Biorheology 47 (2010) 133���141 133 DOI 10.3233/BIR-2010-0565 IOS Press Viscoelastic properties of liver measured by oscillatory rheometry and multifrequency magnetic resonance elastography Dieter Klatt a, Christian Friedrich b, Yasmin Korth b, Robert Vogt b, J��rgen Braun c and Ingolf Sack a,��� a Department of Radiology, Charit��-Universit��tsmedizin, Berlin, Germany b University of Freiburg, FMF, Freiburg, Germany c Institute of Medical Informatics, Charit��-Universit��tsmedizin, Berlin, Germany Received 13 November 2009 Accepted in revised form 3 May 2010 Abstract. The mechanical properties of liver can sensitively indicate the progression of hepatic fibrosis. Mechanical tissue characterization involves the analysis of the complex shear modulus measured either by oscillatory rheometry or by in vivo elastography. In this study, bovine liver specimens were investigated by oscillatory rheometry and multifrequency magnetic resonance elastography (MRE) in a common frequency range between 25.0 and 62.5 Hz. The results were compared with in vivo MRE of human liver. Storage and loss moduli were quantified, and the data were also analyzed employing a springpot model, yielding a stiffness-related parameter of 2.96 �� 0.53 kPa in bovine liver by rheometry and of 2.20 �� 0.45 kPa in human liver by in vivo MRE. Furthermore, MRE of excised bovine liver showed that stiffness tended to increase with decreasing sample temperature. In conclusion, mechanical tissue characterization by multifrequency MRE agrees well with oscillatory rheometry, which validates MRE as a method for investigating the rheology of liver tissue. Keywords: Magnetic resonance elastography, rheometry, liver viscoelasticity, springpot 1. Introduction One of the most traditional diagnostic methods in medicine, manual palpation, is based on the cor- relation between pathological conditions of soft tissue and changes in its mechanical properties. In the past, a mechanical characterization of biological tissue was limited to excised samples. For instance, compression tests were performed to determine the grade of hepatic fibrosis from liver stiffness [19]. Dynamic magnetic resonance elastography (MRE) [8,12] and shear-wave based ultrasound elastogra- phy (USE) [11,18] are noninvasive techniques capable of measuring tissue mechanical properties inside the human body. Both modalities have been used for noninvasive staging of hepatic fibrosis [2,3,13, 20]. In conventional MRE, mechanical vibrations of a single frequency, the so-called drive frequency, are introduced into the target tissue, which is positioned inside the magnetic resonance (MR) imager. *Address for correspondence: Ingolf Sack, PhD, Department of Radiology, Charit��-Universit��tsmedizin Berlin, Charit��platz 1, 10117 Berlin, Germany. E-mail: ingolf.sack@charite.de. 0006-355X/10/$27.50 �� 2010 ��� IOS Press and the authors. All rights reserved

134 D. Klatt et al. / MRE and rheometry of liver Motion-sensitive image acquisition techniques can measure minimal phase variations of the MR signal induced by shear vibrations. The resulting wave images are analyzed by solving the inverse problem of elastography [9,10]. Multifrequency MRE relies on broadband motion encoding, which allows the acquisition of multiple harmonic vibrations in one experiment [1,6]. In this experiment the dispersion of the complex shear modulus, G���(��), with �� being the angular drive frequency, is accessible by a single time-resolved MRE scan. Hence, material parameters can be calculated by fitting the analytical G���(��) function of any rheological model to the data. Recently, it has been shown that the springpot model, also referred to as the ���single fractional element��� in the literature [15], is very well suited for analyzing multifrequency MRE of in vivo liver and brain [5,17]. The springpot represents a linear interpolation of spring and dashpot, yielding two independent material parameters: a stiffness-related parameter �� with the dimension kPa and the dimensionless ��, which is a parameter that characterizes the alignment of mechanical structure-building elements in the tissue. Although in vivo elastography, in particular of the liver, is extensively investigated in patients, there has been no systematic study determining whether the derived material parameters can be reproduced by more established test methods. A material model fitting to elastographic data of liver would improve the significance of in vivo studies and would enable the comparison of data acquired by different modalities at different drive frequencies. Therefore, this study aims to determine the complex shear modulus of liver by rotational rheometry and multifrequency MRE in the common frequency range applicable by MRE on humans. The experi- ments consist of three parts: (i) rotational rheometry of bovine liver at 1���C, (ii) MRE of bovine liver at different temperatures and (iii) in vivo human liver MRE. 2. Materials and methods 2.1. Multifrequency MRE Seventeen volunteers (10 female mean age: 33.6 �� 6.4 years) were repeatedly examined by multifre- quency MRE of the liver. This study was approved by the local ethics committee and written informed consent was obtained from all subjects. Two to three examinations were performed per subject. The vi- bration generator used is described in [4]. Details of the image acquisition sequence and data processing are given in [6]. G���(��) was calculated at four drive frequencies (25.0, 37.5, 50.0 and 62.5 Hz), which were synchronously applied in a superimposed waveform. The same protocol was applied to a bovine liver specimen stuffed into a cubic vessel (11 �� 12 �� 14 cm) and one examination was performed each at 4���C, 12���C and 22���C. In these experiments, a square vibration plate on top of the sample was used for introducing planar waves into the liver. 2.2. Oscillatory shear rheometry Cylindrical samples of fresh bovine liver with 50 mm diameter and a slice thickness of 0.9���2.4 mm were tested by an oscillatory shear device (MCR 301, Anton Paar, Austria). The sample temperature was adjusted to 1���C, which is further discussed below. The linear regime of viscoelasticity was estimated by four amplitude sweeps at frequencies of 5, 20, 40 and 60 Hz using a single tissue specimen. The strain amplitude ��0 was varied between 0.1% and 2.0%. The limit ��max of the linear viscoelastic regime was set to 5% deviation of both real (G ) and imaginary part (G ) of G��� from the plateau value (��0 ��� 0.1) in all four amplitude sweeps. Then, G��� was measured within 2.5 and 62.5 Hz frequency range by increments of 2.5 Hz. ��0 was set below the previously determined linear strain limit given in the results section. The experiments were repeated on six different tissue samples for estimating the variability of the method.