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Published in final edited form as: Ultrasound Med Biol. 2019 Jul 15;45(10):2777–2786. doi: 10.1016/j.ultrasmedbio.2019.06.412

Resolution of Murine Toxic Hepatic Injury Quantified with Ultrasound Entropy Metrics

Jon N Marsh a, Kevin M Korenblat b, Ta-Chiang Liu c, John E McCarthy d, Samuel A Wickline e
PMCID: PMC6718339  NIHMSID: NIHMS1532767  PMID: 31320149

Abstract

Image-based classification of liver disease generally lacks specificity for distinguishing between acute, resolvable injury and chronic irreversible injury. We propose that ultrasound radiofrequency data acquired in vivo from livers subjected to toxic drug injury can be analyzed with information theoretic detectors (ITD) to derive entropy metrics, which classify a statistical distribution of pathological scatterers that dissipate over time as livers heal. Here we exposed 38 C57BL/6 mice to carbon tetrachloride to cause liver damage, and imaged livers in vivo after exposure at 1, 4, 8, 12, and 18 days with a broadband 15 MHz probe. Selected entropy metrics manifested monotonic recovery to normal values over time as livers healed, and were correlated directly with progressive restoration of liver architecture by histological assessment (r2 >= 0.95; p<0.004). Thus, recovery of normal liver microarchitecture after toxic exposure can be delineated sensitively with entropy metrics.

Keywords: Liver toxicity, liver recovery, ultrasound, entropy, tissue characterization, carbon tetrachloride, quantitative ultrasound

INTRODUCTION

Liver injury is a known complication of numerous medications that can initiate either an injury that spontaneously resolves or, alternatively, proceed to either acute liver failure (ALF) or chronic liver disease including cirrhosis (Fisher et al. 2015). Indeed, drug induced liver injury (DILI) is the leading cause of ALF in the United States accounting for more cases of ALF than all other etiologies combined including viral hepatitis (Habib and Shaikh 2017; Lee 2013). Though many cases of DILI recover after cessation of the offending agent, those that result in a more severe and non-resolving injury may require rescue with organ transplantation. The use of imaging (MRI, ultrasound, CT) is common in the evaluation of liver disease but is generally inadequate for ascertaining the nature and severity of the injury and for distinguishing acute from chronic injury (Romero et al. 2014).

Robust and objective methods for characterizing hepatic tissue in the setting of liver injury are limited. Liver biopsy is the most direct method although it is subject to sampling error, is invasive, and is not uniformly available. The recent development of various forms of elastography implemented in both MR and ultrasound platforms are restricted to the assessment of advanced degrees of fibrosis (Friedrich-Rust et al. 2016). A technology that merges noninvasive imaging with quantitative tissue characterization would provide a novel approach for the evaluation and management of diseases of the liver and other vital organs.

Here we propose to investigate the application of information theoretic detectors (ITD’s) to ultrasound data for delineation of liver damage after DILI, and to determine if recovery can be tracked over time following removal of an offending toxin. ITD’s are a class of mathematical operators that utilize unprocessed radiofrequency (RF) data as input to generate a set of entropy metrics that reveal pathological alterations in acoustic backscatter from damaged tissues. We have used this approach previously to sensitively detect cancer angiogenesis, delineate responses to therapeutic agents in cancer and muscular dystrophy(Hughes et al. 2006; Hughes et al. 2007b; Hughes et al. 2009b; Hughes et al. 2009a; Hughes et al. 2011; Hughes et al. 2013; Hughes et al. 2015), and now seek to apply it to acute hepatic damage in rabbits caused by the classic hepatotoxin, carbon tetrachloride (CCl4). In particular, we are interested in determining how well selected entropy metrics derived from ultrasound image data might map the temporal evolution of hepatic injury after drug exposure, which could be applicable to quantification of liver damage for any form of acute liver injury.

MATERIALS AND METHODS

Entropy measures

In general, entropy describes the statistical distribution of amplitude in the backscattered ultrasound RF wave train; traditional ultrasound analysis instead uses the absolute magnitude of backscatter, or other related measures such as integrated backscatter (Hughes 1994). Entropy is most commonly computed via the histogram of input data values for discretely sampled waveforms, or an estimation of the density function in the case of continuous inputs. As such, the entropy associated with some finite region of interest might differ for two dissimilar types of tissue that may have equivalent average backscatter magnitudes or envelopes. Thus, entropy metrics may represent additional useful descriptors of the local structure created by scatterers within a volume of tissue.

Entropy is used to detect changes in the homogeneity of the tissue. This is a complex high dimensional pattern, and an entropy descriptor must reduce it to a single number. While there is strong experimental support that the entropy descriptors provide more robust descriptors of pathology or flaws in noisy environments than do conventional energy-based measures (Hughes et al. 2006; Hughes et al. 2007b; Hughes et al. 2009b), it is still unknown which particular descriptor might be optimal for any particular purpose. Moreover, we propose that the use of a set of different entropy descriptors to process ultrasound waveforms might offer a more objective and robust demonstration of the capability of entropy metrics than would a single selected entropy. The algorithms were applied to 32-point segments of each waveform extracted in sliding-boxcar fashion, either through each segment’s histogram or from the continuous approximation to its time-domain representation via a smoothing spline (Figure 1). Here we briefly review the definitions of each metric and how they were computed.

Figure 1:

Figure 1:

Discretely digitized waveform segments (three examples are shown in the center column) were used to derive either a histogram for computation of Shannon entropy (left column), or a continuous time-domain approximation using a smoothing spline for computation of continuous, Rényi, and joint entropies via computation of the density function (right column).

Shannon Entropy

The Shannon entropy, HS, is determined from the histogram of values {pi}i=1,…,N in the digitized waveform (where N is the number of discrete digitizer levels) and defined as (Hughes et al. 2005b; Hughes et al. 2006)

HS=i=1Npilog[pi],where0ln[0]:=0. Eq. 1

In the results presented below, 256-bin histograms were used with maximum/minimum values corresponding to the maximum amplitude setting of the digitizer.

Continuous Entropy

The finite part of the Shannon entropy in the limit of infinitely small sampling intervals and digitization levels (Hughes 1994; Hughes et al. 2007b) is given by

HC=w(y)log[w(y)]dy, Eq. 2

where w(y) is the probability density function (PDF) of the waveform y = f (t) (note that we have changed the sign convention of this value relative to the references listed above, in order to maintain consistency with the definition of the Shannon entropy). Because the PDF of a continuous, smoothly varying oscillating waveform can have multiple singularities and is therefore nontrivial to compute, we make use of an alternative formulation derived from the time-domain function through the relation

HC=log[f(t)]dt, Eq.3

where f(t) denotes the increasing rearrangement of f(t).(Hughes et al. 2007b) In the case of discretely sampled waveforms, this may be approximated quickly by sorting the input waveform (Hughes et al. 2007b). It should be noted, however, that the increasing rearrangement of a sufficiently long, discretely digitized, oscillating signal will likely have regions of zero slope, leading to singularities in this approximation. For the present results, waveform segments were resampled using cubic spline interpolation at points between the original sampling times to effectively remove artifacts associated with digitization before applying the approximation. This procedure yields results consistent with the PDF approach of equation Eq. 2 while permitting efficient computation (Hughes et al. 2011).

Singular Rényi Entropy

The Rényi entropy is a generalization of the Shannon entropy and is defined as

If(r)=11rlog[wf(y)rdy], Eq. 4

where r is an adjustable parameter. In the limit as r → 1, we get If(r) → HC. Prior work has demonstrated that this quantity exhibits sensitivity to small changes in scattering parameters that is enhanced in the limit r → 2 (Hughes et al. 2009b). It is important to note that the density function wf(y) of a continuous, smoothly varying oscillating waveform, f(t), yields an expression for If(r) that is undefined when r ≥ 2 because of the singularities in wf(y). However, it has been shown that the asymptotic form of If(r) as r → 2 from below can be given by

If,=log[{tk|f(tk)=0}1|f(tk)|], Eq. 5

where the tk are the zeroes of the derivative of f(t) (again note the change of sign convention) (Hughes et al. 2009a). In the present study, an optimal smoothing spline (Reinsch 1967) was used to compute the required first and second derivatives of the input waveform segment and reduce the impact of noise on the computation of derivatives needed for computation of If, (Hughes et al. 2011).

Joint Entropy

The joint entropy of two functions f(t) and g(t) having associated joint density w(x,y) is given by

H(f,g)=w(x,y)log[w(x,y)]dxdy. Eq. 6

As with the continuous and singular Rényi entropies, the density function w(x,y) for the types of “well-behaved” time-domain input functions considered here renders this equation not well-defined, because the support of w(x,y) is one-dimensional. It has been shown, however, that the following relationship holds true (note change in sign convention) (Hughes et al. 2013):

Hf,g12dtmin[|f(t)|,|g(t)|]max[|f(t)|,|g(t)|]+dtlog[|max[|f(t)|,|g(t)|]|]. Eq. 7

In this case we again made use of an optimal smoothing spline fit to each waveform segment to obtain the required first derivatives of the functions f(t) and g(t). As described above, RF waveform segments are assigned to f(t). The choice for the reference waveform g(t) is an additional degree of freedom, which in this case was derived from the reflection of the imaging system’s interrogating pulse from a planar reflector (Hughes et al. 2015).

Treatment

All animal experiments used in this study were conducted in an ethical and humane fashion governed by protocols approved by the Institutional Animal Care and Use Committee of Washington University. Normal mice (C57BL/6J, The Jackson Laboratory, Bar Harbor, ME, USA) at 12 weeks of age were administered intraperitoneal injections of CCl4 twice weekly for 4 weeks. CCl4 (Sigma-Aldrich, St. Louis, MO, USA) was prepared in a vehicle of sunflower oil and administered at a dose of 0.4 μL/g body weight. The mice were divided into groups according to the interval of time between the final injection and data acquisition/sacrifice: 1 day (n=9), 4 days (n=8), 8 days (n=9), 12 days (n=6), or 18 days (n=6). Sample numbers were larger for the 1-, 4- and 8-day recovery groups because of inclusion of additional mice from a smaller, identically-prepared pilot study (not previously published) conducted to determine project feasibility. A separate group of control mice (n=5) was left untreated. After ultrasound data acquisition (described below), each mouse was euthanized by cervical dislocation, and thoracotomy/laparotomy was performed. While the heart was still beating, physiologic saline solution was infused continuously into the left ventricle until the liver turned pale and stopped changing color. The liver was then excised, immersed in optimal cutting temperature compound (Tissue-Plus, Fisher Scientific, Waltham, MA, USA), and frozen for histological processing and biochemical collagen assay.

Data Acquisition

At selected intervals during recovery after liver injury, mice were lightly anesthetized with 1.5% isoflurane prior to depilation of the abdomen. Each mouse was placed semi-supine on a heated platform and maintained on isoflurane anesthetic. Pre-warmed ultrasound gel was liberally applied to the skin above the liver. A handheld 15-MHz linear array (Spark Imaging System, Ardent Sound, Inc., Mesa, AZ, USA) was used to acquire transcutaneous images of the liver. Prior to the start of the study, optimal system settings for transmit power (−3 dB), receive gain (0.0 dB), and focal zones (single focal zone at position #4, with 30-mm field of view) were selected to provide the best view of the right medial lobe of the liver, while ensuring RF signal output levels were within the dynamic range of the digitizer. These settings remained constant for all time points and all mice in order to maintain consistency between measurements

The imaging system was modified to output beamformed raw radiofrequency (RF) data and associated line and frame trigger signals. The RF output for each A-line was digitized to 12 bits at a sampling rate of 66.67 MHz with an externally clocked PCI-based digitizer card (GaGe Compuscope 12400, DynamicSignals LLC, Lockport, IL, USA) using custom software written in LabVIEW (National Instruments Corporation, Austin, TX, USA). A 3-second cine loop (200 frames, with 256 lines per frame and 2048 points per A-line) was acquired in this manner as the probe was manually positioned over the abdomen proximal to the right medial lobe of the liver, and the resulting data stored for offline processing.

Data Processing

Data were processed using custom plugins written in Java for the open-source image-editing package ImageJ (Schneider et al. 2012). Data processing was performed using 32-point (0.48-μs, equivalent to 0.37-mm) moving-window analysis, in which a specific ITD (Hs, HC, If,, or Hf,g) was computed for each window segment. The window segment length was selected based on the approximate length of the transducer output pulse, and corresponded to approximately 7 cycles at the transducer center frequency. Each computed value was mapped to the center point of the original segment. The fully processed dataset was mapped to grayscale and the resulting image scaled to the appropriate aspect ratio.

For each mouse, a representative frame showing a portion of the right liver lobe (having uniform texture and free from major ducts or vessels) was selected from the conventional ultrasound cine loop. Figure 3 illustrates grayscale rendering of an example frame using conventional processing (i.e., log of signal magnitude) and entropy processing with each of the ITD’s, from an untreated mouse (top row) and a mouse exposed to 4 weeks of CCl4 (bottom row). A 15-mm2 circular region of interest (ROI) was positioned within the central portion of the right medial lobe approximately 3 mm below the skin (see Figure 3 for illustration). The same ROI was applied to images generated with each of the previously described quantities, and the mean values within the ROIs were computed. A two-parameter exponential equation of the form ΔH = aebF (where ΔH is an entropy metric’s difference from baseline and F is the fibrosis metascore, defined below) was fit to the results as a means of modeling the correlation with liver recovery.

Figure 3:

Figure 3:

B-scan view (conventional ultrasound, i.e., log of analytic signal magnitude) of right lobe of example mouse livers after varying lengths of treatment with CCl4. Circular region of interest shown with white dotted line indicates area from which entropy metrics were extracted.

Histology

Frozen liver tissue was sectioned and treated with hematoxylin and eosin (H&E) and picrosirius red stains for visualization of fatty and fibrous components. Slides were imaged at 20X and large representative areas (e.g., between 6 to 12 contiguous visual fields) were captured and stitched together digitally for subsequent blinded examination by an expert pathologist (T-C.L.). Example H&E fields for control livers and livers exposed to CCl4 with sequential stages of recovery are shown in Figure 4. Liver sections were graded on a nominal scale for portal fibrosis (0: none; 1: thickened basement membrane; 2: mild periportal fibrosis; 3: moderate periportal fibrosis; 4: portal-portal bridging), perivenular fibrosis (0: none; 1: thickened basement membrane; 2: fibrosis extending into parenchyma; 3: long fibrosis bands extending into parenchyma; 4: zone3-zone3 bridging), cholestasis (0: none; 1: mild; 2: moderate; 3: severe), and zone 3 chronic inflammation (0: none; 1: mild; 2: moderate; 3: severe). Area of necrosis also was estimated visually. Steatosis was not graded because no significant fat accumulation was observed in any of the groups.

Figure 4:

Figure 4:

Example fields of H&E stains of mouse liver for untreated mice (A), and for mice given CCl4 for 4 weeks and left to recover for 1 day (B), 4 days (C), 8 days (D), 12 days (E), and 18 days (F). Scale bars = 100 μm.

Liver function and collagen content

Samples of excised liver tissue from each mouse were assayed to determine total liver collagen content (Cedarlane Labs kit, Burlington, NC, USA). Aminotransferases were determined in a subset of mice from the 1-day recovery group and a set of untreated mice (n=3 for each group).

RESULTS

Histological analysis revealed substantial changes in liver morphology associated with acute exposure to CCl4, with moderate necrosis (typically ~20%) and focal fibrosis especially evident in perivenular areas (zone 3). Zone 3 inflammation, fibrosis and cholestasis decreased during the recovery period. To succinctly express the degree of pathology exhibited in the tissue from each mouse, a single metascore was computed by expressing each of the individual pathology grades as a fraction of the maximum value and taking the mean of the resulting normalized scores. The continuously improving liver metascore clearly reflects liver healing over time, although recovery to normal values was incomplete within the 18-day recovery time frame of this study (Figure 5; for all whisker plots, an X symbol marks the mean value, the horizontal line within the box marks the median, the box top and bottom mark the limits of the 75th and 25th percentiles respectively, and the whiskers mark the extent of the rest of the data. Outliers, defined as lying more than 1.5 times the interquartile range from either end of the box, are plotted as individual points). Elevated liver enzymes for the earliest recovery group (1-day recovery: ALT=1710±170 u/L, AST=1020±5 u/L) further confirmed impaired liver function relative to untreated animals (ALT=70±10 u/L, AST=70±20 u/L). In contrast the liver collagen content did not exhibit a clear trend over the recovery times (Figure 6).

Figure 5:

Figure 5:

Fibrosis metascore exhibits continuous improvement with recovery time, although not yet to baseline level at the final observed timepoint at 18 days.

Figure 6:

Figure 6:

Collagen fraction (measured by histochemical assay) exhibits no clear trend as a function of recovery time.

Entropy metric mean values likewise exhibited a dependence on recovery time (Figure 7). Significant differences at the p<0.05 level (unpaired two-tail t-tests) with respect to untreated cohort were observed at the 1-day and 4-day recovery time points. Unlike the fibrosis scores however, these metrics demonstrated a return to normal values by the 18-day recovery point. Moreover, all metrics demonstrated a monotonic relationship to fibrosis score with a recovery process that fit an exponential model well over the range of data in this study (Figure 8, Table 1). All entropy metrics behaved similarly, outside of expected differences in magnitude and offset.

Figure 7:

Figure 7:

Mean entropy values as a function of recovery time. All metrics demonstrate a return to normal values at the 4-week recovery point.

Figure 8:

Figure 8:

Difference in mean entropy metrics from baseline (no treatment) shows a clear monotonic increase with increasing fibrosis metascore. Dotted line shows exponential fit to data (see Table 1 for details).

Table 1:

Exponential model fit parameters for difference in mean entropy metrics from baseline as a function of fibrosis metascore (see Figure 7). The exponential model is of the form ΔH = aebF, where ΔH is the associated entropy metric difference from baseline, and F is the fibrosis metascore.

Shannon Continuous Rényi Joint
a b r2 a b r2 a b r2 a b r2
0.0135 11.53 0.953 0.0152 11.67 0.951 0.0082 12.93 0.966 0.0039 12.06 0.966

DISCUSSION

In the present investigation, we acquired radio-frequency ultrasound backscatter waveforms in vivo from mouse livers suffering reversible toxic damage and quantified the natural healing response with the use of sensitive and objective information-theoretic detector (ITD) signal processing techniques (Hughes 1994; Hughes et al. 2005b; Hughes et al. 2006; Hughes et al. 2007b; Hughes et al. 2009b; Hughes et al. 2009a; Hughes et al. 2011; Hughes et al. 2013; Hughes et al. 2015; Wallace et al. 2007). In general, ITD methods operate by analyzing the statistical distribution of digitized voltage levels from an acoustic signal and are sensitive to diffuse, low-amplitude features of the signal that often are obscured by noise or lost in large specular echoes which can inhibit recognition (Cheng et al. 2009; Hughes 1992; Hughes 1993a; Hughes 1993b; Hughes et al. 2005b). The relative insensitivity to confounding atypical bright spot scatterers, noise, and specular echoes indicates that these features would not dominate the outcome for entropy analysis as they might for measures of the average magnitudes of energy in a windowed region of interest, for example. The family of entropy metrics investigated here all performed similarly well to depict tissue recovery suggesting that any or all might be candidates for further evaluation in actual patients with liver diseases.

We have shown previously that ultrasound entropy metrics can detect subtle tissue damage in a number of distinct pathologies. For example, in the mdx mouse, a model of Duchenne muscular dystrophy resulting from a complete lack of the membrane stabilizing protein dystrophin, entropy metrics were able to differentiate diseased from normal biceps in mdx versus non-dystrophic control mice (Hughes et al. 2007b; Hughes et al. 2011). Moreover, treatment of mdx mice with corticosteroids elicited improvements in muscle disease that could be sensitively depicted after only 2 weeks as a restoration of more normal entropy values. Traditional energy metrics (e.g., “integrated backscatter”) proved insensitive for detection of the therapeutic response to steroids in this study. Exceptional sensitivity to weak scattering perfluorocarbon nanoparticles that are molecularly targeted to neovasculature in tumors and injured tissues in animal models in vivo has been demonstrated at concentrations that are undetectable with conventional methods (Hughes et al. 2006; Hughes et al. 2007b; Hughes et al. 2009b). In industrial applications, these receivers allow detection of subtle flaws in materials that are obscured by strong specular reflectors, thereby overcoming some of the limitations of more conventional signal processing schemes (Hughes 1994; Hughes et al. 2005b; Hughes et al. 2015).

Alternative strategies have been proposed for quantifying and/or staging liver disease processes using ultrasound tissue characterization (Oelze and Mamou 2016). Well-known metrics such as backscatter and attenuation show increased magnitude associated with hepatopathy (Guimond et al. 2007; Lu et al. 1997). Multiparametric combinations of these quantities with other conventional metrics such as speed of sound discriminate fibrosis better than when considered singularly (Bouzitoune et al. 2016). Statistical modeling of the envelope-detected backscatter from liver (Ho et al. 2012; Ma et al. 2016; Owjimehr et al. 2017) has shown promise for evaluating the degree of hepatic fibrosis and steatosis, while B-scan texture analysis (Vicas et al. 2011) has proved less useful in the clinic. Recently, photoacoustic techniques have been used utilized to differentiate healthy and fibrotic livers in a CCl4 mouse liver injury model (van den Berg et al. 2016).

The recent advent of shear wave ultrasound imaging for quantification of liver fibrosis is a welcome addition to the diagnostic armamentarium of noninvasive imaging; however, this approach requires the use of equipment capable of propagating shear waves transcutaneously into the liver and to simultaneously receive and process backscattered compressional waves that are used to register the speed of sound in regions of interest for calculation of an elastic modulus (Barr 2018). The ability to employ conventional clinical imaging platforms would render point of care applications more viable as entropy detection now can be done in real time if unprocessed RF data are available (Hughes et al. 2009a).

What is not addressed in this study is the fundamental nature of the scattering elements that are responsible for the basic signal and its progressive recovery over time. Because there is no specific trend in overall liver collagen concentration over time, we do not attribute the observed behavior to gross changes in physical characteristics such as material compressibility or density that would be indicative of resolving fibrosis. However, our blinded pathological analyses do indicate changes in the organization of collagen over time even if the total amounts of collagen are not changing enough to account for restoration of entropy values. Therefore, we propose that the entropy metrics are sensitive to the specific microscopic organization of disrupted liver tissue elements rather than collagen amount as far as this model of toxic injury is concerned. This notion is entirely consistent with the expectation that entropy metrics more likely represent how scatterers are arranged, in the sense of local information content, rather than their average backscatter cross-section per se. Whether entropy metrics would be sensitive to collagen formation characteristic of cirrhosis is an interesting question for future study. Other potential mechanisms that could influence entropy metrics include cellular ballooning, hepatocyte necrosis/apoptosis, hemorrhage, and inflammatory infiltrates, many of which are represented in our liver metascore metric (Figure 5) and are topics for further exploration.

In terms of limitations, the current study was performed with an experimental broadband imaging system operating at a nominal center frequency of 15 MHz. Whether the same sensitivities of entropy metrics to liver damage might be obtained at lower frequencies with clinical imaging systems is conjectural, but certainly testable in patients. We have applied entropy imaging and analytical techniques in vivo to actual patients with Duchenne Muscular Dystrophy (DMD) versus normal control subjects using broadband clinical 7MHz (~4.5–9.5MHz) ultrasound to reveal clear differences between damaged and normal biceps muscle tissues (Hughes et al. 2007a). These muscles harbor many similarities in altered and disordered cellular and matrix structures as do the damaged livers (edema, fibrosis, cellular damage, etc.) indicating that at clinical imaging frequencies, ITD’s are sensitive to tissue damage. We also have reported in vivo sensitivity to pathological changes in muscular dystrophy and cancer at frequencies up to 40MHz, indicating the applicability of entropy metrics over a broad range of frequencies (Hughes et al. 2005a; Wallace et al. 2007). Testing of entropy metrics against well-characterized phantom scattering models for relevant clinical imaging units would be required to ensure equivalent performance of the various platforms.

In conclusion, we suggest that the entropy metrics derived from conventional longitudinal wave ultrasound RF backscatter data could offer more sensitivity to early changes in liver architecture, whereas shear wave-based readouts appear to be somewhat less sensitive, and conventional spectral tissue characterization metrics (e.g., integrated backscatter, frequency dependence, etc.) appear even less sensitive in larger clinical trials than those mentioned above (Audière et al. 2011). With recent algorithmic improvements in entropy computation allowing real time quantification, the opportunity now exists for porting these procedures to any imaging platform for patient imaging and stand-alone point-of-care analyses.

Figure 2:

Figure 2:

Grayscale rendering of an example frame using conventional processing (i.e., log of signal magnitude) and entropy processing with each of the ITD’s. Top row represents a frame from an untreated mouse, bottom row is from a mouse exposed to 4 weeks of CCl4.

Acknowledgements

We appreciate the assistance of John S. Allen and Michael J. Scott (Washington University Department of Medicine) for technical support. Grant support: NIH: EB019569, DK102691, HL073646

Footnotes

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