2nd Moment Research Articles

The effects of exercise therapy on knee joint biomechanics during walking in patients with knee osteoarthritis: secondary outcome analyses from a randomized controlled trial

Purpose: Exercise is recommended as a cornerstone in the non-pharmacological management of knee OA in order to improve mobility, pain, and function. Besides aiming at pain reduction, neuromuscular exercise programs for knee OA have a specific aim of optimization of the knee joint movements related to walking, while the effects on knee joint biomechanics of these exercises remain to be clarified. The objective of this analysis was to assess the effects of a neuromuscular and individualized exercise program on knee joint biomechanics during walking in patients with knee OA. Methods: This was a randomized trial with blinded outcome assessors (NCT01545258). Participants were randomly assigned (1:1) to 12 weeks of facility-based functional and individualized neuromuscular exercise therapy (ET), 3 sessions per week supervised by trained physical therapists, or a no attention control group (CG). To assess knee joint biomechanics during walking, 3-dimensional gait analyses were used, from which self-selected walking speeds, sagittal knee joint angles and internal knee joint moments were extracted. The pain subscale of the KOOS was used to assess the effects on pain. According to the protocol the analyses were based on the ‘Per-Protocol’ population, defined as participants following the protocol with complete and valid gait analyses. Analyses of covariance adjusting for the level at baseline were used to determine differences between groups (95% confidence intervals) in the changes from baseline at follow-up. Results: 60 participants were randomized to ET (n= 31) or CG (n=29). In the ET group, 1 participant had an invalid baseline gait analysis and 6 participants were lost to follow-up; in the CG 1 participant had invalid gait analysis at baseline, 4 were lost, 1 violated the protocol (exercise outside study), and 1 had invalid gait analysis at follow-up. Thus per protocol population included 46 participants (24 ET/22 CG). Summaries of baseline charateristics and KOOS pain (with changes) are given in table 1. Baseline values and changes in knee joint biomechanics during walking are presented in table 2. Besides a statistically significant group difference in the change from baseline in 2nd peak knee flexor moment (late stance), there were no group differences in the changes in knee joint biomechanics during walking (table). Conclusions: A 12-week supervised individualized neuromuscular exercise program has no effect on knee joint biomechanics during walking, except for a slight difference in the change in the knee flexor moment during late stance, indicating an increased moment in the ET. These results indicate that beneficial effects of neuromuscular exercise therapy on pain are not mediated through altered knee joint biomechanics during walking.Table 1Control group (n=22)Exercise group (n=24)-BaselineBaselineMean(SD)Mean(SD)Age, yr61.4(7.2)64.9(9.1)--Female sex, no. (%)16(73%)22(92%)--Height, m1.71(0.09)1.69(0.08)--Weight, kg83.2(15.7)83.1(14.0)--Body Mass index, kg/m228.4(4.6)29.1(4.1)-Baseline Mean (SD)Mean Change(95% CI)Baseline Mean (SD)Mean Change(95% CI)Mean difference (95%CI)PKOOS pain, 0-10059.2 (12.8)−1.1 (−4.9:2.6)63.6 (17.6)6.3 (2.7:9.9)−7.4 (−12.7:−2.2)0.006 Open table in a new tab Table 2Knee biomechanics during walkingControl group (n=22)Exercise group (n=24)Group differenceBaselineChangeBaselineChangeKnee biomechanics variableMean (SD)Mean (95% CI)Mean (SD)Mean (95% CI)Mean (95% CI)PKnee angle at heel strike, deg12.2 (5.7)1.3 (−1.3:3.9)13.8 (5.9)−0.2 (−2.8:2.3)1.5 (2.1:5.2)0.411st Knee flexion angle (early stance), deg23.1 (6.2)1.7 (−0.8:4.2)25.8 (7.6)−1.2 (−3.6:1.3)2.9 (−0.7:6.4)0.11Midstance knee extension angle, deg6.2 (6.3)1.1 (−1.6:3.7)10.1 (7.0)−1.3 (−3.8:1.3)2.3 (−1.4:6.1)0.22Swing phase peak flexion angle, deg59.5 (8.9)−0.6 (−3.8:2.7)61.4 (9.4)−1.1 (−4.2:2.1)0.5 (−4.0:5.1)0.811st peak knee extensor moment(early stance), Nm/Kg0.80 (0.25)0.04 (−0.10:0.180.65 (0.22)−0.01 (−0.15:0.12)0.05 (−0.14:0.25)0.592nd peak knee flexor moment(late stance), Nm/Kg−0.14 (0.16)0.05 (−0.02:0.11)−0.03 (0.16)−0.5 (−0.11:0.01)0.10 (0.01:0.19)0.041st peak knee adductor moment(early stance), Nm/Kg0.67 (0.25)0.05 (−0.03:0.12)0.65 (0.22)0.06 (−0.01:0.13)−0.01 (−0.11:0.09)0.842nd peak knee adductor moment(late stance), Nm/Kg0.50 (0.23)0.07 (0.01:0.014)0.44 (0.18)0.09 (0.02:0.16)−0.02 (−0.12:0.08)0.72Knee abductor angular impulse, Nm*s/kg24.7 (11.4)2.91 (−0.60:6.41)23.2 (9.4)3.09 (−0.27:6.45)−0.18 (−5.04:4.58)0.941st peak knee resultant moment (early stance), Nm/Kg1.04 (0.26)0.05 (−0.05:0.15)1.11 (0.29)0.04 (−0.06:0.14)0.01 (−0.14:0.15)0.912nd peak knee resultant moment (late stance), Nm/Kg0.58 (0.17)0.04 (−0.02:0.10)0.56 (0.12)0.06 (0.01:0.11)−0.02 (−0.10:0.06)0.59Walking speed, m/s1.36 (0.14)−0.05 (−0.14:0.04)1.35 (0.27)−0.03 (−0.12:0.06)−0.02 (−0.15:0.11)0.79 Open table in a new tab

Does increasing step width alter knee biomechanics in medial compartment knee osteoarthritis patients during stair descent?

BackgroundResearch shows that one of the first complaints from knee osteoarthritis (OA) patients is difficulty in stair ambulation due to knee pain. Increased step width (SW) has been shown to reduce first and second peak internal knee abduction moments, a surrogate variable for medial compartment knee joint loading, during stair descent in healthy older adults. This study investigates the effects of increased step width (SW) on knee biomechanics and knee pain in medial compartment knee OA patients during stair descent. MethodsThirteen medial compartment knee OA patients were recruited for the study. A motion analysis system was used to obtain three-dimensional joint kinematics. An instrumented staircase was used to collect ground reaction forces (GRF). Participants performed stair descent trials at their self-selected speed using preferred, wide, and wider SW. Participants rated their knee pain levels after each SW condition. ResultsIncreased SW had no effect on peak knee abduction moments and knee pain. Patients reported low levels of knee pain during all stair descent trials. The 2nd peak knee adduction angle and frontal plane GRF at time of 2nd peak abduction moment were reduced with increasing SW. ConclusionsThe findings suggest that increases in SW may not influence knee loads in medial compartment knee OA patients afflicted with low levels of knee pain during stair descent.

The Curious Nonexistence of Gaussian 2-Designs

Ensembles of pure quantum states whose 2nd moments equal those of the unitarily uniform Haar ensemble—2-designs—are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space $${L^2(\mathbb{R})}$$ . This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have a density matrix because its defining integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and continuous quantum mechanics has important implications for optical state and process tomography.

Four Points Beginner Risk Managers Should Learn from Jeff Holman's Mistakes in the Discussion of Antifragile

Using Jeff Holman's comments in Quantitative Finance to illustrate 4 critical errors students should learn to avoid: 1) Mistaking tails (4th moment) for volatility (2nd moment), 2) Missing Jensen's Inequality, 3) Analyzing the hedging wihout the underlying, 4) The necessity of a numeraire in finance.

Model comparison of the dark matter profiles of Fornax, Sculptor, Carina and Sextans

We use orbit based dynamical models to fit the 2nd and 4th moments of the line of sight velocity distributions of the Fornax, Sculptor, Carina and Sextans dwarf spheroidal galaxies. Our goal is to compare dark matter profile models of these four systems using Bayesian evidence. We consider NFW, Einasto and several cored profiles for their dark halos and present the probability distribution functions of the model parameters. When considering each system separately, we find there is no preference for one of these specific parametric density profiles. However, the combined evidence shows that it is unlikely that all galaxies are embedded in the same type of cored profiles of the form \rho_{DM} \propto 1/(1 + r^2)^{\beta/2}, where \beta = 3, 4. For each galaxy, we also obtain an almost model independent, and therefore accurate, measurement of the logarithmic slope of the dark matter density distribution at a radius ~ r_{-3}, i.e. where the logarithmic slope of the stellar density profile is -3. This slope ranges from ~ -1.4 for Fornax to ~ -1.1 for Sextans, both at ~ 1 kpc. All our best fit models essentially have the same mass distribution over a large range in radius (from just below r_{-3} to the last measured data point). This remarkable finding likely implies much stronger constraints on the characteristics that subhalos extracted from cosmological simulations should have in order to host the dSph galaxies around the Milky Way.

High frame-rate tracking of multiple color-patterned objects

In this study, we develop a high frame-rate vision system that can execute color histogram-based tracking of multiple color-patterned objects in a 512 × 512 image at 2,000 fps by implementing an expanded cell-based labeling algorithm as the hardware logic. In the hardware implementation of the expanded cell-based labeling algorithm, the 16-bin hue-based color histograms of 1,024 color-patterned objects in an image can be extracted simultaneously by dividing the image into 8 × 8 cells concurrently, after calculating the 0th, 1st, and 2nd moment features to obtain the positions, areas, and orientation angles of multiple objects. We verified the effectiveness of our developed tracking system by performing several experiments using multiple color-patterned objects, which were always tracked even when they moved rapidly with occlusions in the camera views.

Retrievals of vertical profiles of stratus cloud properties from combined oxygen A‐band and radar observations

A synergetic algorithm of retrieving vertical distribution of cloud drop effective radius (Re), liquid water content (LWC), and optical depth has been developed by combining oxygen A‐band spectral measurements with radar reflectivity. The underlying physics is to utilize the photon path length information from oxygen A‐band measurements to constrain the retrievals of cloud microphysical properties from radar reflectivity. Through a radiation closure of the rotating shadowband spectrometer (RSS) diffuse‐horizontal irradiances in the oxygen A‐band (which is sensitive to vertical distribution of the 2nd moment of particle size distribution), vertical distributions of cloud microphysical property (the 3rd moment of particle size distribution) are optimized and retrieved from Millimeter Wave Cloud Radar (MMCR) reflectivity (the 6th moment of particle size distribution). The critical issues in the synergetic cloud retrievals of combining passive and active instruments are discussed and carefully taken into account. Evaluation and validation through case studies show that the retrieved column mean values of cloud optical depth, effective radius, and liquid water path agree well with independent measurements from the microwave radiometer (MWR) and independent retrievals from a combined algorithm of multifilter rotating shadowband radiometer (MFRSR) and MWR and the column physical characterization (CPC) of MMCR. These studies demonstrate that this active‐passive synergetic retrieval algorithm is feasible and accurate for retrievals of vertical distribution of cloud Re and LWC for stratus clouds.

Sexual selection in a polygynous rodent (Ctenomys talarum): an analysis of fighting capacity

The South American subterranean rodent genus Ctenomys (Caviomorpha: Octodontoidea), which uses both claws and teeth to dig, shows striking morphological adaptations to its specialized mode of life. Among other traits, the genus has evolved a powerful jaw musculature and procumbent incisors that are used for dento-excavation. Behavioral observations indicate that these traits are also used during male aggressive encounters, which characterize the polygynous mating system of one of the species of the genus, Ctenomys talarum. A question emerges about sexual selection: could it have induced further changes in traits primarily evolved as adaptations for digging? To address this issue, we studied functional and morphological attributes of the jaw and incisors in specimens of C. talarum. Incisor bite forces were measured on wild females and males from a local population (Mar de Cobo; Buenos Aires Province) by means of a strain gauge load cell force transducer. Museum specimens coming from the same population were studied to assess anatomical attributes of both sexes. Since this species exhibits dimorphism in body size, the possible effect of body mass on the studied traits was analyzed. Males and females showed significant differences in biting performance and mandibular width, but when size was taken into account these differences disappeared. However, other dimorphic traits can vary with a certain independence with respect to size, particularly the 2nd moment of area of the incisors and, to a lesser extent, incisor procumbency. The former geometrical parameter, which is proportional to the bending strength, was highly dimorphic. This fact suggests that, during aggressive encounters between males, biting would place large bending loads on the incisors.

Axially and transversely loaded Timoshenko and laced built-up columns with arbitrary supports

The two main effects that should be taken into account in the design of built-up columns are the shearing effect due to their reduced shear rigidity and the interaction between global and local buckling modes in the presence of imperfections. EC3 considers such columns as Timoshenko members for accounting for shear deformation and provides guidance for the calculation of their collapse load under axial compression only for the simply supported case.In the present work an approximate analytical procedure for the calculation of the maximum 2nd order bending moment along imperfect Timoshenko members with arbitrary rotational and translational boundary conditions under combined axial and lateral external loading is formulated. The procedure is verified by means of geometrically nonlinear numerical analyses with the use of shear deformable beam elements. This method is then used for the evaluation of the maximum actions due to combined axial and lateral loading along laced built-up columns with various end conditions accounting also for initial imperfections. Incorporating the 2nd order bending moments in an interaction equation specifically formulated for laced built-up columns, the collapse load is calculated. Analytically obtained results based on the proposed method are compared with the ones found from geometrically and materially nonlinear imperfection analyses (GMNIA) of laced built-up columns modeled using either beam or shell elements. The accuracy of the analytical results is found to be very satisfactory. Due to its simplicity and accuracy the proposed method is a useful tool for the design of laced built-up columns in structural engineering practice.

Validation of LES Predictions of Scalar Mixing in High-swirl Fuel Injector Flows

A combined experimental and computational study is described, aimed at validation of LES predictions of the flow and mixing fields created by a fuel injector which incorporates a single, radially-fed annular swirl stream surrounding a central axial jet flow. The focus of this work was on turbulent mixing processes, so an isothermal (water flow) experiment was carried out, using a representative injector geometry operated at appropriate Reynolds and Swirl Numbers. Combined SPIV and PLIF instrumentation allowed simultaneous instantaneous measurements of velocity vector and a conserved scalar introduced into the fuel stream. For the first time in such a flow, all 3 components of the turbulent scalar flux were available for validation of LES-based CFD predictions. A careful assessment of experimental errors was carried out. Very close to the injector exit plane (x/DS < 0.1), the measured data were prone to larger errors (~20%). Further downstream (x/DS = 0.2 − 1.5), spatial filtering errors were much smaller (~5 − 10%). Comparison of LES predictions with experimental data showed very good agreement for both 1st and 2nd moment statistics, as well as spectra and scalar pdfs. It is particularly noteworthy that comparison between LES computed and measured scalar fluxes was very good; this represents successful validation of the simple (constant Schmidt No.) SGS model used for this complex and practically important flow.

Stability and Electronic Structures of Pt-Rh Icosahedral Nanoparticles

We investigate the energetic stability and electronic structures of Pt-Rh icosahedral nanoparticles based on first-principles calculations. We find that Pt atom energetically prefers vertex and edge sites at the surface rather than subsurface and core sites, which is a tendency similar to Pt-Rh cuboctahedral nanoparticles. This can be attributed to lower surface energy of Pt compared with Rh. Edges of nanoparticles with second-lowest coordination number are the most favorable sites for Pt atom. This could be attributed to the enhanced interatomic distance at the edge site. 1st order moment of d-state electronic contribution for Pt atom exhibits almost negative dependence in terms of Pt coordination number. This can be qualitatively interpreted by positive dependence of 2nd order moment of the density of states for the Pt atom on the coordination number. Pt surface segregation is expected mainly due to contribution from Pt on-site segregation energy compared with weak ordering tendency of Pt-Rh unlike-atom pairs.

On the use of single-crystal diffractometer data necessary for performing the 2nd and 4th restricted moment method

On the use of single-crystal diffractometer data necessary for performing the 2nd and 4th restricted moment method

SHAPE SLOPE PARAMETER DISTRIBUTION MODELLING OF ELECTROMAGNETIC SCATTERING BY RAIN DROPS

Gamma model parameters using 2nd, 3rd and 4th moments are calculated from the drop size data of Singapore. The gamma model is simplifled into two parameter model by flnding a relation between the shape and slope parameters, and ⁄. Due to the poor correlation found between and ⁄, the drop size data is flltered based on their rain rates before a good correlation between the two parameters can be found. The -⁄ relations are then fltted for the difierent ranges of rain rate flltering. Scatter plots of and ⁄ are plotted with constant median volume diameter (D0) lines. The -⁄ relations for the difierent rain types for the tropical island of Singapore are proposed and compared with the -⁄ relations from three other countries of difierent climatic zones. T-Matrix calculations are performed to flnd the polarimetric variables at S-band by using the gamma DSD calculated from the Singapore's drop size data. The calculated difierential re∞ectivity and horizontal re∞ectivity are used along with the best -⁄ relations to flnd the gamma model parameters. The retrieved rain rate using polarimetric variables is compared with the distrometer's measured rain rate. Results show a good agreement between the retrieved rain rate and the measured rain rate. Therefore, the proposed shape slope relationship is found to be suitable for rain rate retrieval.

On the Characterization of Slowly Varying Sinusoids

We give a brief discussion on the amplitude and frequency variation rates of the sinusoid representation of signals. In particular, we derive three inequalities that show that these rates are upper bounded by the 2nd and 4th spectral moments, which, in a loose sense, indicates that every complex signal with narrow short-time bandwidths is a slowly varying sinusoid. Further discussions are given to show how this result helps providing extra insights into relevant signal processing techniques.

On the Characterization of Slowly Varying Sinusoids

We give a brief discussion on the amplitude and frequency variation rates of the sinusoid representation of signals. In particular, we derive three inequalities that show that these rates are upper bounded by the 2nd and 4th spectral moments, which, in a loose sense, indicates that every complex signal with narrow short-time bandwidths is a slowly varying sinusoid. Further discussions are given to show how this result helps providing extra insights into relevant signal processing techniques.

Towards Analytical Approaches to the Dynamical-Cluster Approximation

I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a cluster solver for the Hubbard model. Thermodynamic properties are found to be practically indistinguishable from those computed using the full self-consistent scheme in all cases where the non-interacting partial density of states is replaced by simplified analytic forms with matching 1st and 2nd moments. Green functions are also compared and found to be in close agreement, and the density of states computed using Padé approximant analytic continuation shows that dynamical properties can also be approximated effectively. Extensions to two-particle properties and multiple bands are discussed. Simplified approaches to the dynamical cluster approximation should lead to new analytic solutions of the Hubbard and other models.

The mechanical properties of cranial bone: The effect of loading rate and cranial sampling position

Linear and depressed skull fractures are frequent mechanisms of head injury and are often associated with traumatic brain injury. Accurate knowledge of the fracture of cranial bone can provide insight into the prevention of skull fracture injuries and help aid the design of energy absorbing head protection systems and safety helmets. Cranial bone is a complex material comprising of a three-layered structure: external layers consist of compact, high-density cortical bone and the central layer consists of a low-density, irregularly porous bone structure. In this study, cranial bone specimens were extracted from 8 fresh-frozen cadavers ( F=4, M=4; 81±11 years old). 63 specimens were obtained from the parietal and frontal cranial bones. Prior to testing, all specimens were scanned using a μCT scanner at a resolution of 56.9 μm. The specimens were tested in a three-point bend set-up at different dynamic speeds (0.5, 1 and 2.5 m/s). The associated mechanical properties that were calculated for each specimen include the 2nd moment of inertia, the sectional elastic modulus, the maximum force at failure, the energy absorbed until failure and the maximum bending stress. Additionally, the morphological parameters of each specimen and their correlation with the resulting mechanical parameters were examined. It was found that testing speed, strain rate, cranial sampling position and intercranial variation all have a significant effect on some or all of the computed mechanical parameters. A modest correlation was also found between percent bone volume and both the elastic modulus and the maximum bending stress.

Temporal characteristics and variability of point rainfall: a statistical and wavelet analysis

AbstractRainfall characteristics at different temporal resolutions play a significant role in sustainable urban water management. In this study we attempted to identify the temporal characteristics and variability of point rainfall measured in Melbourne, Australia. Statistical moments, lag1 autocorrelation, the Buishand's Q test for homogeneity, the Mann–Kendall (MK) test for trend and wavelet analyses for temporal variability were carried out for rainfall intensities at resolutions of 0.1, 0.5, 1, 3, 6, 12 h and for the monthly rainfall depths and proportion dry ratios. Series of rainfall intensities at different temporal scales and the monthly rainfall depths and proportion dry ratios were accumulated from the high resolution rainfall dataset for the period from 1925 to 2002. Homogeneity of rainfall intensity was found to increase as the temporal scale increases. Both rainfall intensities and monthly rainfall depths were found to be serially correlated. The 2nd, 3rd and 4th statistical moments of rainfall intensities increased as the resolution increased. While no statistically significant trends were found using the MK test, there were indications that trends are more likely as the temporal scale increases. Wavelet power spectra identified a dominant frequency scale (0.25–1 year) in the 3, 6 and 12 h rainfall intensities that were periodically observed in a 5 to 10–year cyclic order. This phenomenon could be influenced by the inter‐annual variability of the El Niño Southern Oscillation (ENSO). Copyright © 2009 Royal Meteorological Society

Influence of water, temperature and sucrose on dynamics in glassy starch-based products studied by low field 1H NMR

In this study, the influence of both water content and temperature on the mobility of glassy starch-based matrices (starch alone or mixed with sucrose at the ratio 0% to 20% db) were studied using time domain 1H NMR. The 2nd moment M 2, and transversal relaxation time T 2 ∗ were used to study the molecular mobility of the rigid and mobile fraction of the NMR signal, respectively. The molecular mobility of the protons constituting the samples increased with water content (up to 13% wb) at all temperatures. For a given water content, both rigid and mobile protons exhibited a lower mobility in the presence of sucrose. When mobility characteristic parameters, M 2 second moment values and spin–spin relaxation times T 2 ∗, were normalized by T g, i.e plotted versus T g/ T, the effect of water was no longer visible whereas the effect of sucrose remained marked. The temperature increase induced an increase in both rigid and mobile protons mobility. Whereas no clear change could be observed on the rigid protons mobility around the glass transition temperature the mobile fraction exhibited a marked mobility change in that temperature range.

SU-GG-T-52: Sensitivity of Respiratory Motion Pattern On 4D Inverse Planning Dose

Purpose: Patient respiratory motion density function (pdf) has been successfully included in 4D inverse planning in managing lungcancerradiotherapy. The resulting dose distribution is comparable to the one planned using the real‐time tracking technique. However, the motion pdf varies during and between treatment deliveries resulting dose deviation from the one originally planned. In this study, we applied clinically observed pdf variation to evaluate the effect of the variation on the dose distribution obtained from the 4D inverse planning. Method and Materials: 4D inverse planning performed for each of 4 lungcancer patients was used. The reference pdf was obtained using 4D CT with target excursion of 1.5∼3.0cm. Treatmentpdf was constructed by deviating the second and higher orders of moments of the reference pdf, meanwhile the baseline (the first order of moment) was assumed to remain 0. This assumption is supported by online CBCT guided correction. The ranges of the higher order moments' deviation were determined from clinical measurements of 8 lungcancer patients. The treatmentdose in organs of interest was then simulated using the treatmentpdf. The minimal dose (D99%) for target (GTV), and the DVH and EUD in lung,heart and cord were used for the evaluation. Results:Dosimetric effect of respiratory pattern (pdf) variation is dominated by its 2nd order moment (or the standard deviation) variation. The minimal dose in GTV decreases −0.9% ± 1.1%, −2.8% ± 0.6% and −5.5% ± 2.1% respectively with the reference standard deviation increase of 0.5, 1 and 2 mm. The pdf variation has minimal effect on lung,heart and cord EUDs. Conclusion: Variation in respiratory motion pattern causes dose reduction in target. However, the deviation is relatively insensitive to the variation, ass long as the baseline position of the target remains in the treatment course.