An analytical solution to the dispersion‐by‐inversion problem in magnetic resonance elastography

Purpose: Magnetic resonance elastography (MRE) measures stiffness of soft tissues by analyzing their spatial harmonic response to externally induced shear vibrations. Many MRE methods use inversion-based reconstruction approaches, which invoke first- or second-order derivatives by finite difference operators (first- and second-FDOs) and thus give rise to a biased frequency dispersion of stiffness estimates. Methods: We here demonstrate analytically, numerically, and experimentally that FDO-based stiffness estimates are affected by (1) noise-related underestimation of values in the range of high spatial wave support, that is, at lower vibration frequencies, and (2) overestimation of values due to wave discretization at low spatial support, that is, at higher vibration frequencies. Results: Our results further demonstrate that second-FDOs are more susceptible to noise than first-FDOs and that FDO dispersion depends both on signal-to-noise ratio (SNR) and on a lumped parameter A, which is defined as wavelength over pixel size and over a number of pixels per stencil of the FDO. Analytical FDO dispersion functions are derived for optimizing A parameters at a given SNR. As a simple rule of thumb, we show that FDO artifacts are minimized when A/2 is in the range of the square root of 2SNR for the first-FDO or cubic root of 5SNR for the second-FDO. Conclusions: Taken together, the results of our study provide an analytical solution to a long-standing, well-recognized, yet unsolved problem in MRE postprocessing and might thus contribute to the ongoing quest for minimizing inversion artifacts in MRE

Real‐time MR elastography for viscoelasticity quantification in skeletal muscle during dynamic exercises

Purpose: To develop and test real-time MR elastography for viscoelastic parameter quantification in skeletal muscle during dynamic exercises. Methods: In 15 healthy participants, 6 groups of lower-leg muscles (tibialis anterior, tibialis posterior, peroneus, extensor digitorum longus, soleus, gastrocnemius) were investigated by real-time MR elastography using a single-shot, steady-state spiral gradient-echo pulse sequence and stroboscopic undersampling of harmonic vibrations at 40 Hz frequency. One hundred and eighty consecutive maps of shear-wave speed and loss angle (φ) covering 30.6 s of total acquisition time at 5.9-Hz frame rate were reconstructed from 360 wave images encoding 2 in-plane wave components in an interleaved manner. The experiment was carried out twice to investigate 2 exercises-isometric plantar flexion and isometric dorsiflexion-each performed over 10 s between 2 resting periods. Results: Activation of lower-extremity muscles was associated with increasing viscoelastic parameters shear-wave speed and phi, both reflecting properties related to the transverse direction relative to fiber orientation. Major viscoelastic changes were observed in soleus muscle during plantar flexion (shear-wave speed: 20.0% ± 3.6%, φ: 41.3% ± 12.0%) and in the tibialis anterior muscle during dorsiflexion (41.8% ± 10.2%, φ: 27.9% ± 2.8%; all P < .0001). Two of the muscles analyzed were significantly activated by plantar flexion and 4 by dorsiflexion based on shear-wave speed, whereas φ changed significantly in 5 muscles during both exercises. Conclusion: Real-time MR elastography allows mapping of dynamic, nonperiodic viscoelasticity changes in soft tissues such as voluntary muscle with high spatial and temporal resolution. Real-time MR elastography thus opens new horizons for the in vivo study of physiological processes in soft tissues toward functional elastography

Zeitaufgelöste Charakterisierung von Gewebestrukturen mittels In-vivo-Bestimmung viskoelastischer Kenngrößen in der Magnetresonanz-Elastographie

Magnetic resonance elastography (MRE) is an emerging modality for quantitative viscoelasticity mapping of soft tissues in vivo. However, long acquisition times and poor temporal resolution limit the capacity of MRE to study moving organs and short-term temporal variations of viscoelasticity. Therefore, a new method for rapid time-resolved MRE has been developed based on a cardiac-gated steady-state MRE (ssMRE) pulse sequence with a multi-shot segmented spiral readout and respiratory navigation combined with stroboscopic displacement encoding and an adapted reconstruction algorithm. The method was extended to a single-shot real-time ssMRE (rtMRE) variant that can map non-periodic processes in a single measurement without any repeated readout. The feasibility of the developed methods was demonstrated in 3 in vivo studies. In each study, time-resolved viscoelasticity maps on the order of 6–29 Hz depicting stiffness (shear wave speed in m/s or magnitude of the complex shear modulus in Pa) and fluidity (phase of complex shear modulus in rad) were inverted and analyzed. In the first study, the influence of cerebral arterial pulsation (CAP) on the brain viscoelasticity was investigated in 12 healthy participants. In the second study, 20 healthy participants were examined to quantify differences in viscoelasticity along the aortic tree, including the ascending thoracic (AA), descending thoracic (AD), and abdominal (AAb) aorta. In a third study, rtMRE was applied to investigate dynamic muscle activation in the lower extremities during isometric plantar flexion and dorsiflexion in 15 healthy participants. A global systolic CAP-induced decrease in stiffness of 6.6 ± 1.9% (p < .001) and a weak increase in fluidity of 0.5 ± 0.5% (p = .002) was found in the brain parenchyma. In the aorta, an increase in stiffness from the aortic root to the aortic bifurcation was found with 1.6 ± 0.2 m/s in AA, 2.4 ± 0.3 m/s in AD and 2.5 ± 0.6 m/s in AAb. In the muscle, it was observed that muscle activation is associated with significantly increased stiffness and fluidity. The most pronounced increase in viscoelastic parameters was observed in the soleus during plantar flexion (stiffness: 20.0 ± 3.6%, fluidity: 41.3 ± 12.0%, p < .001) and in the tibialis anterior during dorsiflexion (stiffness: 41.8 ± 10.2%, fluidity: 27.9 ± 2.8%, p < .001). ssMRE and rtMRE proved to be versatile methods, yielding viscoelasticity maps with high spatial and temporal resolution. The results show CAP-induced transient effects on brain viscoelasticity, stiffness differences along the aortic tree, and an abrupt increase in stiffness and fluidity resulting from muscle activation. This dissertation contributes to the field of MRE by providing, for the first time, time-resolved viscoelasticity maps of soft tissues to study physiological processes in future diagnostic applications.Die Magnetresonanz-Elastographie (MRE) ist eine neue Methode zur quantitativen viskoelastischen Bildgebung von Weichgewebe in vivo. Allerdings sind die Möglichkeiten der MRE, bewegte Organe und kurzzeitige Variationen der Viskoelastizität zu untersuchen, aufgrund langer Messzeiten und geringer zeitlicher Auflösung begrenzt. Daher wurde eine schnelle zeitaufgelöste MRE-Methode auf Grundlage einer herzgetriggerten steady-state MRE-Pulssequenz (ssMRE) mit segmentierter Spiralauslese und Atemnavigation in Kombination mit stroboskopartiger Schwingungskodierung und angepasstem Rekonstruktionsalgorithmus entwickelt. Die Methode wurde zu einer Echtzeit-ssMRE-Variante (rtMRE) erweitert, die selbst nicht-periodische Prozesse in einer einzigen Messung ohne wiederholte Auslese abbilden kann. Die Durchführbarkeit der Methoden wurde in 3 In-vivo-Studien überprüft. Dafür wurden zeitaufgelöste Viskoelastizitätskarten mit einer Bildrate von 6–29 Hz rekonstruiert, die die Steifigkeit (Scherwellengeschwindigkeit in m/s bzw. Magnitude des komplexen Schermoduls in Pa) und die Fluidität (Phase des komplexen Schermoduls in rad) der jeweiligen Gewebe abbilden. In der ersten Studie wurde der Einfluss der zerebral-arteriellen Pulsation (CAP) auf die Viskoelastizität des Gehirns von 12 gesunden Teilnehmern untersucht. In der zweiten Studie wurde bei 20 gesunden Teilnehmern die Viskoelastizität entlang des Aortenbaums, einschließlich der Aorta ascendens thorakal (AA), descendens thorakal (AD) und abdominales (AAb) quantifiziert. In der dritten Studie wurde mit der rtMRE dynamische Muskelaktivierung in den unteren Extremitäten während isometrischer Plantar- und Dorsalflexion bei 15 gesunden Teilnehmern analysiert. Im Hirnparenchym wurde eine globale systolische Abnahme der Steifigkeit um 6,6±1,9% (p<.001) und eine geringe Zunahme der Fluidität um 0,5±0,5% (p=.002) festgestellt. Der Aortenbaum zeigte eine Zunahme der Steifigkeit von der Aortenwurzel bis zur Aortenbifurkation mit 1,6±0,2 m/s in AA, 2,4±0,3 m/s in AD und 2,5±0,6 m/s in AAb. Ferner konnten bei Muskelaktivierung eine erhöhte Steifigkeit und Fluidität beobachtet werden. Den stärksten Anstieg wiesen der Soleus während der Plantarflexion (Steifigkeit: 20,0±3,6%, Fluidität: 41,3±12,0%, p<.001) und der Tibialis anterior während der Dorsalflexion (Steifigkeit: 41,8±10,2%, Fluidität: 27,9±2,8%, p<.001) auf. ssMRE und rtMRE erwiesen sich als erfolgreiche Methoden für die Bildgebung von Viskoelastizität mit hoher räumlicher und zeitlicher Auflösung. Die Ergebnisse zeigen CAP-induzierte transiente Effekte auf die Viskoelastizität des Gehirns, Steifigkeitsunterschiede entlang des Aortenbaums und einen abrupten Anstieg der Steifigkeit und der Fluidität in Folge von Muskelaktivierung. Diese Dissertation leistet einen wichtigen Beitrag auf dem Gebiet der MRE, indem sie erstmalig zeitaufgelöste Viskoelastizitätskarten von Weichgewebe zur Untersuchung physiologischer Prozesse für zukünftige diagnostische Anwendungen bereitstellt

In vivo time-harmonic ultrasound elastography of the human brain detects acute cerebral stiffness changes induced by intracranial pressure variations

Abstract Cerebral stiffness (CS) reflects the biophysical environment in which neurons grow and function. While long-term CS changes can occur in the course of chronic neurological disorders and aging, little is known about acute variations of CS induced by intracranial pressure variations. Current gold standard methods for CS and intracranial pressure such as magnetic resonance elastography and direct pressure recordings are either expensive and slow or invasive. The study objective was to develop a real-time method for in vivo CS measurement and to demonstrate its sensitivity to physiological aging and intracranial pressure variations induced by the Valsalva maneuver in healthy volunteers. We used trans-temporal ultrasound time-harmonic elastography (THE) with external shear-wave stimulation by continuous and superimposed vibrations in the frequency range from 27 to 56 Hz. Multifrequency wave inversion generated maps of shear wave speed (SWS) as a surrogate maker of CS. On average, cerebral SWS was 1.56 ± 0.08 m/s with a tendency to reduce with age (R = −0.76, p < 0.0001) while Valsalva maneuver induced an immediate stiffening of the brain as reflected by a 10.8 ± 2.5% increase (p < 0.0001) in SWS. Our results suggest that CS is tightly linked to intracranial pressure and might be used in the future as non-invasive surrogate marker for intracranial pressure, which otherwise requires invasive measurements

Superviscous properties of the in vivo brain at large scales

There is growing awareness that brain mechanical properties are important for neural development and health. However, published values of brain stiffness differ by orders of magnitude between static measurements and in vivo magnetic resonance elastography (MRE), which covers a dynamic range over several frequency decades. We here show that there is no fundamental disparity between static mechanical tests and in vivo MRE when considering large-scale properties, which encompass the entire brain including fluid filled compartments. Using gradient echo real-time MRE, we investigated the viscoelastic dispersion of the human brain in, so far, unexplored dynamic ranges from intrinsic brain pulsations at 1 Hz to ultralow-frequency vibrations at 5, 6.25, 7.8 and 10 Hz to the normal frequency range of MRE of 40 Hz. Surprisingly, we observed variations in brain stiffness over more than two orders of magnitude, suggesting that the in vivo human brain is superviscous on large scales with very low shear modulus of 42±13 Pa and relatively high viscosity of 6.6±0.3 Pa∙s according to the two-parameter solid model. Our data shed light on the crucial role of fluid compartments including blood vessels and cerebrospinal fluid (CSF) for whole brain properties and provide, for the first time, an explanation for the variability of the mechanical brain responses to manual palpation, local indentation, and high-dynamic tissue stimulation as used in elastography

Real-Time Multifrequency MR Elastography of the Human Brain Reveals Rapid Changes in Viscoelasticity in Response to the Valsalva Maneuver

Modulation of cerebral blood flow and vascular compliance plays an important role in the regulation of intracranial pressure (ICP) and also influences the viscoelastic properties of brain tissue. Therefore, magnetic resonance elastography (MRE), the gold standard for measuring in vivo viscoelasticity of brain tissue, is potentially sensitive to cerebral autoregulation. In this study, we developed a multifrequency MMRE technique that provides serial maps of viscoelasticity at a frame rate of nearly 6 Hz without gating, i.e., in quasi-real time (rt-MMRE). This novel method was used to monitor rapid changes in the viscoelastic properties of the brains of 17 volunteers performing the Valsalva maneuver (VM). rt-MMRE continuously sampled externally induced vibrations comprising three frequencies of 30.03, 30.91, and 31.8 Hz were over 90 s using a steady-state, spiral-readout gradient-echo sequence. Data were processed by multifrequency dual elasto-visco (MDEV) inversion to generate maps of magnitude shear modulus | G*| (stiffness) and loss angle phi at a frame rate of 5.4 Hz. As controls, the volunteers were examined to study the effects of breath-hold following deep inspiration and breath-hold following expiration. We observed that | G*| increased while phi decreased due to VM and, less markedly, due to breath-hold in inspiration. Group mean VM values showed an early overshoot of | G*| 2.4 +/- 1.2 s after the onset of the maneuver with peak values of 6.7 +/- 4.1% above baseline, followed by a continuous increase in stiffness during VM. A second overshoot of | G*| occurred 5.5 +/- 2.0 s after the end of VM with peak values of 7.4 +/- 2.8% above baseline, followed by 25-s sustained recovery until the end of image acquisition. phi was constantly reduced by approximately 2% during the entire VM without noticeable peak values. This is the first report of viscoelasticity changes in brain tissue induced by physiological maneuvers known to alter ICP and detected by clinically applicable rt-MMRE. Our results show that apnea and VM slightly alter brain properties toward a more rigid-solid behavior. Overshooting stiffening reactions seconds after onset and end of VM reveal rapid autoregulatory processes of brain tissue viscoelasticity