Contrast-enhanced CT with a high-affinity cationic contrast agent for imaging ex vivo bovine, intact ex vivo rabbit, and in vivo rabbit cartilage

Contrast-enhanced μCT of the intervertebral disc: A comparison of anionic and cationic contrast agents for biochemical and morphological characterization

The objective of this study was to quantify and compare the contrast-enhancing properties of the anionic contrast agent ioxaglate/Hexabrix, and cationic contrast agent CA⁴⁺ for biochemical and morphological characterization of the intervertebral disc (IVD) via μCT. Optimal contrast agent concentrations were determined by incubating rat lumbar IVDs in dilutions of Hexabrix-320 (20%, 30%, 40%, and 50%) and CA⁴⁺ (10, 20, 30, and 40 mg I/ml). μCT imaging was performed at 70 kVp, 114 μA, and 250 ms integration time, 12 μm voxel size. The kinetics of contrast enhancement were quantified with cumulative incubations for 0.5, 1, 2, 12, 16, 20, and 24 h using both agents. Agreement in morphological quantification was assessed via serial scans of the same IVDs. Correlation of attenuation to glycosaminoglycan (GAG) content was determined by enzymatic digestion of IVDs, subsequent μCT imaging, and GAG quantification via dimethylmethylene blue assay. Forty percent Hexabrix and 30 mg I/ml CA⁴⁺ were chosen as optimal concentrations. Hexabrix enabled greater delineation of the IVD from surrounding tissues, and CA⁴⁺ had the lowest uptake in surrounding soft tissue. Twenty-four hour incubation was sufficient for >99% equilibration of both agents. A high level of agreement was observed in the quantification of IVD volume (ICC = 0.951, r = 0.997) and height (ICC = 0.947, r = 0.991). Both agents exhibited strong linear correlations between μCT attenuation and GAG content (Hexabrix: r = -0.940; CA⁴⁺ : r = 0.887). Both agents enable biochemical and morphological quantification of the IVD via contrast-enhanced μCT and are effective tools for preclinical characterization. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:1067-1075, 2017.

Contrast-enhanced CT imaging as a non-destructive tool for ex vivo examination of the biochemical content and structure of the human meniscus

The biochemical and histopathological techniques used to investigate meniscal content and structure are destructive and time-consuming. Therefore, this study evaluated whether contrast-enhanced computed tomography (CECT) attenuation and contrast agent flux using the iodinated contrast agents CA4+ and ioxaglate correlate with the glycosaminoglycan (GAG) content/distribution and water content in human menisci. The optimal ioxaglate and CA4+ contrast agent concentrations for mapping meniscal GAG distribution were qualitatively determined by comparison of CECT color maps with Safranin-O stained histological sections. The associations between CECT attenuation and GAG content, CECT attenuation and water content, and flux and water content at various time points were determined using both contrast agents. Depth-wise analyses were also performed through each of the native surfaces to examine differences in contrast agent diffusion kinetics and equilibrium partitioning. The optimal concentrations for GAG depiction for ioxaglate and CA4+ were ≥80 and 12 mgI/ml, respectively. Using these concentrations, weak to moderate associations were found between ioxaglate attenuation and GAG content at all diffusion time points (1-48 h), while strong and significant associations were observed between CA4+ attenuation and GAG content as early as 7 h (R²  ≥ 0.67), being strongest at the equilibrium time point (48 h, R²  = 0.81). CECT attenuation for both agents did not significantly correlate with water content, but CA4+ flux correlated with water content (R²  = 0.56-0.64). CECT is a promising, non-destructive imaging technique for ex vivo assessment of meniscal GAG concentration and water content compared to traditional biochemical and histopathological methods. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:1018-1028, 2017.

Cationic Contrast Agent Diffusion Differs Between Cartilage and Meniscus

Contrast enhanced computed tomography (CECT) is a non-destructive imaging technique used for the assessment of composition and structure of articular cartilage and meniscus. Due to structural and compositional differences between these tissues, diffusion and distribution of contrast agents may differ in cartilage and meniscus. The aim of this study is to determine the diffusion kinematics of a novel iodine based cationic contrast agent (CA(2+)) in cartilage and meniscus. Cylindrical cartilage and meniscus samples (d = 6 mm, h ≈ 2 mm) were harvested from healthy bovine knee joints (n = 10), immersed in isotonic cationic contrast agent (20 mgI/mL), and imaged using a micro-CT scanner at 26 time points up to 48 h. Subsequently, normalized X-ray attenuation and contrast agent diffusion flux, as well as water, collagen and proteoglycan (PG) contents in the tissues were determined. The contrast agent distributions within cartilage and meniscus were different. In addition, the normalized attenuation and diffusion flux were higher (p < 0.05) in cartilage. Based on these results, diffusion kinematics vary between cartilage and meniscus. These tissue specific variations can affect the interpretation of CECT images and should be considered when cartilage and meniscus are assessed simultaneously.

Contrast-enhanced CT using a cationic contrast agent enables non-destructive assessment of the biochemical and biomechanical properties of mouse tibial plateau cartilage

Mouse models of osteoarthritis (OA) are commonly used to study the disease's pathogenesis and efficacy of potential treatments. However, measuring the biochemical and mechanical properties of articular cartilage in these models currently requires destructive and time-consuming histology and mechanical testing. Therefore, we examined the feasibility of using contrast-enhanced CT (CECT) to rapidly and non-destructively image and assess the glycosaminoglycan (GAG) content. Using three ex vivo C57BL/6 mouse tibial plateaus, we determined the time required for the cationic contrast agent CA4+ to equilibrate in the cartilage. The whole-joint coefficient of friction (μ) of 10 mouse knees (some digested with Chondroitenase ABC to introduce variation in GAG) was evaluated using a modified Stanton pendulum. For both the medial and lateral tibial plateau cartilage of these knees, linear regression was used to compare the equilibrium CECT attenuations to μ, as well as each side's indentation equilibrium modulus (E) and Safranin-O determined GAG content. CA4+ equilibrated in the cartilage in 30.9 ± 0.95 min (mean ± SD, tau value of 6.17 ± 0.19 min). The mean medial and lateral CECT attenuation was correlated with μ (R(2)  = 0.69, p < 0.05), and the individual medial and lateral CECT attenuations correlated with their respective GAG contents (R(2)  ≥ 0.63, p < 0.05) and E (R(2)  ≥ 0.63, p < 0.05). In conclusion, CECT using CA4+ is a simple, non-destructive technique for three-dimensional imaging of ex vivo mouse cartilage, and significant correlations between CECT attenuation and GAG, E, and μ are observed. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1130-1138, 2016.

Cationic gadolinium chelate for magnetic resonance imaging of cartilaginous defects

The ability to detect meniscus defects by magnetic resonance arthrography (MRA) can be highly variable. To improve the delineation of fine tears, we synthesized a cationic gadolinium complex, (Gd-DOTA-AM4 )(2+) , that can electrostatically interact with Glycosaminoglycans (GAGs). The complex has a longitudinal relaxivity (r1) of 4.2 mM(-1) s(-1) and is highly stable in serum. Its efficacy in highlighting soft tissue tears was evaluated in comparison to a clinically employed contrast agent (Magnevist) using explants obtained from adult bovine menisci. In all cases, Gd-DOTA-AM4 appeared to improve the ability to detect the soft tissue defect by providing increased signal intensity along the length of the tear. Magnevist shows a strong signal near the liquid-meniscus interface, but much less contrast is observed within the defect at greater depths. This provides initial evidence that cationic contrast agents can be used to improve the diagnostic accuracy of MRA. Copyright © 2016 John Wiley & Sons, Ltd.

Contrast-enhanced CT facilitates rapid, non-destructive assessment of cartilage and bone properties of the human metacarpal

OBJECTIVE

The aim of this work is to establish the human metacarpal as a new whole joint surface early-stage osteoarthritis (OA) model that enables comparisons of articular cartilage and subchondral bone through high resolution contrast-enhanced CT (CECT) imaging, mechanical testing, and biochemical analysis.

DESIGN

The fourth metacarpal was obtained from 12 human cadaveric donors and baseline μCT imaging was followed by indentation testing. The samples were then immersed in anionic (Ioxaglate) and cationic (CA4+) iodinated contrast agent solutions followed by CECT. Cartilage GAG content and distribution was measured using the 1,9 dimethylmethylene blue (DMMB) assay and Safranin-O histology staining. Linear regression was performed to compare cartilage and subchondral bone properties.

RESULTS

Strong and significant positive correlations were observed between CA4+ CECT attenuation and both GAG content (R(2) = 0.86) and equilibrium modulus (R(2) = 0.84), while correlations using Ioxaglate were insignificant (R(2) ≤ 0.24, P > 0.05). Subchondral bone plate (SBP) thickness negatively and significantly correlated with SBP mineral density (R(2) = 0.49). Cartilage GAG content significantly correlated with several trabecular bone properties, including positive correlations with bone volume fraction (%BV/TV, R(2) = 0.67), trabecular number (Tb.N, R(2) = 0.60), and trabecular thickness (R(2) = 0.42), and negative relationships with structural model index (SMI, R(2) = 0.78) and trabecular spacing (Tb.Sp, R(2) = 0.56). Similarly, equilibrium modulus correlated positively with %BV/TV (R(2) = 0.50), Tb.N (R(2) = 0.59) and negatively with Tb.Sp (R(2) = 0.55) and SMI (R(2) = 0.60).

CONCLUSION

This study establishes the human metacarpal as a new early-stage OA model suitable for rapid, high resolution CECT imaging, mechanical testing, and biochemical analysis of the cartilage and subchondral bone, and for examining their inter-relationships.

Engineering iodine-doped carbon dots as dual-modal probes for fluorescence and X-ray CT imaging

X-ray computed tomography (CT) is the most commonly used imaging technique for noninvasive diagnosis of disease. In order to improve tissue specificity and prevent adverse effects, we report the design and synthesis of iodine-doped carbon dots (I-doped CDs) as efficient CT contrast agents and fluorescence probe by a facile bottom-up hydrothermal carbonization process. The as-prepared I-doped CDs are monodispersed spherical nanoparticles (a diameter of ~2.7 nm) with favorable dispersibility and colloidal stability in water. The aqueous solution of I-doped CDs showed wavelength-dependent excitation and stable photoluminescence similar to traditional carbon quantum dots. Importantly, I-doped CDs displayed superior X-ray attenuation properties in vitro and excellent biocompatibility. After intravenous injection, I-doped CDs were distributed throughout the body and excreted by renal clearance. These findings validated that I-doped CDs with high X-ray attenuation potency and favorable photoluminescence show great promise for biomedical research and disease diagnosis.

Depth-Dependent Glycosaminoglycan Concentration in Articular Cartilage by Quantitative Contrast-Enhanced Micro-Computed Tomography

OBJECTIVE

A quantitative contrast-enhanced micro-computed tomography (qCECT) method was developed to investigate the depth dependency and heterogeneity of the glycosaminoglycan (GAG) concentration of ex vivo cartilage equilibrated with an anionic radiographic contrast agent, Hexabrix.

DESIGN

Full-thickness fresh native (n = 19 in 3 subgroups) and trypsin-degraded (n = 6) articular cartilage blocks were imaged using micro-computed tomography (μCT) at high resolution (13.4 μm(3)) before and after equilibration with various Hexabrix bathing concentrations. The GAG concentration was calculated depth-dependently based on Gibbs-Donnan equilibrium theory. Analysis of variance with Tukey's post hoc was used to test for statistical significance (P < 0.05) for effect of Hexabrix bathing concentration, and for differences in bulk and zonal GAG concentrations individually and compared between native and trypsin-degraded cartilage.

RESULTS

The bulk GAG concentration was calculated to be 74.44 ± 6.09 and 11.99 ± 4.24 mg/mL for native and degraded cartilage, respectively. A statistical difference was demonstrated for bulk and zonal GAG between native and degraded cartilage (P < 0.032). A statistical difference was not demonstrated for bulk GAG when comparing Hexabrix bathing concentrations (P > 0.3214) for neither native nor degraded cartilage. Depth-dependent GAG analysis of native cartilage revealed a statistical difference only in the radial zone between 30% and 50% Hexabrix bathing concentrations.

CONCLUSIONS

This nondestructive qCECT methodology calculated the depth-dependent GAG concentration for both native and trypsin-degraded cartilage at high spatial resolution. qCECT allows for more detailed understanding of the topography and depth dependency, which could help diagnose health, degradation, and repair of native and contrived cartilage.

Cartilage-Specific Near-Infrared Fluorophores for Biomedical Imaging

A novel class of near-infrared fluorescent contrast agents was developed. These agents target cartilage with high specificity and this property is inherent to the chemical structure of the fluorophore. After a single low-dose intravenous injection and a clearance time of approximately 4 h, these agents bind to all three major types of cartilage (hyaline, elastic, and fibrocartilage) and perform equally well across species. Analysis of the chemical structure similarities revealed a potential pharmacophore for cartilage targeting. Our results lay the foundation for future improvements in tissue engineering, joint surgery, and cartilage-specific drug development.

Effect of mechanical convection on the partitioning of an anionic iodinated contrast agent in intact patellar cartilage

To determine if mechanical convection accelerates partitioning of an anionic contrast agent into cartilage while maintaining its ability to reflect the glycosaminoglycan (GAG) content in contrast-enhanced computed tomography (CECT) of cartilage. Bovine patellae (N = 4) were immersed in iothalamate and serially imaged over 24 h of passive diffusion at 34°C. Following saline washing for 14 h, each patella was serially imaged over 2.5 h of mechanical convection by cyclic compressive loading (120N, 1 Hz) while immersed in iothalamate at 34°C. After similar saline washing, each patella was sectioned into 15 blocks (n = 60) and contrast concentration per time point as well as GAG content were determined for each cartilage block. Mechanical convection produced 70.6%, 34.4%, and 16.4% higher contrast concentration at 30, 60, and 90 min, respectively, compared to passive diffusion (p < 0.001) and boosted initial contrast flux 330%. The correlation between contrast concentration and GAG content was significant at all time points and correlation coefficients improved with time, reaching R(2)  = 0.60 after 180 min of passive diffusion and 22.5 min of mechanical convection. Mechanical convection significantly accelerated partitioning of a contrast agent into healthy cartilage while maintaining strong correlations with GAG content, providing an evidence-based rationale for adopting walking regimens in CECT imaging protocols.

Rapid, automated imaging of mouse articular cartilage by microCT for early detection of osteoarthritis and finite element modelling of joint mechanics

OBJECTIVE

Mouse articular cartilage (AC) is mostly assessed by histopathology and its mechanics is poorly characterised. In this study: (1) we developed non-destructive imaging for quantitative assessment of AC morphology and (2) evaluated the mechanical implications of AC structural changes.

METHODS

Knee joints obtained from naïve mice and from mice with osteoarthritis (OA) induced by destabilization of medial meniscus (DMM) for 4 and 12 weeks, were imaged by phosphotungstic acid (PTA) contrast enhanced micro-computed tomography (PTA-CT) and scored by conventional histopathology. Our software (Matlab) automatically segmented tibial AC, drew two regions centred on each tibial condyle and evaluated the volumes included. A finite element (FE) model of the whole mouse joint was implemented to evaluate AC mechanics.

RESULTS

Our method achieved rapid, automated analysis of mouse AC (structural parameters in <10 h from knee dissection) and was able to localise AC loss in the central region of the medial tibial condyle. AC thickness decreased by 15% at 4 weeks and 25% at 12 weeks post DMM surgery, whereas histopathology scores were significantly increased only at 12 weeks. FE simulations estimated that AC thinning at early-stages in the DMM model (4 weeks) increases contact pressures (+39%) and Tresca stresses (+43%) in AC.

CONCLUSION

PTA-CT imaging is a fast and simple method to assess OA in murine models. Once applied more extensively to confirm its robustness, our approach will be useful for rapidly phenotyping genetically modified mice used for OA research and to improve the current understanding of mouse cartilage mechanics.

Imaging of cartilage and bone: promises and pitfalls in clinical trials of osteoarthritis

Imaging in clinical trials is used to evaluate subject eligibility, and/or efficacy of intervention, supporting decision making in drug development by ascertaining treatment effects on joint structure. This review focusses on imaging of bone and cartilage in clinical trials of (knee) osteoarthritis. We narratively review the full-text literature on imaging of bone and cartilage, adding primary experience in the implementation of imaging methods in clinical trials. Aims and constraints of applying imaging in clinical trials are outlined. The specific uses of semi-quantitative and quantitative imaging biomarkers of bone and cartilage in osteoarthritis trials are summarized, focusing on radiography and magnetic resonance imaging (MRI). Studies having compared both imaging methodologies directly and those having established a relationship between imaging biomarkers and clinical outcomes are highlighted. To make this review of practical use, recommendations are provided as to which imaging protocols are ideal for capturing specific aspects of bone and cartilage tissue, and pitfalls in their usage are highlighted. Further, the longitudinal sensitivity to change, of different imaging methods is reported for various patient strata. From these power calculations can be accomplished, provided the strength of the treatment effect is known. In conclusion, current imaging methodologies provide powerful tools for scoring and measuring morphological and compositional aspects of most articular tissues, capturing longitudinal change with reasonable to excellent sensitivity. When employed properly, imaging has tremendous potential for ascertaining treatment effects on various joint structures, potentially over shorter time scales than required for demonstrating effects on clinical outcomes.

Tantalum oxide nanoparticles for the imaging of articular cartilage using X-ray computed tomography: visualization of ex vivo/in vivo murine tibia and ex vivo human index finger cartilage

The synthesis and characterization of tantalum oxide (Ta2O5) nanoparticles (NPs) as new X-ray contrast media for microcomputed tomography (μCT) imaging of articular cartilage are reported. NPs, approximately 5-10 nm in size, and possessing distinct surface charges, were synthesized using phosphonate (neutral), ammonium (cationic), and carboxylate (anionic) ligands as end functional groups. Assessment of a cartilage defect in a human cadaver distal metacarpophalangeal (MCP) joint with the ammonium nanoparticles showed good visualization of damage and preferential uptake in areas surrounding the defect. Finally, an optimized nontoxic cationic NP contrast agent was evaluated in an in vivo murine model and the cartilage was imaged. These nanoparticles represent a new type of contrast agent for imaging articular cartilage, and the results demonstrate the importance of surface charge in the design of nanoparticulate agents for targeting the surface or interior zones of articular cartilage.

Contrast-Enhanced Nanofocus X-Ray Computed Tomography Allows Virtual Three-Dimensional Histopathology and Morphometric Analysis of Osteoarthritis in Small Animal Models

OBJECTIVE

One of the early hallmarks of osteoarthritis (OA) is a progressive degeneration of the articular cartilage. Early diagnosis of OA-associated cartilage alterations would be beneficial for disease prevention and control, and for the development of disease-modifying treatments. However, early diagnosis is still hampered by a lack of quantifiable readouts in preclinical models.

DESIGN

In this study, we have shown the potency of contrast-enhanced nanofocus x-ray computed tomography (CE-nanoCT) to be used for virtual 3-dimensional (3D) histopathology in established mouse models for OA, and we compared with standard histopathology.

RESULTS

We showed the equivalence of CE-nanoCT images to histopathology for the modified Mankin scoring of the cartilage structure and quality. Additionally, a limited set of 3D cartilage characteristics measured by CE-nanoCT image analysis in a user-independent and semiautomatic manner, that is, average and maximum of the noncalcified cartilage thickness distribution and loss in glycosaminoglycans, was shown to be predictive for the cartilage quality and structure as can be evaluated by histopathological scoring through the use of an empirical model.

CONCLUSIONS

We have shown that CE-nanoCT is a tool that allows virtual histopathology and 3D morphological quantification of multitissue systems, such as the chondro-osseous junction. It provides faster and more quantitative data on cartilage structure and quality compared with standard histopathology while eliminating user bias. CE-nanoCT thus should allow capturing subtle differences in cartilage characteristics, carefully mapping OA progression and, ultimately, asses the beneficial changes when testing a candidate disease-modifying treatment.

Contrast enhanced CT attenuation correlates with the GAG content of bovine meniscus

We determined whether contrast-enhanced computed tomography (CECT) attenuation obtained using a µCT scanner correlated with the glycosaminoglycan (GAG) content and distribution in ex vivo bovine menisci. Bovine samples were immersed in different concentrations of the contrast agents CA4+ and Ioxaglate, and the µCT images were compared to Safranin-O staining. CA4+ and Ioxaglate diffusion-in kinetics and the correlation between their CECT attenuations and GAG content were investigated. CA4+ and Ioxaglate both reached steady state in the meniscal regions within 95 h, with tau values of 20.6 ± 3.98 and 25.9 ± 3.71 h (mean ± SD), respectively. Both agents diffused preferentially through the proximal and secondarily through the distal surface. The CA4+ CECT attenuation was strongly and positively correlated with the GAG content of the meniscus regions (R(2)  = 0.89, p < 0.001) at low concentrations (12 mgI/ml), while the Ioxaglate CECT attenuation was moderately and negatively correlated with the GAG content (R(2)  = 0.51, p = 0.03) at 60 mgI/ml. CECT can image ex vivo menisci, and the CA4+, compared to Ioxaglate, enhanced attenuation strongly correlates with the GAG content and distribution in bovine meniscus.

Osteoarthritis year 2013 in review: imaging

PURPOSE

To review recent original research publications related to imaging of osteoarthritis (OA) and identify emerging trends and significant advances.

METHODS

Relevant articles were identified through a search of the PubMed database using the query terms "OA" in combination with "imaging", "radiography", "MRI", "ultrasound", "computed tomography", and "nuclear medicine"; either published or in press between March 2012 and March 2013. Abstracts were reviewed to exclude review articles, case reports, and studies not focused on imaging using routine clinical imaging measures.

RESULTS

Initial query yielded 932 references, which were reduced to 328 citations following the initial review. MRI (118 references) and radiography (129 refs) remain the primary imaging modalities in OA studies, with fewer reports using computed tomography (CT) (35 refs) and ultrasound (23 refs). MRI parametric mapping techniques remain an active research area (33 refs) with growth in T2*- and T1-rho mapping publications compared to prior years. Although the knee is the major joint studied (210 refs) there is interest in the hip (106 refs) and hand (29 refs). Imaging continues to focus on evaluation of cartilage (173 refs) and bone (119 refs).

CONCLUSION

Imaging plays a major role in OA research with publications continuing along traditional lines of investigation. Translational and clinical research application of compositional MRI techniques is becoming more common driven in part by the availability of T2 mapping data from the Osteoarthritis Initiative (OAI). New imaging techniques continue to be developed with a goal of identifying methods with greater specificity and responsiveness to changes in the joint, and novel functional neuroimaging techniques to study central pain. Publications related to imaging of OA continue to be heavily focused on quantitative and semiquantitative MRI evaluation of the knee with increasing application of compositional MRI techniques in the hip.

Cationic agent contrast-enhanced computed tomography imaging of cartilage correlates with the compressive modulus and coefficient of friction

OBJECTIVE

The aim of this study is to evaluate whether contrast-enhanced computed tomography (CECT) attenuation, using a cationic contrast agent (CA4+), correlates with the equilibrium compressive modulus (E) and coefficient of friction (μ) of ex vivo bovine articular cartilage.

METHODS

Correlations between CECT attenuation and E (Group 1, n = 12) and μ (Group 2, n = 10) were determined using 7 mm diameter bovine osteochondral plugs from the stifle joints of six freshly slaughtered, skeletally mature cows. The equilibrium compressive modulus was measured using a four-step, unconfined, compressive stress-relaxation test, and the coefficients of friction were determined from a torsional friction test. Following mechanical testing, samples were immersed in CA4+, imaged using μCT, rinsed, and analyzed for glycosaminoglycan (GAG) content using the 1,9-dimethylmethylene blue (DMMB) assay.

RESULTS

The CECT attenuation was positively correlated with the GAG content of bovine cartilage (R(2) = 0.87, P < 0.0001 for Group 1 and R(2) = 0.74, P = 0.001 for Group 2). Strong and significant positive correlations were observed between E and GAG content (R(2) = 0.90, P < 0.0001) as well as CECT attenuation and E (R(2) = 0.90, P < 0.0001). The CECT attenuation was negatively correlated with the three coefficients of friction: CECT vs μ(static) (R(2) = 0.71, P = 0.002), CECT vs μ(static_equilibrium) (R(2) = 0.79, P < 0.001), and CECT vs μ(kinetic) (R(2) = 0.69, P = 0.003).

CONCLUSIONS

CECT with CA4+ is a useful tool for determining the mechanical properties of ex vivo cartilage tissue as the attenuation significantly correlates with the compressive modulus and coefficient of friction.