Stiffness Maps Research Articles

The nanomechanical signature of breast cancer

Cancer initiation and progression follow complex molecular and structural changes in the extracellular matrix and cellular architecture of living tissue. However, it remains poorly understood how the transformation from health to malignancy alters the mechanical properties of cells within the tumour microenvironment. Here, we show using an indentation-type atomic force microscope (IT-AFM) that unadulterated human breast biopsies display distinct stiffness profiles. Correlative stiffness maps obtained on normal and benign tissues show uniform stiffness profiles that are characterized by a single distinct peak. In contrast, malignant tissues have a broad distribution resulting from tissue heterogeneity, with a prominent low-stiffness peak representative of cancer cells. Similar findings are seen in specific stages of breast cancer in MMTV-PyMT transgenic mice. Further evidence obtained from the lungs of mice with late-stage tumours shows that migration and metastatic spreading is correlated to the low stiffness of hypoxia-associated cancer cells. Overall, nanomechanical profiling by IT-AFM provides quantitative indicators in the clinical diagnostics of breast cancer with translational significance.

Complex Stiffness Gradient Substrates for Studying Mechanotactic Cell Migration

Polyacrylamide gels are cast upon a stiff support with controlled topography, resulting in a thin gel layer of variable height. The topographical profiles project a stiffness map onto the gel, resulting in controlled linear and non-linear 2D stiffness gradients. Fibroblasts, which migrate towards stiffer substrates, accumulate in areas with a gel thickness below 15 μm.

Adhesin Contribution to Nanomechanical Properties of the Virulent Bordetella pertussis Envelope

Adherence to a biological surface allows bacteria to colonize and persist within the host and represents an essential first step in the pathogenesis of most bacterial diseases. Consequently, the physicochemical properties of the outer membrane in bacteria play a key role for attachment to surfaces and therefore for biofilm formation. Bordetella pertussis is a Gram-negative bacterium that colonizes the respiratory tract of humans, producing whooping cough or pertussis, a highly infectious disease. B. pertussis uses various adhesins exposed on its surface to promote cell-surface and cell-cell interactions. The most dominant adhesin function is displayed by filamentous hemagglutinin (FHA). B. pertussis Tohama I wild-type (Vir+) strain and two defective mutants, an avirulent (Vir-) and a FHA-deficient (FHA-) B. pertussis strains were studied by AFM under physiological conditions to evaluate how the presence or absence of adhesins affects the mechanical properties of the B. pertussis cell surface. Quantitative information on the nanomechanical properties of the bacterial envelope was obtained by AFM force-volume analysis. These studies suggested that the presence of virulence factors is correlated with an increase in the average membrane rigidity, which is largely influenced by the presence of FHA. Moreover, for this system we built a nanoscale stiffness map that reveals an inhomogeneous spatial distribution of Young modulus as well as the presence of rigid nanodomains on the cell surface.

Stiffness tomography exploration of living and fixed macrophages

Stiffness tomography is a new atomic force microscopy imaging technique that allows highlighting structures located underneath the surface of the sample. In this imaging mode, such structures are identified by investigating their mechanical properties. We present here, for the first time, a description of the use of this technique to acquire detailed stiffness maps of fixed and living macrophages. Indeed, the mechanical properties of several macrophages were studied through stiffness tomography imaging, allowing some insight of the structures lying below the cell's surface. Through these investigations, we were able to evidence the presence and properties of stiff column-like features located underneath the cell membrane. To our knowledge, this is the first evidence of the presence, underneath the cell membrane, of such stiff features, which are in dimension and form compatible with phagosomes. Moreover, by exposing the cells to cytochalasin, we were able to study the induced modifications, obtaining an indication of the location and mechanical properties of the actin cytoskeleton.

Magnetic Resonance Elastography Methodology for the Evaluation of Tissue Engineered Construct Growth

Traditional mechanical testing often results in the destruction of the sample, and in the case of long term tissue engineered construct studies, the use of destructive assessment is not acceptable. A proposed alternative is the use of an imaging process called magnetic resonance elastography. Elastography is a nondestructive method for determining the engineered outcome by measuring local mechanical property values (i.e., complex shear modulus), which are essential markers for identifying the structure and functionality of a tissue. As a noninvasive means for evaluation, the monitoring of engineered constructs with imaging modalities such as magnetic resonance imaging (MRI) has seen increasing interest in the past decade. For example, the magnetic resonance (MR) techniques of diffusion and relaxometry have been able to characterize the changes in chemical and physical properties during engineered tissue development. The method proposed in the following protocol uses microscopic magnetic resonance elastography (μMRE) as a noninvasive MR based technique for measuring the mechanical properties of small soft tissues. MRE is achieved by coupling a sonic mechanical actuator with the tissue of interest and recording the shear wave propagation with an MR scanner. Recently, μMRE has been applied in tissue engineering to acquire essential growth information that is traditionally measured using destructive mechanical macroscopic techniques. In the following procedure, elastography is achieved through the imaging of engineered constructs with a modified Hahn spin-echo sequence coupled with a mechanical actuator. As shown in Figure 1, the modified sequence synchronizes image acquisition with the transmission of external shear waves; subsequently, the motion is sensitized through the use of oscillating bipolar pairs. Following collection of images with positive and negative motion sensitization, complex division of the data produce a shear wave image. Then, the image is assessed using an inversion algorithm to generate a shear stiffness map. The resulting measurements at each voxel have been shown to strongly correlate (R(2)>0.9914) with data collected using dynamic mechanical analysis. In this study, elastography is integrated into the tissue development process for monitoring human mesenchymal stem cell (hMSC) differentiation into adipogenic and osteogenic constructs as shown in Figure 2.

Accuracy of MR elastography and anatomic MR imaging features in the diagnosis of severe hepatic fibrosis and cirrhosis

To compare the diagnostic accuracy of magnetic resonance imaging elastography (MRE) and anatomic MRI features in the diagnosis of severe hepatic fibrosis and cirrhosis. Three readers independently assessed presence of morphological changes associated with hepatic fibrosis in 72 patients with liver biopsy including: caudate to right lobe ratios, nodularity, portal venous hypertension (PVH) stigmata, posterior hepatic notch, expanded gallbladder fossa, and right hepatic vein caliber. Three readers measured shear stiffness values using quantitative shear stiffness maps (elastograms). Sensitivity, specificity, and diagnostic accuracy of stiffness values and each morphological feature were calculated. Interreader agreement was summarized using weighted kappa statistics. Intraclass correlation coefficient was used to assess interreader reproducibility of stiffness measurements. Binary logistic regression was used to assess interreader variability for dichotomized stiffness values and each morphological feature. Using 5.9 kPa as a cutoff for differentiating F3-F4 from F0-2 stages, overall sensitivity, specificity, and diagnostic accuracy for MRE were 85.4%, 88.4%, and 87%, respectively. Overall interreader agreement for stiffness values was substantial, with an insignificant difference (P = 0.74) in the frequency of differentiating F3-4 from F0-2 fibrosis. Only hepatic nodularity and PVH stigmata showed moderately high overall accuracy of 69.4% and 72.2%. Interreader agreement was substantial only for PVH stigmata, moderate for C/R m, deep notch, and expanded gallbladder fossa. Only posterior hepatic notch (P = 0.82) showed no significant difference in reader rating. MRE is a noninvasive, accurate, and reproducible technique compared with conventional features of detecting severe hepatic fibrosis.

Quantifying Local Stiffness Variations in Radiofrequency Ablations With Dynamic Indentation

Elastographic imaging can be used to monitor ablation procedures; however, confident and clear determination of the ablation boundary is essential to ensure complete treatment of the pathological target. To investigate the potential for ablation boundary representation on elastographic images, local variations in the viscoelastic properties in radiofrequency-ablated regions that were formed in vivo in porcine liver tissue were quantified using dynamic indentation. Spatial stiffness maps were then correlated to stained histology, the gold standard for the determination of the ablation periphery or boundary. Regions of interest in 11 radiofrequency ablation samples were indented at 18-24 locations each, including the central zone of complete necrosis and more peripheral transition zones including normal tissue. Storage modulus and the rate of stiffening were both greatest in the central ablation zone and decreased with radial distance away from the center. The storage modulus and modulus contrast at the ablation outer transition zone boundary were 3.1 ± 1.0 kPa and 1.6 ± 0.4, respectively, and 36.2 ± 9.1 kPa and 18.3 ± 5.5 at the condensation boundary within the ablation zone. Elastographic imaging modalities were then compared to gross pathology in ex vivo bovine liver tissue. Area estimated from strain, shear-wave velocity, and gross pathology images were 470, 560, and 574 mm(2), respectively, and ablation widths were 19.4, 20.7, and 23.0 mm. This study has provided insights into spatial stiffness distributions within radiofrequency ablations and suggests that low stiffness contrast on the ablation periphery leads to the observed underestimation of ablation extent on elastographic images.

A novel tactile-guided detection and three-dimensional localization of clinically significant breast masses

This paper presents a novel robotic sensory system ‘Robo-Tac-BMI’, which manipulates an indentation probe for the detection and three-dimensional localization of an abnormal mass embedded in the breast tissue. The Robo-Tac-BMI is designed based on artificial tactile sensing technology which is a new non-invasive method for mimicking the surgeon’s palpation quantitatively. The intelligent processor of the device provides an overall stiffness map of the scanned areas. The extracted stiffness parameters provide a decisive factor for certifying the mass existence. Results are validated by ‘gold standard’ tests. Following the mass detection, its 3D localization is of essential importance in the treatment procedures. The planar 2D coordinate is readily available for all points on the tissue surface. Mass depth estimation is achieved by a comprehensive model utilizing the logistic regression algorithm and a Receiver Operating Characteristic (ROC) Curve for the highest accuracy. Statistical analysis is performed over 27 cases with 346 scanned areas.

Magnetic resonance elastography: Feasibility of liver stiffness measurements in healthy volunteers at 3 T

To demonstrate the feasibility of obtaining liver stiffness measurements with magnetic resonance elastography (MRE) at 3T in normal healthy volunteers using the same technique that has been successfully applied at 1.5 T. The study was approved by the local ethics committee and written informed consent was obtained from all volunteers. Eleven volunteers (mean age 35 ± 9 years) with no history of gastrointestinal, hepatobiliary, or cardiovascular disease were recruited. The magnetic resonance imaging (MRI) protocol included a gradient echo-based MRE sequence using a 60 Hz pneumatic excitation. The MRE images were processed using a local frequency estimation inversion algorithm to provide quantitative stiffness maps. Adequate image quality was assessed subjectively by demonstrating the presence of visible propagating waves within the liver parenchyma underlying the driver location. Liver stiffness values were obtained using manually placed regions of interest (ROI) outlining the liver margins on the gradient echo wave images, which were then mapped onto the corresponding stiffness image. The mean stiffness values from two adjacent sections were recorded. Eleven volunteers underwent MRE. The quality of the MRE images was adequate in all the volunteers. The mean liver stiffness for the group was 2.3 ± 0.38 kPa (ranging from 1.7-2.8 kPa). This preliminary work using MRE at 3T in healthy volunteers demonstrates the feasibility of liver stiffness evaluation at 3T without modification of the approach used at 1.5 T. Adequate image quality and normal MRE values were obtained in all volunteers. The obtained stiffness values were in the range of those reported for healthy volunteers in previous studies at 1.5 T. There was good interobserver reproducibility in the stiffness measurements.

Transverse shear modulus of SILICOMB cellular structures

This work describes the transverse shear stiffness properties of a novel honeycomb with zero Poisson’s ratio. The cellular configuration is simulated using a series of finite element models representing full-scale and representative unit cells of the honeycomb topology. The models are benchmarked against experimental results from pure shear and 3-point bending ASTM tests. The benchmarked models are used to perform a parametric study of the shear moduli ( G 13 and G 23) against the geometry of the unit cell and the gauge thickness of the honeycomb panels. The shear stiffness maps obtained allow comparison of the SILICOMB configuration against classical centresymmetric and rectangular honeycomb topologies.

Mechanical Mapping of Single Proteins at Subnanometer Resolution using AFM

The structure and function of proteins are determined by their mechanical stability. The temperature- or B-factors obtained from crystallographic data provide an indirect measure of the order and stability of the protein, together with structural information. However, B-factors from crystallography analysis may be related to the protein packing in the 3D-crystal and are not quantitative. A direct quantification of the mechanical stability of proteins based on atomic force microscopy (AFM) consists in mechanically unfolding individual proteins by pulling from two points. However, its correlation with protein structure requires additional measurements. In this work we apply a novel AFM imaging mode based on force spectroscopy (PeakForce) to simultaneously acquire structural and mechanical information of membrane proteins. We used the well-known protein bacteriorhodopsin from Halobaterium salinarum as a model system, obtaining topographical and stiffness maps with subnanometer resolution. The characteristic trimeric organization of the trigonally packed (a = b = 62.5A; γ= 120°) bacteriorhodopsin was clearly visible with inter-monomer distances of 3.2 nm. Overlay of stiffness and topography maps allowed the investigation of nanomechanical properties at the single molecule level providing a map of the structural stability of bacteriorhodopsin.View Large Image | View Hi-Res Image | Download PowerPoint Slide

On an Inverse Problem from Magnetic Resonance Elastic Imaging

The imaging problem of elastography is an inverse problem. The nature of an inverse problem is that it is ill-conditioned. We consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging (MRI). This map is a nonlinear mapping, and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography. In this treatment we consider the tissue to be linearly elastic, isotropic, and spatially heterogeneous. We determine the conditioning of this problem of function reconstruction, in particular for the stiffness function. We further examine the conditioning when determining both stiffness and density. We examine the Frechet derivative of the nonlinear mapping, which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions. We illustrate how use of the implicit function theorem can considerably simplify the analysis of Frechet differentiability and regularity properties of this underlying operator. We present new results which show that the stiffness map is mildly ill-posed, whereas the density map suffers from medium ill-conditioning. Computational work has been done previously to study the sensitivity of these maps, but our work here is analytical. The validity of the Newton-Kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the Frechet differentiability of the appropriate nonlinear operator, which we justify.

WE‐D‐201C‐02: MRI‐Guided Transurethral Diagnosis and Treatment of Localized Prostate Cancer

Minimally‐invasive, image‐guided treatments for localized prostate cancer that provide local control with a low side‐effect profile would have a major impact in improving disease management. Accurate localization of disease with imaging coupled with technologies capable of precise treatment could enable evolution of prostate cancer treatment from a whole gland to a more targeted approach. MRI‐guided transurethral ultrasound therapy is such a technology in which high‐intensity ultrasound energy is delivered to the prostate from a device inserted into the urethra. The goal of the treatment is to generate a prescribed spatial pattern of thermal coagulation in the gland. The treatment is performed in a closed‐bore MR imager to obtain quantitative temperature maps during ultrasound heating of the prostate. This temperature information is used by the treatment delivery system to adapt the exposure conditions dynamically during treatment to compensate for changes in blood flow, tissue absorption and thermal conduction. Previous numerical, phantom, and canine studies have demonstrated that this approach offers a high degree of spatial treatment accuracy (±1–2 mm). Recent clinical evaluation of the technology has confirmed the feasibility of performing this treatment in humans. The desire to deliver more targeted treatments in the prostate for reduced morbidity requires accurate localization of disease, ideally with medical imaging. A unique opportunity that exists in transurethral ultrasound therapy is to generate shear waves in the adjacent prostate gland through vibration of the device. These shear waves can be imaged with MRI and quantitative stiffness maps can be calculated for localization of disease, or evaluation of the pattern of thermal coagulation in the gland. Initial experiments have been performed in phantoms and canines to explore the feasibility of this concept. This presentation will introduce the concept of transurethral ultrasound therapy and will review the results obtained with this technology. In addition the potential to combine this therapy with diagnostic approaches such as MR elastography will be discussed.Learning Objectives:1. Describe the role of high‐intensity ultrasound therapy for prostate cancer treatment.2. Describe the technology for transurethral ultrasound therapy3. Explain the potential role of prostate MR elastography for prostate imaging/diagnosis using transurethral devices4. Describe the potential of quantitative MR temperature feedback in achieving closed‐loop heating in vivo, and challenges in its implementation

Mapping Elasticity Down to the Molecular Scale: a Novel High-Resolution Approach to Study Cell Mechanics

The mechanical properties of cells govern a variety of processes critical for the control of their behavior, and they are strongly determined by the cytoskeleton. These observations have inspired numerous studies on cells and reconstituted cytoskeletal networks. However, it remains a challenging task to relate structural and mechanical properties on the molecular scale within living materials.To analyze cell mechanical properties on the molecular scale, we used recently developed torsional harmonic cantilevers to obtain high-speed force-distance curves in parallel to high-resolution AFM tapping mode images in fluid. By applying this technique, we were able to acquire stiffness maps of living cells at an unparalleled spatial and temporal resolution (50-100 nm, 4-8 min for a 30 µm scan). Furthermore, we were also able to map the elasticity of a reconstituted actin network, which has not been achieved before. In combination with optical techniques this opens up a unique simultaneous view of the mechanics of the living cell and the mechanical properties of its relevant molecular components.View Large Image | View Hi-Res Image | Download PowerPoint SlideElasticity maps of a live HUVEC cell (30 µm scan)

Dynamic Characteristic Analysis for Machine Tools Based on Concept of Generalized Manufacturing Space

Aiming at studying the variation of the machine tools' dynamic characteristics in generalized manufacturing space,a concept of generalized modal and dynamic stiffness is put forward. Finite element method is employed to set up dynamic models for a three-axis gantry-type machine tool and a four-axis vertical machine tool. Modal and dynamic response analysis are carried out through out the whole manufacturing space with dynamic model modified method,in order to establish generalized modal function and stiffness map function respectively. By means of generalized modal analysis for three-axis gantry machine tool,the first five order natural frequencies of the machine tool through out the manufacturing space are obtained. The results show that the maximum change of natural frequencies can reach up to 25% during machining process,so complete modal information is obtained to provide data for performance optimization of machine tool. With the analysis of generalized dynamic stiffness for four-axis vertical machine tool,it can be concluded that the best working state in some frequency is not the best one for another,and then the theoretical support is present for the process optimization and accuracy promotion of machine tools.

Stiffness Analysis of 3-RPR Planar Parallel Mechanism to the Stiffness Control

The analytical stiffness equations of the 3-RPR planar parallel mechanism are derived in this paper based on the Conservative Congruence Transformation (CCT) stiffness matrix proposed in [1-3]. Stiffness maps of the 3-RPR mechanism are plotted in order to show the behaviour of the stiffness with and without external forces. The stiffness characteristics of the mechanism are analyzed and discussed in details. Numerical examples show that the stiffness in x and in y are well balanced, while the stiffness in tends to be lower.

A methodology for static stiffness mapping in lower mobility parallel manipulators with decoupled motions

SUMMARYIn this paper a general methodology for obtaining static stiffness maps in lower mobility parallel manipulators is proposed. The main objective is to define a set of guidelines, which allow the experimental work to be optimized and computational time to be reduced. First, a two-degree-of-freedom (DOF) mechanism will be used for methodology validation, since it is the stiffness of the basic kinematic chain of the manipulator that is to be analysed. Two mathematical models of this mechanism and an experimental prototype will be considered for the validation. After that, the methodology will be applied to a lower mobility (4-DOF) parallel manipulator. In this paper, the experimental prototype and its set-up is highly important because some particular features of the experimental analysis will be defined. This paper introduces a key experimental tool: the preload, which allows the clearances and possible assembling errors to be considered. The added value from the application of this procedure is the obtaining of graphs that describe, in an intuitive and useful way, the behaviour of the manipulator's stiffness inside its workspace as a function of the mobile platform position and orientation.

TREMR: Table‐resonance elastography with MR

Magnetic resonance elastography (MRE) is a noninvasive method of measuring tissue compliance. Current MRE methods rely on custom-built hardware to elicit vibrations that are tracked by MR imaging. Knowledge of the wave propagation can be used to calculate the local shear stiffness of the tissue. We sought to determine whether the vibrations of the patient table that result from low-frequency switching of the imaging gradients could be used as an alternative mechanical driving mechanism for MRE. We designed a pulse sequence that includes a gradient lobe specifically for the excitation of mechanical resonance, allowing control of the time between the onset of the vibrations and the velocity-encoding of the readout. Data collected from a gelatin phantom with stiff cylindrical gelatin inserts demonstrated that wave propagation can be imaged with this method. Postprocessing to estimate the local spatial frequency of the waves also allows estimation of the local shear stiffness, where the stiff inserts are clearly identifiable. Data collected on the brain of a normal healthy volunteer showed clear rotational waves propagating from the skull inwards, also allowing generation of shear stiffness maps.

Characterizing interfacial structure of TPO/CPO/TPO adhesive joints by PFM–AFM and SEM

The influence of annealing and EBR component in injection-molded thermoplastic polyolefin (TPO) plaques on adhesion strength of CPO to TPO was investigated by a lap shear test. The TPO was fabricated as a blend of highly crystalline isotactic polypropylene (iPP) and low crystalline poly(ethylene-butene) impact modifier (EBR28). The CPO was a maleated chlorinated polypropylene containing 21.8wt% Cl. High resolution pulsed force mode–atomic force microscopy (PFM–AFM) combined with the image analysis was used to characterize the interfacial properties of the lap shear joints. Based on PFM–AFM stiffness images, a “transition zone” with a width on the order of 600–1500nm was observed between CPO and the TPO substrate that may play an important role in affecting the adhesion strength. This zone exhibits enhanced stiffness after annealing at 120°C. The PFM–AFM images further show that the interface between iPP and CPO without annealing is very sharp and the interface between TPO and CPO without annealing is wider than the interface between iPP and CPO. Annealing (120°C/20min) leads to broadening of the interface between TPO and CPO. The thickness of the interface in lap shear joints was obtained from the z-directional line profiles of the stiffness maps. The fracture surface morphology was revealed by scanning electronic microscope (SEM), which showed that the fracture structure varied with both the addition of EBR28 in TPO plaques and the annealing condition. Finally, a correlation of interfacial properties to adhesion was obtained: higher stiffness in the transition zone coupled with a thicker interface resulted in stronger adhesion and cohesive failure within the CPO and TPO. In the case of CPO/iPP, the narrow interface and absence of a clearly defined transition zone correlated with interfacial failure between these components.

High-Resolution Quantitative Imaging of Cornea Elasticity Using Supersonic Shear Imaging

The noninvasive estimation of in vivo mechanical properties of cornea is envisioned to find several applications in ophthalmology. Such high-resolution measurements of local cornea stiffness could lead to a better anticipation and understanding of corneal pathologies such as Keratoconus. It could also provide a quantitative evaluation of corneal biomechanical response after corneal refractive surgeries and a tool for evaluating the efficacy of new cornea treatments such as cornea transplant using femtosecond laser or therapy based on Riboflavin/UltraViolet-A Corneal Cross Linking (UVA CXL). In the very important issue of glaucoma diagnosis and management, the fine tuning corneal elasticity measurement could also succeed to strongly correlate the applanation tonometry with the "true" intra-ocular pressure (IOP). This initial investigation evaluates the ability of ultrafast and high-resolution ultrasonic systems to provide a real-time and quantitative mapping of corneal viscoelasticity. Quantitative elasticity maps were acquired ex vivo on porcine cornea using the supersonic shear imaging (SSI) technique. A conventional 15 MHz linear probe was used to perform conventional ultrasonic imaging of the cornea. A dedicated ultrasonic sequence combines the generation of a remote palpation in the cornea and ultrafast (20,000 frames/s) ultrasonic imaging of the resulting corneal displacements that evolve into a shear wave propagation whose local speed was directly linked to local elasticity. A quantitative high-resolution map (150 microm resolution) of local corneal elasticity can be provided by this dedicated sequence of ultrasonic insonifications. Quantitative maps of corneal elasticity were obtained on ex vivo freshly enucleated porcine corneas. In the cornea, a quite homogenous stiffness map was found with a 190 kPa +/- 32 kPa mean elasticity. The influence of photodynamic Riboflavin/UVA induced CXL was measured. A significant Young's modulus increase was obtained with a mean 890 kPa +/- 250 kPa posttreatment Young's modulus (460% increase), located in the anterior part of the cornea. Simulations based on 3-D time domain finite differences simulation were also performed and found to be in good agreement with ex vivo experiments. The SSI technique can perform real-time, noninvasive, high-resolution, and quantitative maps of the whole corneal elasticity. This technique could be real time and straightforward adapted for a very wide field of in vivo investigations.