Magnetic Resonance Imaging 34 (2016) 137–143

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Magnetic Resonance Imaging

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Magnetic resonance imaging of mechanical deformations

Gregor Koder, Igor Serša ⁎Jožef Stefan Institute, Jamova 39, Ljubljana 1000, Slovenia

⁎ Corresponding author at: Jožef Stefan Institute, JamoSlovenia. Tel.: +386 1 477 3696; fax: +386 1 477 3191

E-mail address: igor.sersa@ijs.si (I. Serša).

http://dx.doi.org/10.1016/j.mri.2015.10.0220730-725X/© 2015 Elsevier Inc. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 May 2015Revised 21 October 2015Accepted 25 October 2015Available online xxxx

Keywords:DeformationsStrain imagingPosition encodingPulsed gradients

A method for magnetic resonance imaging of mechanical deformations is presented. The method utilizesan MRI compatible device for inducing elastic deformations of a sample and a modified spin-echo imagingsequence with two position-encoding gradients added to the sequence symmetrically to the RF refocusingpulse. At the end of the first position-encoding gradient pulse, a sample deformation was induced by thedeformational device, which applied a force to a plastic rod embedded in a gelatin cylindrical sample. Thesample had to withstand repeated elastic deformations. Sample displacements up to 400 μmwere encodedin the image signal phase by the use of position-encoding gradients. Images of different displacementcomponents were acquired first by the use of position-encoding gradients in different directions and thenprocessed by the 2D phase unwrap algorithm. Finally, images of normal and shear strain distribution werecalculated from the displacement images. The obtained displacement and strain images enabled clearvisualization of deformations and their extent in the sample with the displacement detection threshold inthe range 0.3–0.6 μm, depending on the image echo time. The results of displacements were verified alsoby a DANTE tagging method and by an optical method. The presented method enables studying of varioustypes of deformations in different soft materials as well as dynamic response of deformations to differentstress functions (static, oscillatory, pulsed…).

va 39, Ljubljana 1000,.

© 2015 Elsevier Inc. All rights reserved.

1. Introduction

Magnetic resonance imaging is a powerful tool for studyingvarious phenomena also due to its ability of providing not only signalmagnitude of each image element but also signal phase. Inconventional MRI signal phase is often irrelevant, however, thereare several methods where the phase plays a crucial role. Theseinclude phase contrast angiography (PCA) [1,2], MR thermometry[3,4], MR elastography [5], current density imaging (CDI) [6,7]… Inall these methods phase carries information on the measuredquantity; in PCA phase is proportional to fluid velocity, in MRthermometry phase is proportional to temperature, in MR elasto-graphy phase is proportional to an amplitude of the propagatedsound wave, in CDI phase is proportional to a magnetic field changeinduced by electric currents… The present work is focused to MRimaging of mechanical deformation, which is also another method ofphase detection based MRI.

In different materials deformations are measured differently. Forexample in solids deformations can be measured optically by Moiréinterferometry [8], in photoelastic materials deformations can beaccessed by the change of the birefringence [9]. Deformations insolids can be imaged also in nanoscale resolution by infrared

near-field microscopy if the materials are infrared-active [10]. It isalso possible to image large-scale deformations; for exampledeformations of the Earth’s surface, can be imaged by the SyntheticAperture Radar (SAR), a satellite-transmitted and received radarsystem [11]. In medical imaging deformations of biological tissuesare often imaged by ultrasound. An important application of that ismyocardial deformation imaging [12] which is a novel echocardio-graphic method for assessment of global and regional myocardialfunction. By MRI, deformations of biological tissues can be assessedby the tagging method, which is a popular method in cardiac MRI forassessing ventricular function. The method was first introduced as aSPAtial Modulation of Magnetization (SPAMM) method [13] andthen improved with inclusion of Delay Alternating with Nutationsfor Tailored Excitation (DANTE) RF pulses that together with anappropriate combination of magnetic field gradients result in a gridpattern of excited spins [14]. Later improvements in the field includeComplementary SPAMM (CSPAMM) [15], HARmonic Phase (HARP)[16] and Strain ENCoding (SENC) [17] methods. By the taggingmethods the heart motion can be assessed from the grid deformationformed in time between the excitation and image acquisition. MRIenables displacement field measurement also by texture correlation,a technique which relies on unique image patterns within a pair ofdigital images to track displacement [18]. Another way of resolvingmyocardial kinematics is by using a phase contrast approach. Theapproach is used in the Strain Phase MRI (SP-MRI) method [19] inwhich sample displacements are encoded by a readout gradient of a

B0 RF coil

HolderCoil

Moving rod

Sample

y

x

z

b

a

ad

b

l

Fig. 1. A scheme of the deformational device (a) and a setup for displacemenmeasurements by a laser beam reflection (b). The device was placed in magnetic fieldof the NMR magnet. A current pulse applied to the coil therefore resulted in a torqueto the coil that was converted via the lever arm to a force on the moving rod(embedded in the gelatin sample) that deformed the sample.

138 G. Koder, I. Serša / Magnetic Resonance Imaging 34 (2016) 137–143

conventional spin-echo sequence. Larger encoding times are enabledby the Displacement ENcoding with Stimulated Echoes (DENSE)method [20,21], which is used primarily in cardiac functional MRI. InMR elastography [5] acoustic sound is emitted to a samplesynchronously with oscillating gradients that have the samefrequency as the sound which results in a phase shift proportionalto the sound amplitude in the sample. As the sample is dynamicallydeformed during sound propagation in it, MR elastography can alsobe considered as a way deformation imaging.

Motivation for this study was strain imaging of elastic materialswith a precise displacement detection. Sensitivity of one micrometerat a spatial resolution of the order of 100 μm is desired. As most ofthe abovementioned methods are optimized for cardiac imagingwhere displacements are two orders of magnitude larger, animproved detection method is needed. For that we propose aspin-echo imaging sequence to which two short and strongposition-encoding gradient pulses are added, i.e., a pulsed gradientspin-echo (PGSE) sequence. The first gradient pulse encodessample’s initial position, while the second gradient pulse encodessample’s final position. In between the gradient pulses the sample isdeformed by applying an external force to it in a pulse of variableduration. This approach enables imaging of deformation progressionas a function of the applied force pulse duration as well asobservation of transition phenomena, such as sample oscillationsor shock wave propagation that follow the pulse. First, theoreticalbackground of the method along with a pulse sequence fordeformation imaging is presented. This is then followed by ademonstration of the method on a gelatin cylindrical sample thatwas repeatedly deformed by force pulses generated by a special MRIcompatible deformational device. Finally, the measured data wereanalyzed to obtain sample displacement and strain maps. For thestudy a special MRI compatible deformational device was designedthat enables full control over the applied force and its duration. Theresults of displacements were also verified by a DANTE taggingmethod and by an optical method based on laser beam reflection.

2. Materials and methods

Imaging of mechanical deformations was tested on a gelatinsample that was deformed by an MRI compatible device shown inFig. 1. The device consisted of a flat round coil with N = 60 turns ofcopper wire and with a diameter of 2r = 34 mm. The coil wasattached to a 94 mm long shaft to the center of which was glued anl = 23 mm long lever arm. The arm was joint with a 90 mm longmoving rod embedded in the gelatin sample. During samplepreparation, the rod was immersed to the depth of 14 mm in a25 mm thick gelatin layer during its hardening in a container(glass beaker) with inner diameter of 24 mm. Gelatin (“Želatina”,Dr. Oetker Kft, Janossomorja, Hungary) was prepared according tothe manufacturer’s instructions; 5 g of gelatin powder was admixedto 50 ml of water and then cooked. NMR relaxation times of thesample were shortened to T1 = 266 ms and T2 = 155 ms by addingthe mixture 0.1 g of copper sulfate. The contact between the rod andgelatin was improved by sanding the embedded part of the rod.When gelatin was hardened the sample was inserted in a 27 mmmicro-imaging probe (Bruker, Ettlingen, Germany). The rod wasthen connected with the lever arm of the deformational device andthe device was attached to the probe holder and inserted into a100 MHz (B0 = 2.35 T) horizontal bore superconducting magnet(Oxford Instruments, Abingdon, UK).

Deformations of the sample were induced by applying current ofI0 = 14 mA to the coil. As the coil was in magnetic field of the MRImagnet and the coil axiswas normal to themagnetic field direction, thecurrent induced a torque to the coil equal to τ = Nπr2I0B0 =0.0018 Nm. The torque initially resulted in an acceleration of the

t

moving rod equal to a0 = τl/I = 23 m/s2 (calculated from geometricalparameters of the deformational device); here I = 1.74 · 10−6 kg/m2

is a net moment of inertia of all moving parts of the deformationaldevice. Finally, when the rod came to a rest, the torque resulted in aforce F = τ/l = 0.08 N of the moving rod to the gelatin sample thatdeformed the sample. Current I0was generatedby an amplifier thatwascontrolled by TTL pulses (line I of pulse sequences in Fig. 2) of aspectrometer (Tecmag Apollo, Houston, TX, USA). As the coil had lowresistance and inductance (R = 2.6 Ω, L = 150 μH) change from zerocurrent to constant current I0 was reached only after a fewmicroseconds. During the experiment temperature of the gelatinsample was monitored by a copper-constantan thermocouple ther-mometer inside the micro-imaging probe.

A PGSE sequence, shown in Fig. 2a, was used to image sampledeformations. To a spin-echo sequence two position-encoding shortand strong gradient pulses positioned symmetrically to the refocus-ing RF pulse were added. The pulses had a duration δ = 2 ms,amplitude G = 200 mT/m and were apart for different deformationtimes Δ = 6, 10, 20, and 30 ms. The function of the pulses was toencode in a signal phase the initial r

*1 and the final r

*2 position of a

sample volume element. The two gradient pulses had an oppositeeffect to the signal phase shift due to the RF refocusing pulse inbetween them so that a phase shift of the signal from the elementwas equal to

Δφ ¼ γδ G* � r*2−γδ G

* � r*1 ¼ γδ G* � u* : ð1Þ

Here u*¼ r

*2− r

*1 is the element’s displacement that is formed in

the time interval Δ by the activation of the deformational device atthe end of the first position-encoding gradient pulse (line I in

a

b

/2[x] AQ[x]

Gp

Gr

RF

[y]

I

echo

TE

Gs

AQ[x]

Gp

Gr

RF

I

echo

Gs

TE

[y]

TI

5* /5 5* /5

5

5

tagging

/2[x]

Fig. 2. Sample deformations were imaged by a modified spin-echo sequence to whichtwo strong and short position-encoding gradient pulses were added (a) and by aDANTE tagging sequence (b). Line I in the sequences corresponds to the TLL pulseused to activate the deformational device.

139G. Koder, I. Serša / Magnetic Resonance Imaging 34 (2016) 137–143

Fig. 2a). To minimize a possible effect of the readout gradient on thephase shift, the readout dephasing gradient was applied immedi-ately before the acquisition gradient. In one experiment, only thedisplacement component along the gradient pulse direction can bemeasured. Therefore, to measure the remaining spatial componentsof the displacement the gradient direction was rotated to theremaining perpendicular spatial directions (dashed gradient pulseoutlines in Fig. 2a). Sample deformations were studied in sagittal(yz) and transversal (xy) planes by imaging displacements along themoving rod direction (in the sagittal and transversal plane) andperpendicular to it (only in the sagittal plane). Other imagingparameters were: imaging field of view 35 mm, imaging matrix 256by 256, echo time Δ + 8 ms, repetition time 600 ms, slice thickness4 mm; no signal averaging was used.

Sample deformations imaged by the PGSE sequence were verifiedalso by a DANTE tagging sequence (Fig. 2b). The sequence had in theinitial part two blocks of five 32° short RF pulses separated by 200 μsthat were applied at a constant gradient of 84 mT/m in the read (firstblock) and phase (second block) direction. The pulses resulted in a

grid of inverted magnetization with a grid constant of ten pixels(1.37 mm) and with lines of invertedmagnetization two pixels wide(274 μm). The invertedmagnetization relaxed to zero after inversiontime of TI = T1ln(2) = 184 ms. At that time image signal acquisi-tion was started using a standard spin-echo imaging sequence thuseliminating the signal from the grid lines. Parameters for imageacquisition were identical to those used with the PGSE sequence(field of view 35 mm, imaging matrix 256 by 256, slice thickness4 mm, echo time 8 ms, repetition time 600 ms). In the sequence, thedeformational device was activated Δ = 30 ms before beginning ofthe spin-echo image acquisition part.

Results of moving rod displacements for deformation timeΔ = 30 ms, that were obtained by phase sensitive and taggingmethods, were verified also by an optical method. The method isbased on a laser beam that is reflected from the lever arm and isthen projected on the wall (Fig. 1b). During the deformation time,the lever arm was tilted by angle α, which then resulted in adeflection of the reflected laser beam by angle 2α and also in a shiftof its projection on the wall for a distance a. From the measureddistance a and known arm-to-wall distance b = 1130 mm, as wellas from the arm length l = 23 mm, the moving rod displacement dwas calculated as d = al/2b.

The images acquired by the PGSE sequence were processed inMatlab (MathWorks Inc., Natick, MA, USA) by Goldstein’s 2D phaseunwrap algorithm, which was used to extract maps of continuousimage phase shift from the initial complex signal images [22]. Thephase shift maps were also corrected for background phasedeviations by subtraction of an appropriate linearly increasingphase. The subtraction resulted in a zero phase shift (no displace-ments) in the sample region next to the container. According toEq. (1), displacements along the direction of the applied gradient uGare proportional to the phase shift Δφ and the proportional constantbetween the two was equal to 1/(γδG) = 9.4 μm/rad. This relationwas then used to calculate (rescale) displacement images from thephase shift maps.

The displacement images were also used to calculate images ofsome components of the strain tensor. The tensor has six differentelements. Three of them are normal strain components thatcorrespond to the relative extension or compression of an infinites-imal cubic volume element in the direction normal to the cube’s face

εxx ¼∂ux

∂x; εyy ¼

∂uy

∂y; εzz ¼

∂uz

∂z; ð2Þ

while the other three components are shear strain components thatcorrespond to the change in angle between two initially perpendic-ular faces of the element

εxy ¼ εyx ¼∂ux

∂yþ ∂uy

∂x2

; εxz ¼ εzx ¼∂ux

∂zþ ∂uz

∂x2

; εyz ¼ εzy

¼∂uy

∂zþ ∂uz

∂y2

: ð3Þ

In the study, only εzz, εyz and εyy components of the tensor in thesagittal plane across the sample were calculated.

3. Results

Sample displacements obtained by the PGSE sequence fordifferent deformation times Δ are shown in Fig. 3. The displace-ments, which were caused by activation of the deformational device,are shown in sagittal and transversal planes across the center of thesample with components along the moving rod (uz) and

6 ms

10 ms

300

400

500

200

100

-100

-200

0

[µm]

20 ms

30 ms

uz uy uz

z

y

x

y

z

y

Sagittal Transversal

Fig. 3.Maps of sample displacements in the direction along the moving rod (uz) and perpendicularly to it (uy) in sagittal and transversal planes across the center of the sample fordifferent deformation times Δ = 6, 10, 20, and 30 ms. A color-coded scale represents the displacements in the range −200 to 500 μm.

140 G. Koder, I. Serša / Magnetic Resonance Imaging 34 (2016) 137–143

perpendicularly to it (uy). Comparison of images in different rowsenables following of the deformation progression with time. Fromimages in the first row (Δ = 6 ms) it can be seen that deformationsstart to develop next to the rod where sample displacements wereapproximately 100 μm in the direction along the rod’s action. Withan increasing deformation time the sample deformation developedfurther. With Δ = 10 ms, sample displacements next to the rodalready reached 300 μm and a region of negative displacements(against the rod’s action) of up to 100 μm was formed between therod and the container. Sample displacements were the highest withΔ = 20 ms when they reached 400 μm in the region next to the rod.Interestingly, with Δ = 30 ms deformations decreased and thelargest displacements were only 200 μm, which indicates for anoscillation of the sample.

Complex pattern of displacements can be well seen also in vectorplots in Fig. 4. These are shown for displacements in the sagittalplane for different deformation times Δ. The plots are interestingbecause they do not show only the magnitude of displacements butalso their direction. From the plots it can clearly be seen howdisplacements change their direction from along the rod direction, tothe perpendicular direction at the rod tip and finally to the oppositedirection of the rod’s action in the region between the rod and thecontainer (above and below the rod).

In Fig. 5 images of strain tensor components εzz, εyz and εyy areshown in the sagittal plane across the sample for differentdeformation times Δ. From the images it can be seen that normalstrain was the highest in the area at the rod tip and at the opensample surface. Quite different is the shear strain distribution.

ms 0 ms

0 ms 0 ms

10 mm

Fig. 4. Vector fields of sample displacements in the sagittal plane for differendeformation times Δ = 6, 10, 20, and 30 ms. Solid contour corresponds to the outlineof the sample. The largest displacements have a magnitude of approximately 400 μm

141G. Koder, I. Serša / Magnetic Resonance Imaging 34 (2016) 137–143

t

.

Regions of shear strain extended over a larger part of the sample inthe region above and below the rod. Therefore, it may be concludedthat the dominant type of the sample deformation was shear strain.The magnitude of strain in some parts of the sample reached almost0.1 (10%). Changes of strain magnitude and strain distribution withdifferent deformation times Δ are consistent with previous obser-vations of displacement as a function of deformation time Δ, i.e.,strain was the highest with Δ = 20 ms, and it was considerablyreduced with Δ = 6 ms and Δ = 30 ms.

The gelatin sample was tested for its stability over time byreproducibility of results. The test was performed by running thesame PGSE sequence (Δ = 6 ms, sagittal orientation, uz detection)twice; once at the beginning of experiments and after one hour, whenthe deformational devicewas already activated 3600 times in 14 scans.Results of the test scans are shown in Fig. 6with real signal componentimages of the sample at the beginning (a) and at the end (b) of theexperiments. The two images are practically identical with only minordifferences between them, which proves sample stability over time.The thermocouple temperature sensor inside themicro-imagingprobedid not show any significant temperature rise of the sample during theexperiments. Sample temperature was well constant at 22 °C.

Results of the DANTE tagging sequence with Δ = 30 ms that wasperformed on the same gelatin sample are shown in Fig. 7 withMRI-tagged images of deformed (a) and straight (b) sample, asubtraction image (c) (difference between MRI-tagged images ofdeformed and straight sample) and a zoomed section of thesubtraction image (d). From the zoomed image (d) it can be seenthat displacements along the rodwere approximately equal to the sizeof two pixels, which corresponds to a displacement of 270 μm. Thisresult is in an agreement with results of the phase sensitivedisplacement detection method in Fig. 3 (Δ = 30 ms, sagittalorientation, uz detection). Corresponding images of both methodshave also identical spatial distribution of displacements. The opticalmethod that was used to measure a displacement of the moving rodgave with deformation time Δ = 30 ms a laser beam projection shifta = 37 mm,which corresponds to the rod displacement d = 380 μm.

4. Discussion

The PGSE imaging sequence used in the study (Fig. 2a) is usuallyused to study diffusion [23,24]. Contrary to the standard PGSE

sequence, where δ can in principle extent to almost a half of the echotime (TE) interval, it was essential here that δ was short in order toencode in the signal phase sample’s current position and not its timeintegral which would happen with longer δ. However, the use ofshorter δ necessitates the use of a higher gradient amplitude G of theposition-encoding gradient or sensitivity of the phase sensitivemethod is reduced. The sensitivity is determined by phase noise σφ,which is inversely proportional to the signal-to-noise ratio of themagnitude image ( σφ ¼ 1=ð

ffiffiffi2

pSNRÞ ) [7]. In experiments by the

phase sensitive method SNR was equal to 23.3, 18.3, 13, and 11.8yielding σφ=0.030, 0.039, 0.054, and 0.06 rad forΔ = 6, 10, 20, and30 ms, respectively. Therefore, as follows from the relation for thedisplacement induced phase shift (Eq. (1)), the correspondingdisplacement detection thresholds were equal to 0.29, 0.36, 0.51and 0.56 μm. This is two orders of magnitude better than with thetagging method of which detection limit is determined by imageresolution and settings of the tagging grid. Comparison of MRI-tagged images of deformed (Fig. 7a) and straight sample (Fig. 7b)shows that it is very difficult to detect displacements as small as apixel size by the tagging method. The difference between the imagesbecomes more apparent after their subtraction (Fig. 7c). Therefore,for displacements smaller than the pixel size, the tagging methodcan provide only very basic, mostly qualitative information, if at all.In addition, only displacements in the direction of the imaging planecan be detected with the tagging method, while with the phasesensitive method displacements can be detected also in the directionperpendicular to the imaging slice.

The phase sensitive displacement detection method was verifiedby measuring displacements of the moving rod with Δ = 30 ms alsoby the tagging method and by the optical method. The threemethods gave comparable results of 200 μm (phase sensitive),270 μm (tagging) and 380 μm (optical) considering their precisions.In case of the tagging method the precision cannot be better that thepixel size (137 μm), while with the optical method the measureddisplacement is somewhat larger on account of imperfections in thedeformational device (loose axis, insufficient rigidity…).

Test of the sample stability over time by reproducibility of results inFig. 6 confirmed that the sample deformations were all elastic and thatthe sample properties did not change between the scans. The stabilitycan be explained by small sample deformations and constant temper-ature of the sample. It is very likely that the samplewould degrademuchfaster with larger deformations and in case of a temperature raise farfrom the room temperature range. Another important property of thesample is that it gives high enough signal at echo times determined bythe deformation time. In the study the longest deformation time was30 ms and the corresponding echo time was 38 ms. The effect of signallosswith the increasing echo time andwith it associated deterioration ofdisplacement (phase) images is most apparent in the strain images inFig. 5 which were obtained as derivatives of the displacement images(Eqs. (2) and (3)). Thus, the strain images with Δ = 30 ms have muchhigher noise than the strain images with Δ = 6 ms.

Gelatin was found a very appropriate material for the sample as itis easy to deform and has a long NMR signal. However, it is relativelysoft and relaxes back to the initial shape relatively slowly. Therefore,one may want to use for the sample a material with another elasticproperties, for example silicone gel, rubber or similar material.Unfortunately, some of these materials have also much shorter T2relaxation times that would prevent the use of the PGSE sequence forimaging of deformations. Namely, the sequence requires, due to itsspin-echo origin, use of materials with relatively long T2 relaxationtime. For the materials with shorter T2 relaxation times, a betterapproach would be use of a stimulated-echo version of the sequencethat would have instead of one 180° RF pulse, in the middle of thedeformation interval, two 90° RF pulses. One at the beginning andthe other at the end of the deformation interval. Similar approach is

6 ms

10 ms

20 ms

30 ms

zz yz yy

z

y

0.1

-0.05

-0.1

0

0.05

Fig. 5. Maps of normal (εzz, εyy) and shear (εyz) strain components of the deformed sample for different deformation times Δ = 6, 10, 20, and 30 ms. A color-coded scalerepresents strains in the range −0.1 to 0.1.

142 G. Koder, I. Serša / Magnetic Resonance Imaging 34 (2016) 137–143

used in studies of diffusion by pulsed field gradients (PFG) inmaterials with short T2 [25].

The deformational device presented in the study is just one simpleexample that was designed to demonstrate a simple way of inducingelastic sample deformations synchronously with an imaging se-quence. There are several other options for a deformational devicedesign thatmay differ in away of deforming a sample or in the devicetriggering with respect to the imaging sequence. For example, evenwith the same sample and deformational device, it would be possibleto observe sample deformation relaxation rather than progression ofdeformation with time. For that, in the imaging sequence thedeformational TTL pulse would need to end at the end of the firstposition-encoding gradient (Fig. 2a). Another interesting phenome-non that could be studied by the same setup is propagation of a shockwave. In that case, the deformational TTL pulse would need to bestrong and short and should be positioned immediately after the firstposition-encoding gradient. Propagation of the shock wave couldthenbe studied simply by deformation imagingwith increasing timesΔ. Most likely, wave propagation was detected also in the presented

experiments. This effect could explain oscillating behavior ofdisplacements with different times Δ (higher displacements withΔ = 10, and 20 ms and lower displacements with Δ = 6, and30 ms). The oscillations are a result of a sudden force on the movingrod. In a simple model for the oscillations, acceleration of the rod is aresult of the opposing forces of the coil (position independent) and ofgel (position depended) a(x) = a0(1 − x/x1); here a0 is the initialacceleration of the rod immediately after the activation of thedeformational device and x1 is an equilibrium displacement of therod. Result of the equation is an oscillatory motion of the rod x ¼ x1ð1− cosð ffiffiffiffiffiffiffiffiffiffiffiffi

a0=x1p

tÞÞ with a period of 2πffiffiffiffiffiffiffiffiffiffiffiffix1=a0

p= 26 ms assuming

a0 = 23 m/s2 and x1 = 400 μm. This result is just approximate as themodel does not include oscillation damping and the initial acceler-ation does not take into account gel inertia.

5. Conclusion

In this study, a method for magnetic resonance imaging ofmechanical deformations is presented. The method utilizes a

Fig. 6. A test of the sample’s stability over time by reproducibility of results. Both reasignal component images of the sample were acquired by the same phase sensitivedisplacement detectionmethod (Δ = 6 ms, sagittal orientation, uz detection). Image (awas acquired at the beginning while image (b) was acquired at the end of experimentwhen the deformational device was already activated 3600 times in 14 scans.

a b

c d

Fig. 7. MRI-tagged images of deformed (a) and straight (b) sample, a subtraction image(c) (difference between MRI-tagged images of deformed and straight sample) and azoomed section of the subtraction image (d) (encircled in yellow in the subtractionimage). The images were acquired using the DANTE tagging sequence with Δ = 30 ms

143G. Koder, I. Serša / Magnetic Resonance Imaging 34 (2016) 137–143

l

)s

modified spin-echo pulse sequence with two position-encodinggradients added to the sequence and a specially designed device forinducing elastic deformations of a sample synchronously with theimaging sequence. The method was tested on a gelatin sample thatwas easy to deform. Differences in voxel positions between thedeformed and straight sample are proportional to the phase shift of

.

the image signal thus allowing calculation of a sample displacementmap and ultimately also calculation of normal and shear straindistribution in the sample. The method can easily be adopted for thestudy of various types of deformations in different soft materials bythe use of another deformational device or its triggering. It alsoenables studying of material dynamic response to differentstress functions.

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