Investigating confounding factors in shear wave speed measurements of fibrotic liver tissues: a computer simulation study

Abstract

Screening patients with liver fibrosis and identifying those at risk of developing advanced liver fibrosis is of clinical interest. Shear wave elastography (SWE), a promising non-invasive screening tool used to distinguish healthy tissue from diseased tissue, measures tissue shear wave speed (SWS) to describe tissue stiffness and identify liver fibrosis. However, considerable variations in the reported results have been found. We propose that the heterogeneity of the liver tissue background, such as the presence of fatty liver tissue and the preferred local orientation of the scarred fibrotic liver tissues embedded into the liver parenchyma, may contribute to the uncertainty in SWE measurements. Therefore, this study aims to systematically investigate four cofounding factors, the size, volume fraction, and orientation of the fibrotic inclusions, as well as the fatty background, using computer simulations, to describe the multifaceted impact on SWS variability (i.e., SWS standard deviation). The simulations implemented in this preliminary study demonstrated that both fibrosis and fatty background impact the SWS STD and that the SWS STD distributions do not follow a Gaussian distribution. While the SWS STD increased with fibrosis size and volume fraction, the SWS STD decreased as the fatty background increased. The shape of the distribution did not follow a consistent trend across fibrosis inclusion levels, fibrosis sizes, fibrosis orientations, and percent fatty background for either the Mean SWS or the SWS STD. The current study provided evidence that the current clinical guidelines, regarding cut-off values for the different METAVIR Fibrosis stages, overestimate the fibrosis levels in the presence of steatosis.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13246-026-01712-8.

Introduction

Liver fibrosis refers to a scar tissue accumulation process in the liver. A fraction of liver fibrosis can develop into advanced liver fibrosis, i.e., cirrhosis, and eventual liver failure. In contrast, the majority of patients with early-stage liver fibrosis often have no symptoms and do not exhibit specific abnormalities. Thus, these patients often do not progress into advanced liver fibrosis. Screening patients with liver fibrosis and subsequently identifying those at high risk of developing advanced liver fibrosis is of clinical interest. That is why significant research and development efforts have been devoted to non-invasive assessment of liver fibrosis, as an alternative to liver biopsy [1–12].

Shear wave elastography (SWE) is a non-invasive screening tool that can be used in real-time to describe tissue properties and distinguish healthy tissue from diseased tissue by attributing differences in tissue stiffness measurements to pathology [13, 14]. Quantitative SWE parameters, specifically the biomechanical parameter shear wave speed (SWS), an indicator of tissue stiffness, are clinically useful for identifying liver fibrosis [15].

In one study, SWE results have shown a high correlation with fibrosis stage, i.e., the SWS increased with the histologic fibrosis stage [16]. However, unreliable results have also been reported in 16% of measurements [17, 18]. We think the heterogeneity of liver tissue background may explain the varying accuracy of SWS measurements.

The first significant contributing factor to the liver tissue heterogeneity is the presence of fatty liver tissue. Recall that the global prevalence of non-alcoholic fatty liver disease (NAFLD) is approximately 30%; the prevalence is likely increasing in many countries, where their residents have a high rate of obesity and type 2 diabetes. From the perspective of physics, liver fat softens the liver [19], and it has been suggested that the steatosis may attenuate the shear wave propagation and possibly underestimate the liver damage [20]. Current clinical guidelines do not include separate cut-off values for liver tissue with a fatty background, though the impact of steatosis for staging liver fibrosis has been debated [2, 21]. Some clinical studies have concluded that steatosis does not affect the correlation between liver stiffness values and fibrosis stage [4, 11, 21–24]; however, others claim the opposite [18, 20, 25, 26]. Previous computational studies have demonstrated that as fat levels increase, the SWS decreases due to the slower speed of the shear waves in the fat [13, 14].

If we consider scarred fibrotic liver tissues embedded into the liver parenchyma, these fibrotic liver tissues may exhibit a preferred local orientation when they interact with an arriving shear wave. Thus, the second significant contributing factor to the liver tissue heterogeneity is such orientation preference.

In reality, how those two mentioned contributing factors influence SWS measurements is further complicated by the size and volume fraction of fibrotic lesions. Hereafter, we refer to these four factors as confounding factors in SWS measurements. To this end, this study aims to systematically investigate these four cofounding factors using computer simulations, where the size, volume fraction, and orientation of the fibrotic inclusions, as well as the fatty background, all have a multifaceted impact on SWS variability. It is not possible to discern in vivo how each of these factors impacts SWS measurements. Computer simulations, particularly those that are realistic, can help in understanding the in vivo accuracy of SWE.

Methods

Simulated fibrotic liver tissue pathologies (sFLP)

A statistical random biphasic tissue model was created to realistically represent fibrotic liver tissue. The biphasic model consists of background material (simulated as either normal liver tissue or diseased fatty liver tissue) and (simulated) fibrotic liver tissue. For clinical evaluations, the fibrosis level is assessed using histopathological techniques and is based on the ratio of the collagen proportional area to liver tissue area [27, 28]. The collagen inclusions are assumed to be randomly distributed in the liver tissue [29]. The method used to develop the simulated fibrotic liver tissue model is based on the nonlinear transformation of Gaussian fields developed by Feng et al. [30] and the detailed implementation by our group has been described previously [31].

Impact of fatty background

To evaluate the impact of the fatty background, the elastic modulus of the simulated liver background tissue was varied to represent liver tissue with three different percentages of fat corresponding to three different disease states (i.e., 0% fat - healthy tissue, 50% fat - moderate disease, 100% fat - severe disease). The histology scale of the fat particles was much smaller than the grid size scale of the simulated fibrotic liver tissue model and the wavelength of the propagating shear wave [19, 32]. We also assumed that fat is a global disease that impacts the entire liver and that it is not isolated locally within the liver [19]. For these reasons, the simulated liver background was modeled as a homogeneous medium for three different simulated background fat tissue compositions.

Impact of fibrotic inclusion size and volume fraction

To evaluate the impact of size and volume fraction of the fibrotic inclusions, the size (i.e., small = 1.2 mm, medium = 2.0 mm, large = 2.8 mm) and the percentage (5, 12, and 20%) of the disc inclusions in the reference medium used to create the simulated fibrotic liver pathology tissue model was varied to represent a range of fibrotic tissue levels within the total tissue model area. The fibrotic tissue levels represented early and advanced stage liver fibrosis and fell within the four distinct METAVIR scoring system stages of liver fibrosis (F1: 2%–10%, F2: 2%–16%, F3: 5%–21%, F4: 8%–33%) [33].

Impact of fibrotic inclusion orientation and volume fraction

To evaluate the impact of the orientation (i.e., shape dependency) of the fibrotic inclusions, ellipse-shaped inclusions (2:1 horizontal-vertical ratio, 1.6 mm:0.8 mm) in the reference medium were used to create the simulated fibrotic liver pathology tissue model. The inclusions were oriented either parallel or perpendicular to the direction of shear wave propagation, and the percentage (i.e., 5, 12, 20% inclusion rate) of the ellipse inclusions in the reference medium was varied to represent a range of fibrotic tissue levels within the total tissue model area. See Fig. 1 for an example of this reference medium and the resultant simulated fibrotic liver pathology tissue (sFLP) model.

Fig. 1.

Reference medium (left) and corresponding resultant Simulated Fibrotic Liver Tissue Pathology (right) for a 5% fibrosis with horizontal inclusions oriented parallel to the direction of shear wave propagation and b 20% fibrosis with vertical inclusions oriented perpendicular to the direction of shear wave propagation. The Simulated Fibrotic Liver Pathology (sFLP; right) Tissue is directly inserted into the K-Wave Simulation model. The Simulated Fibrotic Liver Tissue Pathology model was used as the region of interest (20 mm x 20 mm), with grids assigned as fibrotic inclusions (white) and background liver parenchyma (black). The arrow indicates the direction of shear wave propagation

Elastic shear wave propagation solver

The model developed by our group for the elastic wave propagation solver for sFLP has been described in detail in a previous publication [31]. Thus, only essential details are provided below for completeness. In brief, the sFLP was the region of interest in the K-Wave model for Elastic Shear Wave Propagation. More specifically, it was input to a numerical solver simulating elastic wave propagation. K-Wave is an open-source platform that uses a pseudo-spectral finite difference solver for the elastic wave equation to simulate acoustic and shear wave propagation in physiological tissue models [34, 35]. In the simulation model developed for this study, the waveform source/duty cycle is 1, equivalent to a fractional bandwidth close to 100%, with a center frequency of 100 Hz. Thus, the excitation energy is likely concentrated between 0 and 200 Hz, centered around 100 Hz (Table 1).

Table 1.

Simulated liver background and fibrotic inclusions tissue properties [13, 36, 37]

	0% fat (Healthy tissue)	50% fat (Moderate disease)	100% fat (Severe disease)	Fibrotic inclusions
Shear wave speed (m/s)	1.4	1.2a	1.0 m/s	20
Compressional sound speed (m/s)	1540			2000
Mass density (kg/m3)	1000			1200

^aDerived using composite theory, with 0% and 100% fat conditions as upper and lower limits

Shear wave speed (SWS)

The Elastic Wave Propagation Solver reported time-varying particle velocity curves perpendicular to the direction of shear wave propagation as output over the entire simulation period at discrete locations (i.e., sensors). The sensors were defined throughout the entire sFLP at every other grid point in the vertical and horizontal directions for a total of 2500 curves (50 rows x 50 columns). The time lag (Δt) between the particle velocity curves for two adjacent sensors in the direction of wave propagation within the sFLP was determined using a correlation-based method [38]. The known distance (Δd = 0.004 m) between the adjacent sensors and the corresponding time lag was used to calculate the SWS (i.e., SWS = Δd/Δt). From the resultant two-dimensional SWS map (49 × 50) for each simulation, the Mean SWS and the SWS standard deviation (STD) for the entire sFLP medium were calculated [31].

Statistical analysis

Violin plots will illustrate the SWS STD distribution for each data set, where each data set consists of 25 SWS STD values, each representing a unique, randomly generated sFLP designed to study one of the confounding factors in SWS measurements. Based on our previous experience [31], we expect that the SWS STD for each data set will not be normally distributed. The Mann-Whitney test (statistical significance, P < 0.05) will be used to determine if there is a statistical difference between the SWS STD distributions between groups. The skewness and kurtosis were also calculated to assess the asymmetry around the mean and the shape of the distribution of the Mean SWS and the SWS STD. The skewness and kurtosis calculations were not designed to accommodate bimodal and trimodal data sets, so prior to calculating the skewness and kurtosis, the top and bottom outliers were removed from each data set. For this analysis, skewness values between − 0.5 and 0.5 indicate low skewness, values between − 1.0 to -0.5 and 0.5 to 1.0 indicate moderately skewed, and values less than − 1 or greater than 1 indicate highly skewed. Additionally, a kurtosis value of 3 represented a normal distribution, while values greater than 3 indicated a distribution with a higher peak and heavier tails than a normal distribution, and values less than 3 indicated a distribution with a lower peak and lighter tails than a normal distribution.

Results

To analyze the impact of fatty background and fibrotic inclusion size and fibrosis volume fraction, twenty-five discrete sFLP models were created for each of the three reference inclusion sizes (i.e., small = 1.2 mm, medium = 2.0 mm, large = 2.8 mm) at each of the three fatty backgrounds (i.e., 0% fat - healthy tissue, 50% fat - moderate disease, 100% fat - severe disease) resulting in a total of 225 simulations (see Fig. 2a) at each of the three fibrosis levels (i.e., 5, 12, and 20% inclusion rate), for a total number of 675 sFLPs. To analyze the impact of fatty background fibrotic inclusion orientation and fibrosis volume fraction, twenty-five discrete sFLP models were created for each of the two reference inclusion orientations (i.e., parallel or perpendicular to shear wave propagation), at each of the three fatty backgrounds (i.e., 0% fat - healthy tissue, 50% fat - moderate disease, 100% fat - severe disease) resulting in a total of 150 simulations (see Fig. 2b) at each of the three fibrosis levels (i.e., 5, 12, and 20% inclusion rate), for a total number of 450 sFLPs.

Fig. 2.

Representation of the number of Simulated Fibrotic Liver Tissue Pathology Models developed for a single fibrosis level (i.e., 5, 12, and 20% inclusion rate) to investigate the impact of a fatty background, fibrotic inclusion size and fibrosis level b fatty background, fibrotic inclusion orientation and fibrosis level, the arrow indicates the direction of shear wave propagation

Within each fibrosis level (i.e., 5, 12, and 20% inclusion rate), the SWS STD increased as the size of the reference inclusion increased (see Fig. 3a–c). At most of the fibrosis levels (i.e., 5 and 12% inclusion rate - small, medium, and large inclusion size, 20% inclusion rate – small, medium inclusion size), within each fibrosis size, as the percentage of fatty background increased, the mean SWS STD decreased, but the SWS STD range remained consistent, except for the 20% inclusion level where the range decreased. At the 20% inclusion fibrosis level and the large inclusion size, the mean SWS STD remained constant for the 0% and 50% fatty background conditions and increased for the 100% fatty background conditions. For comparisons of the reference inclusion size and fatty background between fibrosis levels (i.e., small reference inclusion size at 0% fatty background 5% inclusion rate vs. 12% inclusion rate vs. 20% inclusion rate), the differences for the SWS STD distributions were statistically significant [P-value < 0.001]. For comparisons of the fibrosis levels and fatty background between reference inclusion sizes (i.e., 5% inclusion rate at 0% fatty background small vs. medium vs. large reference inclusion size), the differences for the SWS STD distributions were statistically significant [P-value < 0.001] for all but five comparisons. The non-statistically significant [P-value range = 0.06–0.66] comparisons were between the medium vs. large reference size for the 12% fibrosis level across all fatty background conditions and for the 20% fibrosis level for the 0% and 50% fatty background conditions. Lastly, for comparisons of the fibrosis level and reference inclusion size across fatty background conditions (i.e., 5% inclusion rate and small reference inclusion size, 0% vs. 50% vs. 100% fatty background condition), nine comparisons for the SWS STD distributions were not statistically significant (see Table 2).

Fig. 3.

Shear Wave Speed (SWS) Standard Deviation (STD) for a 5%, b 12%, and c 20% Fibrosis for small, medium, and large reference fibrosis inclusions for three fatty background conditions (0% = white, 50% = light grey, 100% dark grey) and for d 5%, e 12%, and f 20% Fibrosis for two fibrosis inclusion orientations (perpendicular to SWS propagation, parallel to SWS propagation) for two fatty background conditions (0% = white, 100% dark grey)

Table 2.

P-Values for Mann-Whitney test to compare the differences for SWS STD distributions for fibrosis level and reference inclusion size between fatty background conditions

Fibrosis level	Size	0% vs. 50% fat	50% vs. 100% fat	0% vs. 100% fat
5%	Small	0.0004***	< 0.0001***	< 0.0001***
	Medium	0.0018**	0.0083**	0.0001***
	Large	0.0682	0.0263*	0.0010**
12%	Small	< 0.0001***	0.0123*	< 0.0001***
	Medium	0.0019**	0.1138	0.0012**
	Large	0.0361*	0.5094	0.0270*
20%	Small	0.1188	0.6312	0.0489*
	Medium	0.1806	0.1160	0.0074**
	Large	0.5671	0.0313*	0.0758

*p < 0.05, **p < 0.01, ***p < 0.001; BOLD values were not statistically significant

Additionally, within each fibrosis level (i.e., 5, 12, and 20% inclusion rate), the SWS STD increased for reference inclusions oriented parallel to the shear wave propagation compared to reference inclusions oriented perpendicular (see Fig. 3d–f). For all the fibrosis levels (i.e., 5, 12, and 20% inclusion rate) and both reference inclusion orientations (i.e., parallel and perpendicular to shear wave propagation), the mean SWS STD and SWS STD range remained constant for both the 0% and 100% fatty background conditions. Except for the 5% inclusion fibrosis level at the perpendicular orientation, there were no statistical differences between the SWS STD distributions for the perpendicular or parallel orientations for each fibrosis level between the two fatty background conditions. However, for all the inclusion rates and both fatty background conditions, the differences for the SWS STD distributions between the perpendicular and parallel orientations (i.e., 5% inclusion rate, 0% fatty background perpendicular vs. parallel orientation) were statistically significant [P-value < 0.001]. Additionally, for each orientation at each fatty background condition, the differences between the SWS STD distributions across the three different inclusion rates (i.e., perpendicular orientation, 0% fatty background 5%, vs. 12%, vs. 20% inclusion rate) were also statistically significant [P-value < 0.001].

As demonstrated in Fig. 3, the mean SWS and SWS STD distributions do not follow a Gaussian distribution. Interestingly, their skewness and kurtosis values did not follow a consistent trend across fibrosis inclusion levels, reference inclusion sizes, and percent fatty background, or for fibrosis inclusion levels, fibrosis orientations, and percent fatty background for either the Mean SWS or the SWS STD (see Online Resource Tables 3 and 4).

The results of this study demonstrated that the uncertainty in the SWS STD increased as the fibrosis level and the size of the fibrosis inclusion increased, since the mean SWS STD values elevated and their variances became more heterogeneous. However, this trend was reversed at the largest fibrosis level, the largest fibrotic inclusion size, and 100% fatty background condition, and the mean SWS STD slightly decreased from the 50% fatty background condition. But such a decrease had no statistical significance. Additionally, the results from this study showed that the orientation of the fibrosis was more influential than the fatty background. When the fibrosis was aligned for each orientation, the SWS STD had a minimal reduction with the 100% fatty background. For the 5% and 12% fibrosis levels, the perpendicular orientation violin plots were fatter, which indicated that the SWS STD was closer to the mean value, and the parallel orientation violin plots were longer/thinner, which indicated that the SWS STD was more random.

Discussion

This study demonstrated that the fatty background impacted the simulated SWS STD across a range of fibrosis levels and fibrosis sizes. The findings from this study were consistent with previous simulation studies that evaluated the effect of fibrosis and steatosis on SWS [13, 14]. However, in addition to the varying presence of discrete fat inclusions and fibrosis [13, 14], the current simulation models incorporate a range of fibrosis sizes and fibrosis volume fractions, as well as varying percentages of fatty background. A previous clinical study showed that fibrosis and steatosis are not linearly related and that within each fibrosis stage, there are varying stages of steatosis [20]. Therefore, it was important to analyze fibrotic size, fibrotic level, and fatty background.

It was also important to understand the uncertainty of the simulation data compared to histology-determined fibrotic and steatotic clinical data [15] and analyze the range of the simulation data compared to clinical cut-off values established in the literature [1, 4, 6, 9–11, 20, 21, 24, 39–44]. Overall, our simulation results are consistent with data reported in the clinical literature, as shown in Figs. 4 and 5. To better understand the comparisons shown in Figs. 4 and 5, it is important to note that the fibrosis levels for the simulation data directly represent the Collagen Proportionate Area (CPA) values. CPA values of 5%, 12%, and 20% correspond to METAVIR fibrosis (F) stages F1-F2, F2-F3, and F2-F4, respectively, based on findings in the literature [45].

Fig. 4.

Comparison of simulation data mean shear wave speed ± standard deviation (m/s) to fibrosis grade cut-off values reported in the literature for patients with Nonalcoholic fatty liver disease [1, 4, 6, 9–11, 20, 21, 24, 39–44] and clinical shear wave speed data (m/s) for patients with Nonalcoholic fatty liver disease (star markers) [15]. The simulation data is grouped by fatty background (white markers = 0% fat, healthy tissue; grey markers = 50% fat; moderate disease, black markers = 100% fat, severe disease). The simulation fibrosis level is denoted by the shape of the black, grey, and white markers (5% = circle, 12% = square, 20% = triangle) and the simulation reference inclusion size is denoted by the size of the black, grey, and white markers (small, medium, and large). The Han et al. data (mean ± std) is grouped by histology fibrosis grade. The steatosis levels were not provided [15]. The METAVIR fibrosis stages established by the cut-off values reported in the literature are denoted by light (F1) to dark grey (F4)

Fig. 5.

Comparison of simulation data mean shear wave speed ± standard deviation (m/s) to fibrosis grade cut-off values reported in the literature for patients with Nonalcoholic fatty liver disease [1, 4, 6, 9–11, 20, 21, 24, 39–44] and clinical shear wave speed data (m/s) for patients with Nonalcoholic fatty liver disease (star markers) [15]. The simulation data is grouped by fatty background (white markers = 0% fat, healthy tissue; black markers = 100% fat, severe disease). The simulation fibrosis level is denoted by the shape of the black and white markers (5% = circle, 12% = square, 20% = diamond) and the simulation reference inclusion orientation is denoted by the orientation of the black and white markers (horizontal = parallel to shear wave propagation, vertical = perpendicular to shear wave propagation). The Han et al. data (mean ± std) is grouped by histology fibrosis grade. The steatosis levels were not provided [15].The METAVIR fibrosis stages established by the cut-off values reported in the literature are denoted by light (F1) to dark grey (F4)

At the lower fibrosis levels, the SWS range increases as the inclusion size increases. Similarly, at lower fibrosis levels, the SWS range increases from a perpendicular to a parallel orientation. In the 0% fatty background condition, the range of the mean SWS across fibrosis levels and fibrotic inclusion size, was consistent with the fibrosis stages for each of the CPA values (see Fig. 4). However, as the percentage of fatty background increased across fibrosis levels and fibrotic inclusion sizes, the mean SWS decreased. The simulation data shifted to lower METAVIR fibrosis stages than the corresponding fibrosis stages established in the literature. This is consistent with clinical data reported in the literature. Gaia et al. showed that in patients with advanced fibrosis (i.e., METAVIR F3) and severe steatosis (i.e., > 33%), liver stiffness measurements were lower than expected and similar to those of patients with initial fibrosis (i.e., METAVIR F1) and lower fat levels (i.e., < 33%) and that SWE underestimated the fibrosis stage in 75% of patients with advanced fibrosis (i.e., METAVIR F3) and severe steatosis (i.e., > 33%) [20]. Petta et al. also reported that the fat droplets altered the propagation time of the shear wave and that failing to account for the severity of steatosis resulted in an overestimation of the degree of liver fibrosis [26]. Similarly, in the 0% fatty background condition, the range of the mean SWS across orientations was consistent with the fibrosis stages for the 5% and 20% CPA values. The 12% perpendicular orientation, while the 12% parallel orientation was greater than the values established in the literature (see Fig. 5). In the 100% fatty background condition, the 5% parallel and perpendicular and 12% perpendicular results fell within fibrosis stages lower than the stages established in the literature, while the 12% parallel and 20% perpendicular and parallel results, although lower than the 0% fatty background condition, were still consistent with the fibrosis stages established in the literature. These simulations demonstrate that the fatty background decreases the SWS in the presence of fibrosis, providing evidence that clinical guidelines should consider the fatty background when establishing cut-off values for patients with both liver fibrosis and steatosis. This is perhaps why the fibrotic and steatotic clinical data (see Figs. 4 and 5) for fibrosis level F3 are not consistent with the literature-established clinical cut-off values. All the patients had histology-determined steatosis, but the scores were not provided by Han et al. [15]. Based on the findings from the current simulation study, it is possible that the F3 group (only three patients) had significant levels of steatosis which decreased the SWS, even in the presence of elevated fibrosis levels.

There were competing mechanisms influencing the shear wave scattering and SWS STD. As the percentage of fat increased in the fatty background, the elastic contrast between the background and the fibrotic inclusions increased. The increase in elastic contrast led to greater shear-wave scattering. However, as the percentage of fat increased, the fatty background became softer, which decreased the shear wave speed and the likelihood of multiple scattering/interference. At the lowest fibrosis level, as the fatty background increased and the medium became softer, the wave speed decreased, the scattering decreased, and as a result, the SWS STD decreased. As the fibrosis levels and fibrotic inclusion size increased, the elastic contrast effect between the soft fatty background and the stiffer fibrotic inclusions was diminished.

There was also a size effect impacting the shear wave scattering and SWS STD. Generally, shear wave scattering increased, and SWS STD increased compared to lower fibrosis levels. As the fibrosis levels increased, the shear wave scattering and SWS STD increased accordingly for two reasons. First, the size of the fibrotic inclusions generally increased; thus, there were more targets to create interference for the shear wave. Second, as the size of the fibrotic inclusions increased, the distance between the fibrotic inclusions decreased, increasing the likelihood of multiple scattering/interference.

At the lowest fibrotic levels, there was a lower percentage of fibrosis inclusions, which decreased scattering compared to the higher fibrotic levels, so the speed of travel of the shear waves played a bigger role. Except for the highest fibrosis level (i.e., 20% inclusion rate) and largest reference inclusion size, while the SWS STD increased as the fibrosis level and reference inclusion size increased, the SWS STD decreased as the percentage of fat in the fatty background increased. However, at the highest fibrosis level (i.e., 20% inclusion rate) and the largest reference inclusion size, the 100% fatty background condition had a higher SWS STD than the 0% fatty background condition. These results are consistent with other clinical measurements that showed an increase in SWS variability for advanced fibrosis (i.e., stage 4) and advanced steatosis (i.e., > 66%) compared to advanced fibrosis (i.e., stage 4) and low steatosis (i.e., 5–33%) [4].

This study also demonstrated that the SWS STD was dependent on the orientation of the fibrotic inclusions with respect to shear wave propagation and that measurement direction impacts SWS STD. In the two-dimensional simulations developed for this study, the SWS is measured along a line. When the shear wave encounters an inclusion-oriented perpendicular to the direction of propagation, there is more surface interaction, but less material (i.e., distance for the wavelength to travel) between the shear waves and the inclusion. However, when the shear wave encounters an inclusion oriented parallel to the direction of propagation, the wavelength travels for a longer time through the inclusion. The inclusion oriented parallel to the direction of propagation results in higher variability because it provides greater interference. Studies have shown that histologic legions of fibrosis in the liver are unevenly distributed in the liver [46] and that while globally, the orientation of fibrosis in the liver is not aligned with a specific direction, the fibrosis is anisotropic [47]. Since only a few SWE measurements are taken from each patient, and the local shear wave propagation induced by an ultrasound pushing pulse cannot be controlled, it is reasonable to consider that the local fibrotic tissue orientation concerning the local shear wave propagation may appear stochastic. This study is preliminary and using parallel and perpendicular orientations is a good first step. In the future, we plan to improve our simulations by incorporating histopathology results. Then, our work can be integrated into sophisticated human liver models, similar to that reported for breast ultrasound elastography simulations [48, 49]. As a result, the integrated simulation platform can help us gain a deeper understanding of these confounding factors. More importantly, better SWS cut-off values can be determined to enhance the classification of liver fibrosis.

Conclusions

The simulations implemented in this preliminary study demonstrated that both fibrosis and fatty background impact the SWS STD in sFLP tissue models. While the SWS STD increased with fibrosis size and volume fraction, the SWS STD decreased as the fatty background increased. Additionally, the current study provided evidence that the current clinical guidelines, regarding cut-off values for the different METAVIR Fibrosis stages, overestimate the fibrosis levels in the presence of steatosis. These results confirm that the fatty background should be considered for establishing clinical cut-off values to improve the accuracy of staging liver fibrosis. Lastly, this study also illustrated that the orientation of the fibrotic inclusions with respect to shear wave impacted the SWS STD propagation, which demonstrates that measurement direction impacts SWS STD.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

All authors contributed to the study conception and design. Material preparation, simulation development, and data collection were performed by Emily Miller. All authors contributed to data analysis. The first draft of the manuscript was written by Emily Miller and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Ethical approval

This is computational study. No ethical approval is requried.