Shear-Wave Anisotropy of the Vastus Lateralis During Low-Level Isometric Contraction Measured with Ultrasound Time-Harmonic Elastography

Shear-Wave Anisotropy of the Vastus Lateralis During Low-Level Isometric Contraction Measured with Ultrasound Time-Harmonic Elastography | medRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-P4HH5NV'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search Shear-Wave Anisotropy of the Vastus Lateralis During Low-Level Isometric Contraction Measured with Ultrasound Time-Harmonic Elastography Tom Meyer , Stefan Klemmer Chandía , Pascal Engl , Giacomo Valli , Yanglei Wu , Klaus Jenderka , Thomas Bartels , René Schwesigd , Jing Guo , Eduard Kurz , Ingolf Sack , View ORCID Profile Hossein S. Aghamiry doi: https://doi.org/10.1101/2025.09.30.25336813 Tom Meyer 1 Department of Radiology, Charité – Universitätsmedizin Berlin , 10117, Berlin, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Stefan Klemmer Chandía 1 Department of Radiology, Charité – Universitätsmedizin Berlin , 10117, Berlin, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Pascal Engl 2 Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg , 06217, Merseburg, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Giacomo Valli 3 Department of Clinical and Experimental Sciences, University of Brescia , 25121, Brescia, Italy Find this author on Google Scholar Find this author on PubMed Search for this author on this site Yanglei Wu 1 Department of Radiology, Charité – Universitätsmedizin Berlin , 10117, Berlin, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Klaus Jenderka 2 Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg , 06217, Merseburg, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Thomas Bartels 4 MVZ Sportklinik Halle GmbH , 06108, Halle (Saale), Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site René Schwesigd 5 Department of Orthopaedic and Trauma Surgery, Martin-Luther-University Halle-Wittenberg , 06120, Halle (Saale), Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Jing Guo 1 Department of Radiology, Charité – Universitätsmedizin Berlin , 10117, Berlin, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Eduard Kurz 5 Department of Orthopaedic and Trauma Surgery, Martin-Luther-University Halle-Wittenberg , 06120, Halle (Saale), Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Ingolf Sack 1 Department of Radiology, Charité – Universitätsmedizin Berlin , 10117, Berlin, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site Hossein S. Aghamiry 1 Department of Radiology, Charité – Universitätsmedizin Berlin , 10117, Berlin, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Hossein S. Aghamiry For correspondence: hossein.aghamiry{at}charite.de Abstract Full Text Info/History Metrics Data/Code Preview PDF Abstract Purpose Skeletal muscle is commonly modeled as a transverse isotropic medium, however, the behavior of its anisotropy under active loading remains insufficiently characterized. In this study we used ultrasound time-harmonic elastography (THE) to quantify direction-dependent shear-wave speed (SWS) in the vastus lateralis (VL) muscle at rest and during low isometric contraction intensities. Methods Twenty-six healthy adults (15 men, 11 women; 25.0 ± 4.1 y) under-went multi-frequency THE (60–80 Hz). The transducer was aligned parallel (longitudinal) and perpendicular (transverse) to VL fascicles, and measurements were acquired at rest and at 15% and 30% of maximal voluntary contraction (MVC). The anisotropy index (AI) was defined as AI = SW S ∥ /SW S ⊥ . Orientation and contraction effects were tested with repeated-measures analyses. Results At rest, longitudinal SWS exceeded transverse SWS ( 2.5 ± 0.2 vs. 1.4 ± 0.1 m/s; paired t-test p < 0.01 ). With contraction, SWS increased to 3.2 ± 0.2 and 3.8 ± 0.3 m/s (15%, 30% MVC) along fibers, and to 1.6 ± 0.1 and 1.8 ± 0.1 m/s across fibers (all p < 0.01 ). A two-factor repeated-measures ANOVA on SWS showed main effects of orientation and contraction and a significant interaction (all p < 0.01 ). AI increased from 1.7 ± 0.1 at rest to 2.0 ± 0.1 at 15% and 2.1 ± 0.1 at 30% MVC ( p < 0.01 ). No sex- or BMI-related effects were detected. Conclusion VL exhibited marked shear-wave anisotropy at rest that increased with low-level contraction intensities, indicating disproportionate stiffening along the fiber direction. THE provides a rapid, cost-effective, orientation-sensitive readout of muscle mechanics that may support studies of neuromuscular function and pathology. 1 Introduction Skeletal muscle is architecturally complex and mechanically anisotropic, with material properties that differ markedly along versus across fibers [ 1 – 4 ]. Force is transmitted primarily along the fiber direction [ 5 ], while the extracellular matrix channels load across fibers [ 6 ]. Quantifying in vivo anisotropy, the direction-dependent shear stiffness measured along and across muscle fibers, is essential for interpreting normal function [ 7 ], adaptations to training or disuse [ 8 , 9 ], and a wide range of neuromuscular and musculoskeletal conditions [ 10 ]. Shear-wave–based elastography provides a non-invasive window into muscle mechanics [ 11 – 15 ]. In its simplest use, tissue is treated as isotropic and quasi-incompressible, relating shear-wave speed (SWS) to the shear modulus µ via µ = ρ SWS 2 . This approximation is useful in organs such as liver or breast, but it fails in skeletal muscle, whose organized fibers and connective tissue impart transverse isotropy (TI) on a macroscopic level. This means shear waves travel faster along fibers than across them [ 1 , 14 , 16 – 18 ]. Ignoring anisotropy can therefore confound interpretation and apparent “stiffness changes” may instead reflect probe orientation or wave-field directionality [ 3 , 19 ]. Beyond measurement accuracy, anisotropy itself is biologically meaningful. TI-aware modeling of incompressible materials separates three independent parameters— µ ∥ , µ ⊥ , and the ratio of Young’s moduli parallel and perpendicular to the fiber direction [ 19 – 21 ]. This separation provides direction-dependent stiffness needed for realistic force estimation and offers biomarkers that may change with architecture (aging, disuse, spasticity, training) or pathology even when scalar stiffness is only modestly altered [ 3 , 13 , 14 , 22 ]. Magnetic resonance elastography (MRE) has demonstrated that incorporating TI improves separation of healthy and pathological muscle and enables multiparametric characterization with multi-frequency data [ 21 , 23 , 24 ]. However, the cost, post-processing burden, and limited availability of MRE constrain routine use. Ultrasound-based shear-wave elastography (SWE) offers a pragmatic alternative with bedside accessibility; ultrafast imaging, rotational three-dimensional shear-wave elasticity imaging (SWEI) [ 3 ], and Viscoelastic Response (VisR) methods allow real-time, direction-specific assessment in vivo [ 22 ]. Within this ultrasound family, time-harmonic elastography (THE) [ 15 , 25 , 26 ] is particularly cost-effective because it uses low-amplitude external vibration and standard line-by-line acquisition, avoiding high-power acoustic radiation force impulse (ARFI) pushes and ultrafast plane-wave hardware. Here we use THE to quantify direction-dependent SWS in the vastus lateralis (VL) muscle at rest and during low-level isometric contractions. Because externally driven fields contain mixtures of propagation directions and polarizations, we applied narrowband directional filtering and identical processing to acquisitions with the transducer aligned parallel (longitudinal) and perpendicular (transverse) to VL fibers prior to inversion. We report anisotropy based on the index AI = SWS ∥ / SWS ⊥ (subscripts ∥ and ⊥ denote SWS measured along and perpendicular to the fascicle direction, respectively) and, given the pennate architecture of VL, estimated the in-plane fascicle angle and applied a small-angle correction to minimize orientation bias. Our objectives were to (i) quantify VL anisotropy at rest, (ii) test how SWS and AI change from rest to 15% and 30% maximal voluntary contraction (MVC) intensities, and (iii) assess whether muscle contraction affects anisotropy. We hypothesized that SWS would increase with contraction level in both orientations and that anisotropy would be maintained or increase due to disproportionate stiffening along fibers. 2 Materials and Methods 2.1 Participants Twenty-six healthy adults (15 men, 11 women) were included in this study ( Table 1 ). All participants were free of lower-limb injury and neuromuscular disease and refrained from vigorous physical activity for 24 h before testing. The study was approved by the local ethics committee (Berlin: EA4/040/22, Halle: 2024-208) and conducted in accordance with the Declaration of Helsinki. Written informed consent was obtained from all participants prior to enrollment. View this table: View inline View popup Download powerpoint Table 1. Demographic characteristics of the study cohort ( N = 26). Here, BMI denotes Body-mass index. Also, the normalized MVC was computed by multiplying each participant’s maximum MVC by leg length to obtain knee-extension torque and then dividing by body mass, yielding a mass-normalized maximal voluntary torque reported in Nm kg −1 . 2.2 Experimental setup SWS in VL was measured with THE in two transducer orientations—longitudinal (parallel to fibers) and transverse (perpendicular to fibers)—following the anisotropy protocol of Lima et al . [ 2 ]. Participants were seated upright with the right leg sup-ported, the hip at ≈90 ° and the knee at 90 ° ( Fig. 1a ). A THE device (GAMPT, Merseburg, Germany) with a linear ultrasound transducer (5–11 MHz, 54.6 mm foot-print; LF11-5H60-A3, TeleMed) was positioned over VL at 75% of the distance between the greater trochanter and the lateral femoral epicondyle. The transducer was secured using an elastic strap and a custom 3D-printed holder that allowed rotation in 22.5 ° increments ( Fig. 1b ), minimizing movement and operator variability and enabling precise 90 ° rotations between longitudinal and transverse measurements. The initial longitudinal position was marked on the skin to ensure consistent placement before rotating four steps to obtain the transverse orientation. Download figure Open in new tab Fig. 1. Measurement setup for performing THE on the VL muscle. (a) Participant seated upright with the right leg supported, hip at 90 ° and knee at ≈90 ° flexion. The ultrasound transducer was positioned at 75% of the distance between the greater trochanter and lateral femoral epicondyle, then secured with an elastic strap and a custom 3D-printed transducer holder allowing controlled rotations. (b) The holder enabled precise alignment of the transducer parallel and perpendicular to muscle fibers for longitudinal and transverse measurements. Continuous multi-frequency mechanical vibrations (60, 70, 80 Hz) were induced by a custom designed pillow-driver (Elastance Imaging, Ohio, US). These drive frequencies were selected to yield shear wavelengths λ = V S /f in the ≈ 12–67 mm range for the expected V S ≈ 1–4 m s −1 in vastus lateralis, matching muscle thickness and our field of view, while balancing attenuation (lower frequencies penetrate better) and ensuring sufficient energy delivery at depth and subject comfort. The ultrasound system acquired radio-frequency (RF) data line-by-line at 100 frames s −1 for 12 s per acquistion. Given the 100 Hz frame rate (Nyquist frequency 50 Hz), the 60/70/80 Hz inputs alias to 40/30/20 Hz in the recorded time series; we account for this with controlled-aliasing reconstruction to recover the true frequency components [ 27 ]. Three contraction states were tested in each orientation: (i) rest (no external load), (ii) 15% MVC , and (iii) 30% MVC . MVC was determined in a preliminary trial with the participant seated on a custom-built chair and the lower leg individually adjusted and attached to a load cell (SM-2000N, Interface Inc., Scottsdale) with a strap secured above the ankle joint. For each participant, this yielded six acquisitions (two orientations × three contraction levels); each condition comprised a continuous 12 s THE acquisition from which mean SWS was obtained by temporal and spatial averaging within the region of interest (ROI). 2.3 RF data processing The THE pipeline followed Aghamiry et al. [ 26 ] and was applied identically to both transducer orientations to avoid processing-induced bias. For completeness, we summarize each step here and point to detailed derivations and design choices in the Appendices. Monogenic, phase-based displacement estimation: Axial (vertical) tissue displacements between consecutive RF frames were estimated with a monogenic, phase-constancy optical-flow solver. The RF (or IQ-envelope) data were analyzed in a multiscale band-pass pyramid; at each scale, the monogenic signal (Riesz transform pair plus even component) yielded local amplitude, phase, and orientation in a rotation-invariant representation [ 28 , 29 ]. Assuming small interframe motion, phase constancy was linearized to relate temporal and spatial monogenic phase gradients to the vertical displacement. We solved the resulting weighted least-squares problem with Tikhonov regularization via Gauss–Newton updates on a coarse-to-fine pyramid (see Appendices A and B for full formulae). To improve SNR while preserving coherent wave structure, we applied truncated-SVD denoising to the space–time stack, retaining eigenimages of ranks 2–100 [ 25 , 30 ]. Harmonic isolation: Because THE used continuous multi-frequency harmonic driving, we isolated each vibration frequency with third-order Butterworth band-pass filters (center 60/70/80 Hz; ± 1.5 Hz bandwidth), yielding complex, frequency- and time-resolved displacement fields for each vibration frequency. Directional filtering: Our ultrasound acquisition measured predominantly the vertical displacement component. For shear waves that propagate horizontally in- plane, particle motion is largely vertical (shear–vertical, SV-like), which maximizes sensitivity of the measured component and stabilizes the inversion. Conversely, oblique/vertical propagation introduces (i) mode mixing (SV/SH and guided components; SH denotes shear–horizontal, i.e., particle motion perpendicular to the vertical plane containing the propagation direction), (ii) stronger boundary/reflection contamination, and (iii) spatial interference that biases wavelength estimates. We therefore applied a purely angular Gaussian filter in the 2-D wavenumber domain to retain horizontally propagating energy while leaving the radial wavenumber | k | (and thus dispersion) unchanged [ 31 , 32 ]. Specifically, we discretized propagation angle into N =32 directions and summed two antipodal windows cen-tered at 0 ° and 180 ° with angular standard deviation σ = 2 π/N = π/ 16 (FWHM ≈26.5 ° ); see Fig. 2 for the filter shape and Appendix C for definitions. Wavenumber-based inversion ( k -MDEV): Wave number (k) based multifrequency dual elasto visco (k-MDEV) inversion computes the local phase gradient to estimate the wavenumber. These are averaged across directional components and vibration frequencies. Each timepoint of the time-resolved wavefields is processed individually, yielding a time-resolved SWS maps with 1 mm in-plane resolution. Download figure Open in new tab Fig. 2. Directional Gaussian filter in the ( k x , k z ) domain. Two angular Gaussian windows ( N = 32, σ = π/ 16) centered at 0 ° and 180 ° were summed to pass horizontally propagating components while attenuating others (refer to Appendix C for more details). Selected columns of the 2-D filter are highlighted in red to visualize angular bandwidth at different k x . For each measurement, a region of interest (ROI) was drawn on the first B-mode frame to include VL fascicles. To account for in-plane motion, we performed frame-to-frame rigid registration by cross-correlation and propagated the resulting translation to the ROI across all 1,200 frames (12 s). Mean SWS values for the two transducer orientations were then obtained by temporal+spatial averaging within the ROI: SWS ∥ for longitudinal scans (transducer aligned with fibers) and SWS ⊥ for transverse scans (transducer perpendicular to fibers). 2.4 Pennation–angle correction In pennate muscle, the transducer’s lateral imaging axis (dominant propagation direc-tion in our setup) was rarely perfectly aligned with fascicles. A small in-plane fascicle angle θ pen therefore mixed along- and across-fiber shear responses, biasing the apparent SWS. Because muscle was well approximated as a TI medium with symmetry along the fibers, we corrected this bias by mapping the apparent speeds measured in the transducer frame to the principal (fiber) frame (SWS ∥ , SWS ⊥ ). Under small-strain, quasi-incompressible TI assumptions, the in-plane shear mode fol-lows a directional harmonic-mean relation; solving the paired inverse problem yielded (see Appendix D): Fig. 3 schematizes this mapping: the transducer–frame measurements are projections of the fibre–frame ellipse rotated by θ pen , and Eq. (1) back-rotates them to (SWS ∥ , SWS ⊥ ). Download figure Open in new tab Fig. 3. Schematic of coordinate frames and fascicle angle for pennation correction. (a) transducer (image) frame: the imaging plane was rotated by θ pen relative to the fibers (purple stripes). The blue rectangle at the top represents the ultrasound transducer, centered on the y -axis. A harmonic wave was drawn below the transducer to illustrate a shear wave propagating horizontally (along + x ). The vertical arrow on the y -axis indicated the direction of displacement estimation from RF phase. Green arrows mark the apparent squared speeds (lateral) and (axial). (b) Fiber (principal) frame: Eq. (1) maps the apparent measurements to SWS ∥ and SWS ⊥ . We applied Eq. (1) to each measurement using the frame-wise θ pen estimated from the B-mode (below). As reported by Lima et al. [ 2 ], Miyamoto et al. [ 16 ], because | θ pen | ≲ 20 ° in VL, corrections were small but systematic and avoided bias in AI . Estimating θ pen from B-mode Angles were extracted directly from B-mode; the procedure, based on monogenic orientation (Appendix A), is summarized below: Monogenic features and phase asymmetry: For each B-mode frame we computed a multiscale monogenic signal, yielding local orientation ( Fig. 4b ) and a phase-asymmetry (PA) map ( Fig. 4a ) that highlights line-like fascicular texture. Fiber mask: Within the ROI, a PA threshold ( T =0.1) selected fascicle-dominated pixels, suppressing non-fascicular edges. Orientation sampling and histogramming: Monogenic orientations were sampled only inside the fiber mask, wrapped to [−90 ° , 90 ° ], and histogrammed at high angular resolution. Gaussian fit and frame angle: A single Gaussian a exp[−( α − µ ) 2 /σ 2 ] was fitted to the histogram; the fitted mean µ gave the frame-wise θ pen . Frames with insufficient masked pixels or poor fit ( R 2 < 0.9) were excluded. Per trial, the median of valid frame angles was used (5-frame median smoothing). Download figure Open in new tab Fig. 4. Pennation-angle estimation from a B-mode frame. (a) B-mode with monogenic phase-asymmetry overlay (red) highlighting fascicles. (b) Monogenic orientation (ROI). (c) Orientation histogram of masked pixels with Gaussian fit (red) and peak angle θ pen (yellow). The resulting θ pen was then used in Eq. (1) to obtain (SWS ∥ , SWS ⊥ ) from and to compute the corrected AI = SWS ∥ / SWS ⊥ . Figure 4 illustrates the angle-extraction steps. 2.5 Statistical analysis Unless otherwise noted, all tests were two-sided with α = 0.01; results are reported as p < 0.01. Descriptive statistics are mean ± SD. To test how SWS depended on contraction level and transducer orientation, we used a two-factor repeated-measures ANOVA with intra-individual factors Contraction (0%, 15%, 30% MVC) and Orientation (longitudinal, transverse), evaluating main effects and their interaction. For AI, we used a one-factor repeated-measures ANOVA with intra-individual factor Contraction (0%, 15%, 30% MVC). Assumptions were checked on model residuals: normality with Shapiro–Wilk tests and Q–Q plots; sphericity with Mauchly’s test, applying Greenhouse–Geisser corrections when violated. With two levels, sphericity did not apply to Orientation . For the three-level Contraction factor, Bonferroni-adjusted post hoc pairwise comparisons were conducted where appropriate. For intra-individual pairwise contrasts, Bonferroni-adjusted post hoc paired t -tests were conducted within each comparison family. For larger families of exploratory cor-relations, we controlled the false discovery rate (FDR) using the Benjamini–Hochberg procedure ( q = 0.05). Effect sizes were reported as partial for ANOVAs and Cohen’s d z for paired contrasts; 95% confidence intervals for d z were obtained by percentile bootstrap (5,000 resamples). To summarize contraction dependence, we computed per-subject linear slopes of SWS (and AI) versus MVC level (0, 15, 30%). For each orientation, the mean slope was tested against zero (one-sample t -test), and slopes were compared between orientations using a paired t -test. Potential influences of participant characteristics were evaluated via Pearson correlations (age, mass, height, BMI, MVC) with FDR control across outcomes. We also screened for sex differences using independent-samples comparisons at each contraction level (FDR across tests). 3 Results 3.1 Pennation–angle correction Measurements were successful in all 26 participants in both transducer orientations and MVC levels. SWS increased with contraction in both orientations, with a larger increase along fibers, however, these values must be adjust to account for the pennation angle. Using the monogenic orientation pipeline, in–plane fascicle angles were small at all loads (| θ pen | ≲ 10 ° ). Signed means (SD) were: rest 1.9 ° (2.7 ° ), 15% MVC −0.8 ° (3.2 ° ), and 30% MVC 1.5 ° (3.6 ° ). Applying Eq. 1 to SWS, produced small increases in anisotropy while preserv-ing the contraction–dependent pattern: group–mean Δ AI = AI corr − AI meas were ∼ 0.0001 (rest), ∼ 0.0002 (15% MVC), and ∼ 0.0003 (30% MVC). Paired t -tests were statistically significant at all loads (rest and 30%: p < 0.01; 15%: p < 0.01), but the absolute changes were negligible at the group level and did not alter interpretation. Individual volunteers exhibited noticeable paired shifts ( Fig. 5 ), motivating retention of the correction for subject–level analyses. Download figure Open in new tab Fig. 5. Effect of pennation correction (Eq. (1)) on anisotropy. (a) Box plots of AI at rest, 15% and 30% MVC for measured (blue) and angle-corrected (orange) data; gray lines connect each participant to visualize intra-individual shifts. (b) Box plots of Δ AI = AI corr − AI meas . Corrections are negligible at the group level. 3.2 SWS maps in a representative volunteer Figure 6 illustrates the angle dependence and spatial distribution of SWS in a representative volunteer at rest, 15% MVC, and 30% MVC. The first column shows polar plots of time-averaged SWS obtained with the directional filter bank (same as Fig. 2 ) rotated in 11.25 ° steps. Longitudinal acquisitions are shown in blue and transverse acquisitions in red for different loads (rest, 15% MVC, and 30% MVC) in panels (a), (d), and (g), respectively. Across all angles, transverse SWS was lower than longitudinal SWS. In this study, we focused on waves that propagate horizontally in-plane (particle motion predominantly vertical), as these maximize sensitivity of the measured displacement component and stabilize the inversion. Download figure Open in new tab Fig. 6. Representative example of angle-dependent and spatial SWS changes during isometric contraction. (a , d , g) Polar plots of mean SWS within the ROI using directional filters rotated in 11.25 ° increments (same filter bank as Fig. 2 ). Longitudinal (blue) and transverse (red) measurements are shown for rest, 15% MVC, and 30% MVC. (b , e , h) Longitudinal SWS maps reconstructed from horizontally propagating waves and averaged over 12 s for rest, 15% MVC, and 30% MVC. (c , f , i) Corresponding transverse SWS maps. Underlying B-mode images are shown for anatomical reference. With increasing MVC, SWS increases in both orientations but less across fibers, yielding a higher AI . The second and third columns display SWS maps reconstructed from horizontally propagating waves and averaged over 12 s within the selected ROI. Panels (b), (e), and (h) show longitudinal SWS maps for different loads; panels (c), (f), and (i) show the corresponding transverse maps. SWS increased from rest to 15% and 30% MVC in both orientations, with a smaller rate of increase across fibers. Consequently, the anisotropy index increased with contraction level. 3.3 Statistical analysis As it was mentioned before, SWS increased with contraction in both orientations, with a larger increase along fibers. Group means (mean SD) were: longitudinal SWS 2.5 ± 0.2 (rest), 3.2 ± 0.2 (15% MVC), 3.8 ± 0.3 m/s (30% MVC); transverse SWS 1.4 ± 0.1, 1.6 ± 0.1, 1.8 ± 0.1 m/s; and AI : 1.7 ± 0.1, 2.0 ± 0.1, 2.1 ± 0.1, respectively. Box plots for all volunteers are shown in Fig. 7 ; gray lines connect individual participants, illustrating intra-individual increases from rest to higher MVC. The transverse increase was smaller than the longitudinal increase, yielding a rising AI across contraction levels. Download figure Open in new tab Fig. 7. Panels (a–c) show longitudinal SWS, transverse SWS, and AI at 0% (rest), 15%, and 30% MVC. Colored box plots depict the distribution across participants and gray lines connect each participant across contraction levels to visualize intra-individual changes. Brackets and asterisks denote Bonferroni-adjusted post-hoc paired comparisons (** p < 0.01). A two-factor repeated-measures ANOVA on SWS showed strong main effects of Orientation and contraction , and a significant orientation × Contraction interaction . For AI , the one-factor RM-ANOVA was also significant . A priori intra-individual contrasts, aligned with our hypotheses, compared changes across contraction levels (0→15, 15→30, 0→30% MVC) within each orientation and longitudinal vs. transverse at each level. These contrasts were tested with two-sided paired t -tests and Bonferroni adjustment within each comparison family ( p < 0.01). Results are summarized in Table 2 . Briefly, longitudinal SWS increased by +0.73 and +0.60 m/s from 0→15 and 15→30% MVC, respectively; transverse SWS increased by +0.21 and +0.18 m/s. AI increased by +0.22 (0→15%) and +0.14 (15→30%), and the difference between longitudinal and transverse SWS widened from +1.04 m/s at rest to +1.99 m/s at 30% MVC (all p < 0.01). View this table: View inline View popup Download powerpoint Table 2. Planned (pre-specified) pairwise contrasts. Entries are mean intra-individual differences (Δ, mean SD), Cohen’s d z , and Bonferroni-adjusted p thresholds. Expressed as relative change from 0→30% MVC, longitudinal SWS increased by 54.0% and transverse SWS by 27.2%; AI increased by 21.1%. Individual linear trend slopes were positive for both orientations (longitudinal: ; transverse: ) and were larger longitudinally than transversely (mean difference 0.03, t = 18.8, p < 0.01, d z = 3.7). AI slopes were also positive . Finally, no sex differences or correlations with age, anthropometrics, or BMI survived FDR control across outcomes. 4 Discussion Using THE, we quantified direction-dependent SWS in the VL muscle at rest and during low-level isometric contractions. Three results stand out. First, VL exhibited marked baseline anisotropy: longitudinal SWS exceeded transverse SWS at rest (2.5 ± 0.2 vs. 1.4 ± 0.1 m/s), yielding AI = 1.7 ± 0.1. Second, SWS increased with activation in both orientations, but more along fibers (rest → 30% MVC: +54.0% longitudinal, +27.2% transverse), producing a statistically significant rise in AI to 2.1 ± 0.1 (+21.1%). Third, a small in-plane pennation-angle correction (median | θ pen | ≲ 10 ° ) produced small group-level shifts in anisotropy, leaving the contraction-dependent pattern unchanged. While negligible on average, subject-level shifts were sometimes noticeable (cf. Fig. 5a ), supporting retention of the correction in the analysis pipeline. Broadly, our orientation-specific SWS and the observed anisotropy are consistent with prior elastography work showing that skeletal muscle behaves as a transversely isotropic, direction-dependent medium [ 1 , 3 , 19 , 21 , 24 ]. Studies using single-orientation ultrasound (e.g., supersonic shear imaging (SSI)) and TI-aware reconstructions alike report higher along-fiber than across-fiber speeds at rest, with magnitudes depending on muscle, frequency, and wave-mode conditioning [ 2 , 16 – 18 ]. Our findings in VL at rest closely match those obtained with rotational 3D SWEI by Knight et al. [ 17 ]. Using an ARFI-based 3D acquisition with transducer rotation and intentional fiber tilt, they reported shear moduli of µ ∥ = 5.8 ± 1.0 kPa and µ ⊥ = 1.9 ± 0.4 kPa in relaxed VL, corresponding to a shear anisotropy 𝒳 µ = ( µ ∥ − µ ⊥ ) /µ ⊥ = 2.1 ± 0.9 and a tensile anisotropy 𝒳 E = 4.7 ± 1.4. In the same dataset, representative group speeds were c ∥ ≈ 2.3 m/s and c ⊥ ≈ 1.4 m/s (from ellipse fits to the SH mode). In our THE data, the corresponding relaxed values were SWS ∥ = 2.5 ± 0.2 m/s and SWS ⊥ = 1.4 ± 0.1 m/s, giving AI = 1.7 ± 0.1. This is numerically close to the 3D SWEI speed ratio ( ∼ 1.7) and, via 𝒳 µ = AI 2 ™ 1, implies a shear-modulus anisotropy of ≈1.9 at rest—again consistent with Knight et al. [ 17 ]. The agreement is encouraging given substantial protocol differences: Knight et al. [ 17 ] used ARFI pushes with rotational sampling to resolve both shear-horizontal (SH) and shear-vertical (SV) modes and to estimate three TI parameters ( µ ∥ , µ ⊥ , 𝒳 E ); our THE approach uses continuous external vibrations (60–80 Hz), 2-D imaging, and directional filtering to isolate horizontally propagating waves, and we summarize anisotropy by the speed ratio AI . Methodologically, these studies are complementary. The rotational 3D SWEI geometry leverages natural fiber tilt to excite and observe both SH and SV modes, enabling recovery of tensile anisotropy 𝒳 E and demonstrating that accounting for fiber tilt increases µ ∥ estimates relative to 2-D methods. Our pipeline standardizes transducer placement, applies narrow-band angular filtering, and performs a small-angle (penna-tion) correction; while we do not recover 𝒳 E , we obtain stable, field-of-view–wide SWS maps that reproduce the same baseline anisotropy in VL. The greater activation-induced rise of SWS along fibers is consistent with tensiondependent shear behavior of actively cross-bridged myofibrils and with collagenous alignment that preferentially stiffens the fiber axis under load [ 4 – 6 ]. The persistence and amplification of anisotropy with low-level activation suggest that AI captures aspects of the force-bearing architecture beyond scalar stiffness. Whether AI saturates or changes nonlinearly at higher forces remains an open question. Several limitations merit consideration. First, the external vibration source generates a superposition of wave modes and propagation directions; although angular filtering emphasizes in-plane, horizontally propagating shear waves, complete mode isolation is not guaranteed within the finite aperture [ 31 ]. Second, we measured only the vertical displacement component; in TI media both propagation direction and polarization govern phase velocity, which limits full tensor recovery of the third free elasticity-related parameter in an incompressible TI material, and may leave residual mixing. Third, the study covered a narrow force and frequency range (0–30% MVC, 60–80 Hz) in a healthy young cohort. Therefore, anisotropy values may depend on activation level, dispersion, or muscle condition. These factors must be taken into account when interpreting our data, since our results represent apparent direction-dependent SWS under a controlled but incomplete observation model. Despite these limitations, the study shows that THE, combined with directional filtering and TI-aware interpretation, yields robust, orientation-sensitive metrics with tight confidence intervals and strong repeated-measures effects. Reporting SWS ∥ , SWS ⊥ , and AI avoids questionable isotropic conversions ( E ≈ 3 µ ) and is better tai-lored to muscle’s TI behavior [ 19 , 21 , 24 ]. The approach is simple to deploy at the bedside, requires no ARFI pulses or ultrafast plane-wave hardware, and produces consistent maps across contraction states, supporting applications in physiology (activation mapping, fatigue, training adaptation) and disease (e.g., dystrophies, spasticity) [ 13 , 14 , 22 ]. Two avenues are promising for future work. First, measurement completeness : cap-turing multi-component data (2.5D or 3D) and incorporating multi-component motion estimation enhances mode control and enables more comprehensive recovery of TI parameters. [ 3 , 17 , 18 , 33 ]. Second, biophysical integration : combining THE with diffusion tensor imaging or fascicle-tracking ultrasound could link AI to microstructure, pennation dynamics, and force production [ 21 , 34 , 35 ]. Extending the frequency band and MVC range will clarify dispersion and force dependence; clinical studies can test whether direction-resolved metrics add diagnostic or prognostic value [ 15 , 23 , 36 ]. In sum, THE reveals a pronounced and activation-sensitive anisotropy of VL shear-wave propagation. Direction-resolved SWS and their ratio provide compact, reproducible biomarkers of muscle mechanical behavior that complement—and in some scenarios may outperform—isotropic elastography surrogates. 5 Conclusion THE is a cost-effective ultrasound elastography approach that captures the intrinsic anisotropy of skeletal muscle. In this study, we applied THE for the first time to recover SWS longitudinal and transverse to the fiber direction in VL under different loading conditions in healthy volunteers. The measurements revealed marked tissue anisotropy that increased with contraction intensity. These direction-resolved SWS maps demonstrate the feasibility of using THE to characterize muscle mechanics in vivo and provide an orientation-sensitive readout aligned with muscle architecture particularly for low-level isometric contractions of knee extensor muscles. The reported SWS values establish a reference for THE in skeletal muscle and support future translation to clinical assessments. Together, these findings position THE as a practical tool for evaluating neuromuscular function with sensitivity to fiber direction. Data Availability All data produced in the present study are available upon reasonable request to the authors Acknowledgments This study was funded by AIF FKZ KK5611902 BM4 (MUSKEL), German Research Foundation (DFG) projects 513752256 FOR5628, CRC1340, GRK2260 BIOQIC, and GU 172614-1. These sponsors had no role in the study design, collection, analysis and interpretation of data, writing of this manuscript or the decision to submit the article for publication. Appendix A Monogenic signal and phase asymmetry The monogenic signal was used as a 2-D generalization of the 1-D analytic signal to separate a band-limited image into an even (cosine-like) component and two odd (sinelike) quadrature components given by the Riesz transform [ 37 – 39 ]. This representation yielded three local, rotation-invariant descriptors (amplitude, phase, and orientation) that were well suited to ultrasound, where intensity could vary but geometry (phase) was relatively stable. Let f ( x , t ) denote an image at time/frame t with x = ( x, y ). At scale s we computed a band-passed image where g s was an (approximately) isotropic band-pass filter (e.g., Gaussian–derivative or Riesz–Laplace wavelet). The 2-D Riesz transform ℛ= R 1 , R 2 acted through its Fourier symbol The monogenic triplet at scale s was From ( p s , q s ) we obtained i.e., local amplitude A s , local phase ϕ s , and orientation angle θ s (direction of maximal variation). The phase ϕ s is known to be contrast-invariant, which improves robustness for ultrasound. Phase asymmetry (PA) for fiber detection To emphasize line-like texture (muscle fascicles and aponeuroses), we used a phase-based feature known as phase asymmetry (PA) [ 40 ]. With the scale-consistent phase ϕ s we defined PA was strongly positive on ridges/lines (central bright structure), provided a characteristic negative–positive transition across step edges, and was relatively insensitive to intensity scaling. In our workflow, PA was computed on the B-mode (envelope of the RF/IQ data) and thresholded within the ROI to produce a fiber mask that suppressed non-fascicular texture. Monogenic orientations θ s were then sampled only from masked pixels and aggregated across scales to form a high-resolution orientation histogram used to estimate the frame-wise fascicle angle. Appendix B Monogenic displacement estimation method We estimated the axial (vertical) displacement between consecutive RF frames using a monogenic, phase-constancy optical-flow formulation [ 28 , 29 , 41 – 43 ]. The key assumption, valid for small interframe motion, was that local phase was conserved along motion trajectories. Specializing the general phase-constancy linearization to the vertical direction y gave so the per-scale vertical displacement per frame was Here k s converted phase (radians) to cycles/pixel for the chosen band-pass (for a Gaussian-derivative band-pass with scale s, k s ≈ ω 0 ( s ) / (2 π ) with ω 0 ∝ s −1 / 2 ). A stable estimate of the vertical phase derivative was written using the monogenic components [ 28 , 29 ]: Between two consecutive frames, a rotation-invariant signed phase difference was obtained from inner and cross products of monogenic parts: with e y the vertical unit vector. Aggregating scales 𝒮, we estimated the vertical displacement field v by solving a weighted least-squares problem. More stable estimates were achieved by adding Tikhonov regularization: where w s upweighted reliable scales (e.g., proportional to E s ), λ stabilized low-gradient regions, and α was the smoothness weight. We solved this with Gauss–Newton updates on a coarse-to-fine pyramid and frame-to-frame warping to converge for larger motions. In 1-D without band-pass filtering and regularization, this approach reduced to classic phase-shift estimation related to Hilbert/analytic-signal methods [ 44 ]. Appendix C Directional angular filtering in the wavenumber domain External vibration excited a mixture of wave modes and directions. Because we measured only the vertical displacement component (as most ultrasound methods do), we emphasized in-plane shear waves that propagated horizontally, whose particle motion was largely vertical (SV-like). To this end we used a purely angular Gaussian filter in the 2-D wavenumber domain ( k x , k z ), which preserved the radial wavenumber (and thus dispersion) while selecting propagation direction [ 31 ]. Let We discretized the unit circle into N = 32 directions and selected the antipodal horizontal directions I = {1, 17} corresponding to 0 ° and 180 ° . For each selected direction we defined a Gaussian angular window and set the directional passband as the sum The full width at half maximum (FWHM) of each lobe was . We set F ( θ ) = 0 at k = 0 (undefined angle). This filter bank passed horizontally propagating energy in both ± k x directions and attenuated oblique or vertical propagation that was more susceptible to boundary reflections, mode conversion, and standing-wave interference. Appendix D Derivation of the pennation-angle correction Skeletal muscle was modeled as transversely isotropic (TI) with the symmetry axis aligned to fibers. When the transducer’s lateral imaging axis was rotated by an in-plane angle θ relative to fibers, the measured speeds (lateral) and (axial) were apparent values that mixed the true along- and across-fiber shear responses. 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IEEE [44]. ↵ Kasai , C. , Namekawa , K. , Koyano , A. , Omoto , R. : Real-time two-dimensional blood flow imaging using an autocorrelation technique . IEEE Transactions on sonics and ultrasonics 32 ( 3 ), 458 – 464 ( 1985 ) OpenUrl CrossRef View the discussion thread. Back to top Previous Next Posted October 01, 2025. Download PDF Data/Code Email Thank you for your interest in spreading the word about medRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following Shear-Wave Anisotropy of the Vastus Lateralis During Low-Level Isometric Contraction Measured with Ultrasound Time-Harmonic Elastography Message Subject (Your Name) has forwarded a page to you from medRxiv Message Body (Your Name) thought you would like to see this page from the medRxiv website. 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