to illustrate the effectiveness of the designed controller for the ULFNNs with leakage delay.

Speed Adaptive Robot Trajectory Generation Based on Derivative Property of B-Spline Curve

In order to improve the safety of autonomous flight of quadrotor in three-dimensional complex environments, this paper proposes a speed adaptive motion planning method by limiting the distance between two adjacent control points based on the derivative property of B-Spline curve. First the initial B-Spline curve control points and the speed constraints based on derivative property are efficiently obtained by the front-end search that is divided into the shortest safe path search and reasonable step targeted expansion satisfying dynamic constraints. Then the back-end optimization assigns the corresponding safe flight corridor to the local trajectories according to the stage of the initial control points and uses MINVO basis ([1]) to limit the simplexes with minimum volume enclosing local trajectories. The trajectory generation is finally formulated as a Quadratically Constrained Quadratic Program (QCQP) which can be solved efficiently. Both simulations and real-world experiments validate the efficiency and performance of this method in generating safe, smooth, speed adaptive trajectories.

Mind the gap: Effects of canopy clearings on temperate forest bat assemblages

Gaps in the forest canopy appear to play a major role in local species richness as they increase habitat heterogeneity and border effects. In the case of bats, these small clearings seem to play an important role as foraging and commuting sites. However, further research is required to set the actual role of forest gaps on bat biology in order to consider them as conservation targets in forest management. In this study, we test whether bat species richness and activity are higher in gaps within a large Scot pine (Pinus sylvestris) forest than in the adjacent tree covered control sites. We also test these differences in the forest specialists since this group is particularly sensitive to forest management. To investigate this, we used bat detectors in 9 gaps and their adjacent control points during ten nights in July - August 2016 and 2017. The trends resulting from the analysis of 228,108 bat calls support that species richness and activity of bat assemblages were higher in gaps than in the adjacent control points. A similar pattern was detected in the most sensitive tree dwelling bat species. These results stress the importance of gaps as useable areas for the forest bat assemblages and suggest the interest of managing gaps for bat conservation within large areas of continuous tree cover.

A sliding-window approach for improved VMAT dose calculation accuracy

A sliding-window (SW) methodology for VMAT dose calculation was developed. For any two adjacent VMAT control points (CPs) n and n+1, the dose distribution was approximated by a 2-CP SW IMRT beam with the starting MLC positions at CP n and ending MLC positions at CP n+1, with the gantry angle fixed in the middle of the two VMAT CPs. Therefore, for any VMAT beam with N CPs, the dose is calculated with N-1 SW beams. VMAT plans were generated for ten patients in Pinnacle using 4° gantry spacing. For each patient, the VMAT plan was converted to a SW IMRT plan and dose was re-calculated. Another VMAT plan, with 1° gantry spacing, was created by interpolating the original VMAT beam. The original plans were delivered on an Elekta Versa HD and measured with Mapcheck2 using an in-house developed subarc method. For both the isodose distribution and DVH, there were significant differences between the original VMAT plan and either the SW or the interpolated plan. However, they were indistinguishable between the SW and interpolated plans. The average passing rate between the original VMAT plan and measurements was 84%. For both the interpolated and SW plans, the average passing rate was 96%. We conclude that the proposed SW approach improves VMAT dose calculation accuracy without increase in dose calculation time.

Bloch theorem for isogeometric analysis of periodic problems governed by high-order partial differential equations

With the emergence of isogeometric analysis (IGA), numerical rotation-free solutions to high-order partial differential equations (PDEs) are facilitated. Indeed, IGA allows the use of high-order-continuous basis functions through the domain. For periodic systems, the Bloch theorem is useful for analyzing wave propagation, restricting the analysis to a single unit cell and applying periodic boundary conditions. However, in the literature, boundary conditions are only accounting for C0-continuity, and we propose in the present paper to enforce the G1-continuity as well or to maintain the angle in case of unit cells meeting at kinks. While G1-continuity is enforced by maintaining the collinearity between adjacent control points, in the presence of kinks, variations of the field derived with respect to opposite in-plane edge normals are linked by the Rodrigues rotation matrix. This method applied at collocation points belonging to the unit cell edges can be viewed as a novel approach of coupling multi-patch geometries with kinks, avoiding the use of nonlinear multipliers or additional bending strip elements. Both transfer-matrix and indirect methods of the Bloch theorem are investigated, for respectively quasi-one and quasi-two-dimensional wave propagation in periodic structures discretized by NURBS-based IGA. Dispersion curves of a set of numerical problems treating isogeometric rotation-free extensible elastica (beams) and Kirchhoff–Love shells are then analyzed.

SU-E-T-400: Optimized 2D Motion Tracking Using Dynamic Multi-Leaf Collimator (DMLC) for a Clinical Volumetric Modulated Arc Therapy (VMAT) Plan

Purpose: This study is to develop a 2D motion tracking algorithm combined with controlled shallow breathing and collimator angle optimization to improve MLC tracking accuracy. Method and Materials: One SBRT VMAT plan for lung cancer (2 Arcs; 8 Gy/fx in 4 fx) was selected. A non-motion 3D VMAT plan was generated based on GTV from one single selected phase of the 4DCT. A motion tracking algorithm using MATLAB was developed to modify MLC positions of the 3D VMAT DICOM file based on an ideal breathing motion model. We derived the correlations between gantry angle, collimator angle and motion amplitudes in SI and AP directions that projected onto MLC aperture. All delivery constraints followed mechanical limits of Varian TrueBeam. To avoid large time interval between adjacent control points, motion amplitudes restriction and collimator angle optimization were incorporated into the algorithm. Each arc was then divided into 6 sub-arcs corresponding to the 6 breathing phases. Sub-arc doses were individually calculated and merged to acquire the 4D dose distribution. DVH comparison and 3D gamma were used for dosimetric evaluation. Results: Total delivery time of static 3D VMAT plan (collimator=45°), plan with MLC tracking under free breathing (collimator=45°, SI=10mm and AP=8mm), plan with collimator angle optimized only (collimator=77.8°, SI=10mm and AP=8mm) and collimator angle optimized under shallow breathing (collimator=80.1°, SI=8.3mm, AP=6.6mm) were 135.7s, 235.3s, 213.9s and 188.5s, respectively. Compared with the non-motion 3D VMAT, optimized MLC tracking demonstrated small changes in target dose (%ΔD90=1%, 3D gamma passing rate=97.5%). Conclusions: Total delivery time of VMAT with tracking tends to decrease as collimator angle approaches to 90°. At selected angle, plan with shorter breathing cycle period has longer delivery time when using MLC for motion compensation. MLC tracking combined with shallow breathing and optimized collimator angle cannot only reduce delivery time but increase the tracking accuracy.

A novel planar calibration method using the iterative correction of control points information

In the camera calibration using translational planar object instead of 3D target, the skew affected by the imprecision in installation causes the object to deviate from the designated position, which produces errors to the world coordinates of control points and reduces the calibration accuracy. In this paper, a skew correction model is established to correct this skew. We note and prove that the skew bias of control point which is close to the fix point is tiny. According to the projection regulation, the pixel distance between two adjacent control points which is close to the fix point in skewed situation is a value extremely approximate to that in the ideal situation. Based on this property, we utilize the pixel distance to assign the image coordinates based on the fix point. The assigned values are then employed to estimate the skew factors, by which the initial camera parameters are optimized and lens distortion in the calibration images are corrected. This process is then repeated until convergence. Experiments based on real images prove that this method is more accurate than other methods without correcting skew. The parameters obtained by our method can be applied to the 3D reconstruction directly and effectively.

TH-F-211-03: A More Accurate Dose Calculation for Volumetric Modulated Arc Therapy

Purpose: Dose discrepancy emerges between the calculation algorithm and measurements due to MLC tongue and groove (TG) effect, and rapid changes of the MLC apertures between adjacent control points (CP) in hypofractionated Volumetric Modulated Arc Therapy (VMAT) that demands high dose modulation. This study explores methods to correct these dose calculation errors. Methods: Because the physical width of tongue or groove is around 1mm, the 2mm transmission matrix resolution used in the current calculation algorithm may result in errors due to aliasing in the MLC transmission sampling. A new calculation algorithm using 1mm resolution is implemented to remove aliasing and more accurately model TG transmission. The commonly used gantry angle sampling resolution of 2 degree causes significant error when there is large MLC movement from one CP to next. Instead of inserting additional CP which doubles the calculation time, we insert two more apertures that are interpolated at a 0.7 degree resolution before and after each CP. The weighted average transmission is then used for calculation. Dose calculations are compared with film measurements for hypofractionated VMAT in lung, hip, prostate and paraspinal cases to assess accuracy. Results: Up to 10% maximal local and 3.3% average field dose discrepancy exist with the 2mm resolution algorithm. The errors are reduced to 5% maximal and 2% average with the 1mm resolution algorithm, and further reduced to within 3% maximal and 0.5% average using the finer aperture angular resolution. With both corrections built in, the gamma (3%,3mm) pass rate is closer to 100% with improvement ranging from 2% to 14% relative to pass rate without correction. Conclusions: Finer transmission and angular resolution needs to be implemented in the dose calculation algorithm to handle the highly modulated fields in hypofractionated VMAT and consistently achieve a high accuracy required by the QA program.

Impact of leaf motion constraints on IMAT plan quality, deliver accuracy, and efficiency

Intensity modulated arc therapy (IMAT) is a radiation therapy delivery technique that combines the efficiency of arc based delivery with the dose painting capabilities of intensity modulated radiation therapy (IMRT). A key challenge in developing robust inverse planning solutions for IMAT is the need to account for the connectivity of the beam shapes as the gantry rotates from one beam angle to the next. To overcome this challenge, inverse planning solutions typically impose a leaf motion constraint that defines the maximum distance a multileaf collimator (MLC) leaf can travel between adjacent control points. The leaf motion constraint ensures the deliverability of the optimized plan, but it also impacts the plan quality, the delivery accuracy, and the delivery efficiency. In this work, the authors have studied leaf motion constraints in detail and have developed recommendations for optimizing the balance between plan quality and delivery efficiency. Two steps were used to generate optimized IMAT treatment plans. The first was the direct machine parameter optimization (DMPO) inverse planning module in the Pinnacle(3) planning system. Then, a home-grown arc sequencer was applied to convert the optimized intensity maps into deliverable IMAT arcs. IMAT leaf motion constraints were imposed using limits of between 1 and 30 mm∕deg. Dose distributions were calculated using the convolution∕superposition algorithm in the Pinnacle(3) planning system. The IMAT plan dose calculation accuracy was examined using a finer sampling calculation and the quality assurance verification. All plans were delivered on an Elekta Synergy with an 80-leaf MLC and were verified using an IBA MatriXX 2D ion chamber array inserted in a MultiCube solid water phantom. The use of a more restrictive leaf motion constraint (less than 1-2 mm∕deg) results in inferior plan quality. A less restrictive leaf motion constraint (greater than 5 mm∕deg) results in improved plan quality but can lead to less accurate dose distribution as evidenced by increasing discrepancies between the planned and the delivered doses. For example, the results from our patient-specific quality assurance measurements demonstrated that the average gamma analysis passing rate decreased from 98% to 80% when the allowable leaf motion increased from 3 to 20 mm∕deg. Larger leaf motion constraints also led to longer treatment delivery times (2 to 4 folds) due to the additional MLC leaf motion. Leaf motion constraints significantly impact IMAT plans in terms of plan quality, delivery accuracy, and delivery efficiency with the impact magnified for more complex cases. Our studies indicate that a leaf motion constraint of 2 to 3 mm∕deg of gantry rotation can provide an optimal balance between plan quality, delivery accuracy, and efficiency.

SU-GG-T-219: Comparison of Techniques to Simulate VMAT for Matching Delivery to Dose Calculation

Purpose: To simplify the dose calculation process, dynamic delivery techniques such as VMAT are typically approximated using static fields for the dose calculation. A number of techniques have been employed for VMAT dose calculations and delivery. In this work, we have evaluated these different techniques in terms of the accuracy and the agreement between planned and delivered doses. Materials and Methods: Dose calculations for VMAT include static field and Monte‐Carlo simulations. Different methods of setting the control points (CPs) during DICOM export, including MU redistribution, CP insertion, and CP reposition, were tested for dose calculations using static fields. The exported VMAT plans were delivered using the Elekta PreciseBeam® VMAT linaccontrol system. The delivery results were measured using an IBA MatriXX system and were compared with the calculation data to test the delivery accuracy. Results: Using static fields for dose calculation and MU redistribution for VMAT delivery can lead to significant discrepancy between the calculation and delivery. The passing rate of the gamma analysis with 3%/3mm criteria can be as low as 67% when tested using an extreme case. The CP insertion and CP reposition methods can improve the agreement between the planned and measured doses. However, MLC leaf motion between adjacent CPs needs to be limited when static fields are used for VMAT dose calculation. Using Monte‐Carlo dose calculation to simulate the dynamic delivery of VMAT provides excellent agreement between the dose calculations and deliveries regardless of the amount of MLC leaf motion used in the plan with an average gamma analysis passing rate of 98.1% for the 5 selected VMAT plans. Conclusions: Using static fields to simulate VMAT works well as long as CP setting for delivery is handled properly. Monte‐Carlo simulation has a clear advantage in simulating dynamic VMAT delivery. Research partially supported by Elekta

SU‐DD‐A1‐01: Improving Delivery Accuracy of Volumetric Modulated Arc Therapy (VMAT)

Purpose: To evaluate the effect of VMAT sequencer, MLC leaf motion range and MU difference for adjacent control points in VMAT plan, and gantry interval used for dose calculation on the treatment delivery accuracy. Material and Methods: VMAT plans with leaves moving across the field in alternate open‐close pattern for every 10 degrees of rotation were created on Pinnacle SmartArc 8.1v and Ergo++ V1.7.1, where VMAT DICOM RT plans were generated with different sequencers. Various MLC motion range and MU with different ratios were assigned to the adjacent control points. The plans were delivered on Elekta Synergy. Measurements with Matrixx ion‐chamber array were analyzed. Gamma passing rate were evaluated using dose calculated by interpreting the MU and MLC shapes between control points with different gantry intervals. Results: DICOM plans transferred from SmartArc had higher gamma passing rate than those from Ergo++. Passing rate decreased as the MU ratio increased for Ergo++ because its VMAT sequencer averaged the MU from two adjacent control points. Less than 2% difference was observed between dose calculated with 1 and 2 degree gantry interval. Compared to plans with 2.5cm MLC motion, passing rate for 5.0cm plans decreased by 5–15%. Verification results degraded as MU ratio increased from 5:5 to 1:9 if dose was calculated using the gantry interval of 2 degrees or larger. Gamma pass rate decreased as the calculation interval increased from 2 to 10 degrees for VMAT plans were calculated assuming MLC leaves were stationary between control points. Conclusion: Smaller MLC leaf motion range can improve VMAT delivery accuracy. A sequencer capable of keeping original MU for each control point should be used to generate VMAT DICOM RT plan. Fine gantry interval should be used for dose calculation to show the VMAT plan that reflects the delivered dose accurately.Research supported by Elekta.

SU‐FF‐T‐423: Time‐Dependent Monte Carlo Dose Calculation Method for Dynamic Movement of All Linac Components in Presence of Patient Motion

Purpose: Radiation therapy has become increasingly complex over the past several years, with simultaneous moving parts, such as the gantry/MLC (IMAT), or gantry/MLC/couch (Tomotherapy). With multiple moving components, deterministic dose calculation methods will prove ineffective as the computational cost of discretization in n‐dimensions increases exponentially with n. Monte Carlo methods, which are immune to the effects of increased dimensionality, can be exploited for this purpose. In this work, a dynamic Monte Carlo dose calculation engine is developed to account for arbitrary rotational and translational movements of the jaws, MLC, gantry and couch in the presence of patient's breathing motion within the approximation of rigid body motion. Methods and Results: In each history of the dynamic Monte Carlo run, a point in the delivery control point sequence of a dynamic delivery is randomly sampled. The values of 130 variables (angles or positions) are determined by linear interpolation between adjacent control points. A photon is sampled from a source and raytraced through the detailed collimator structure and the patient simulation phantom. Dose is deposited via randomly sampled monoenergetic kernel rays issued from photon interaction poins. The method also enables temporal correlation with breathing motion waveforms, and can be used to evaluate time‐dependent interplay effects of patient motion with respect to all moving parts of the linac. A typical plan using a 4 mm voxel grid requires approximately 5‐10 minutes to compute on a single 2.4 GHz Pentium microprocessor to achieve 2% statistics in the peak dose region. Conclusion: The method allows simultaneous simulation of gantry, collimator, MLC, couch and patient motion, and, therefore, provides an efficient and accurate means to calculate dose for arbitrarily complex dynamic treatments. It opens the computational door for exploring more degrees of freedom in treatment planning to achieve better dose distributions for radiation therapy patients.

SU-FF-T-154: Balancing Plan Quality, Delivery Accuracy and Efficiency in VMAT

Purpose: VMAT has received considerable attention due to its ability to provide improved plan quality and delivery efficiency relative to fixed field IMRT. A key component of VMAT treatment planning is the need to restrict the leaf motion from one control point to the next. In this work, we studied the dependency between restriction on leaf motion and the plan quality, delivery accuracy and efficiency for VMAT. Material and Methods: The leaf motion constraint is the maximum distance one MLC leaf can move between adjacent control points within an arc with a unit of mm per degree of gantry rotation. Three cases with different sites were planed for VMAT treatment using a variety of leaf motion constraints. Final dose calculation for each plan was done with 2-degree control point spacing. All VMAT plans were delivered on an Elekta Synergy linac with PreciseBeam VMAT® control system, and were verified using IBA MatriXX system. A 2%/2mm passing criteria was used in Gamma Evaluation. Results: The as-optimized VMAT DVHs looks very similar for different leaf motion constraints. The final dose, however, reveals degradation in plan quality with increasing leaf motion. Such degradation is most pronounced for the Head-Neck case. Best plan quality was obtained with 2∼3mm/degree leaf motion for Head-Neck and prostate cases, and 3∼5mm/degree for pancreas case. The delivery time increases monotonically with the increase of leaf motion and can be 2∼3 times different. In terms of delivery accuracy, plans with more leaf motion tend to have lower gamma passing rate (93% for 2mm/deg and 71% for 20mm/deg for the Head-Neck case). We recommend a 3mm leaf-motion constrain for creating VMAT plans. Conclusion: The leaf motion constraint in VMAT planning is a critical parameter and has to be considered to ensure plan quality, deliver accuracy and efficiency. Research supported by Elekta.

Bound Estimations on Lower Derivatives of Rational Triangular Bézier Surfaces

Based on the de Casteljau algorithm for triangular patches,also using some existing identities and elementary inequalities,this paper presents two kinds of new magnitude upper bounds on the lower derivatives of rational triangular Bezier surfaces.The first one,which is obtained by exploiting the diameter of the convex hull of the control net,is always stronger than the known one in case of the first derivative.For the second derivative,the first kind is an improvement on the existing one when the ratio of the maximum weight to the minimum weight is greater than 2;the second kind is characterized as being represented by the maximum distance of adjacent control points.

Extending cubic uniform B-splines by unified trigonometric and hyperbolic basis

In this paper, the trigonometric basis {sin t, cos t, t, 1} and the hyperbolic basis {sinh t, cosh t, t, 1} are unified by a shape parameter C (0 ≤ C < ∝). It yields the Functional B-splines (FB-splines) and its corresponding Subdivision B-splines (SB-splines). As well, a geometric proof of curvature continuity for SB-splines is provided. FB-splines and SB-splines inherited nearly all properties of B-splines, including the C 2 continuity, and can represent elliptic and hyperbolic arcs exactly. They are adjustable, and each control point b i can have its unique shape parameter C i . As C i increases from 0 to ∝, the corresponding breakpoint of b i on the curve is moved to the location of b i , and the curvature of this breakpoint is increased from 0 to ∝ too. For a set of control points and their shape parameters, SB-spline and FB-spline have the same position, tangent, and curvature on each breakpoint. If two adjacent control points in the set have identical parameters, their SB-spline and FB-spline segments overlap. However, in general cases, FB-splines have no simple subdivision equation, and SB-splines have no common evaluation function. Furthermore, FB-splines and SB-splines can generate shape adjustable surfaces. They can represent the quadric surfaces precisely for engineering applications. However, the exact proof of C 2 continuity for the general SB-spline surfaces has not been obtained yet.

Measurement of Subcutaneous Impedance by Four-Electrode Method at Acupoints Located with Single-Power Alternative Current

A Single-Power Alternating Current (SPAC) instrument was used to measure the low-impedance acupoints around Ho-Ku (LI-4), Yang-Hsi (LI-5), Yang-Ch'ih (TB-4), Yang-Ku (SI-5), T'ai-Yuan (Lu-9), Ta-Lung (EH-7) and Shen-Men (He-7). A four-electrode instrument was used to measure the subcutaneous impedance at these low-impedance acupoints and adjacent control points on 12 healthy people. The mean subcutaneous impedance at the acupoints was 49.8+/-8.4 omega, significantly lower than the impedance of 53.5+/-omega 9.3 omega for the control points (P < 0.005). Of the seven acupoints, five (71%) had significantly lower impedances than the mean impedance for the adjacent control points. Seven of the 14 control points had significantly higher impedances than the adjacent acupoints, with most control points (93%) having higher impedances than adjacent acupoints. In conclusion, subcutaneous impedance is lower at the low-impedance points as measured with the SPAC two-electrode method. One interpretation of these results is that more interstitial fluid lies beneath the low-impedance acupoints.

Free-form deformation of constructive shell models

Free-form deformation (FFD) is known to be a powerful technique for deforming an object independent of its representation. A point on a solid is deformed by specifying the point relative to a coordinate system defined with a lattice of control points. Adjusting the control points of the lattice deforms the object. The deformed object can be visualized by sampling points on the object surfaces, or by approximating the object with a polyhedral model. However, a conversion of the polyhedral model to the underlining solid representation is required if further solid operations (e.g. Boolean operation) is to be applied. This paper presents a technique for applying FFD on constructive shell models (CSR). A CSR object is constructed by subtracting a set of depression (negative) trunctets from the union of a set of outer (positive) trunctets and a polyhedron core. FFD is applied to the polyhedron core and the trunctets of the model. A trunctet is deformed by applying FFD to a set of selected surface points on the trunctet. The deformed trunctet is obtained by interpolating a surface through the deformed surface points. In the deformation of a trunctet, an outer trunctet may become a depression trunctet (or vice versa). By using the concept of mating trunctet, and an approach for classifying the shape of a trunctet, shape changes of a trunctet in a deformation can be determined. Deformation of a trunctet may also result in an invalid trunctet that bulges out of its enclosing tetrahedron. Besides, the degree of the algebraic surface used determines the size of a trunctet relative to the distance between adjacent lattice control points. A subdivision of a trunctet may have to be performed to maintain the validity of a deformation.

High performance heuristic algorithm for controlling stochastic network projects

An activity-on-arc network project of PERT type with random activity durations is considered. The progress of the project cannot be inspected and measured continuously, but only at preset inspection points. An on-line control model has to determine both inspection points and control actions to be introduced at those points to alter the progress of the project in the desired direction. On-line control is carried out to minimize the number of inspection points needed to meet the target, subject to the chance constraint. In the recently developed control models, determining the next inspection point is carried out via extensive simulation with a constant time step. This determination is based on sequential statistical analysis at each intermediate point to maximize the time span between two adjacent control points. The main shortcoming of the control algorithm is its long computational time due to the need to make numerous decisions. In this paper we present a newly developed heuristic control algorithm in which the timing of inspection points does not comprise intermediate decision making. Given a routine inspection point t i , the adjacent point t i+1 is determined so that even if the project develops most unfavorably in the interval [ t i , t i+1 ], introducing proper control action at moment t i+1 enables the project to meet its target on time, subject to the chance constraint. The newly developed control algorithm is essentially more efficient than the step-by-step control procedures. The computational time is reduced by a factor of 25–30 while the algorithm provides better solutions than would be attained by using on-line sequential statistical analysis. Extensive experimentation has been undertaken to illustrate the comparative efficiency of the presented algorithm.

Production control in semi-automated systems: comparison between constant and stochastic speeds

Abstract This paper deals with a production system which includes n deterministic assembly line and a supplementary production unit processing, with random disturbances, parts for the line. The decision-maker must determine both the speed to be introduced al each control point and the timing of the next control point, given the actual accumulated production observed at the control point, the deterministic rate of demand of the assembly line and a specified probability that there will be no on-line shortage of parts. This problem does not yet have an optimal solution; however, a subproblem can be formulated in which the speed is given and only the next control point has to be determined. Analytical optimal solutions were found for this subproblem under two extreme assumptions: (1) speed is a random variable that changes at the routine control point and remains constant until the next control point; (2) speed behaves like a Brownian motion, i.e. it changes continuously between two adjacent control points. T...