A Noninvasive Clinical Method to Measure in Vivo Mechanical Strains of the Lamina Cribrosa by OCT

Objective

To measure mechanical strain of the lamina cribrosa (LC) after intraocular pressure (IOP) change produced 1 week after a change in glaucoma medication.

Design

Cohort study.

Participants

Adult glaucoma patients (23 eyes, 15 patients) prescribed a change in IOP-lowering medication.

Intervention

Noninvasive OCT imaging of the eye.

Main Outcome Measures

Deformation calculated by digital volume correlation of OCT scans of the LC before and after IOP lowering by medication.

Results

Among 23 eyes, 17 eyes of 12 persons had IOP lowering ≥ 3 mmHg (reduced IOP group) with tensile anterior-posterior Ezz strain = 1.0% ± 1.1% (P = 0.003) and compressive radial strain (Err) = -0.3% ± 0.5% (P = 0.012; random effects models accounting inclusion of both eyes in some persons). Maximum in-plane principal (tensile) strain and maximum shear strain in the reduced-IOP group were as follows: Emax = 1.7% ± 1.0% and Γmax = 1.4% ± 0.7%, respectively (both P < 0.0001 vs. zero). Reduced-IOP group strains Emax and Γmax were significantly larger with greater % IOP decrease (P < 0.0001 and P < 0.0001, respectively). The compliances of the Ezz, Emax, and Γmax strain responses, defined as strain normalized by the IOP decrease, were larger with more abnormal perimetric mean deviation or visual field index values (all P ≤ 0.02). Strains were unrelated to age (all P ≥ 0.088). In reduced-IOP eyes, mean LC anterior border posterior movement was only 2.05 μm posteriorly (P = 0.052) and not related to % IOP change (P = 0.94, random effects models). Only Err was significantly related to anterior lamina depth change, becoming more negative with greater posterior LC border change (P = 0.015).

Conclusions

Lamina cribrosa mechanical strains can be effectively measured by changes in eye drop medication using OCT and are related to degree of visual function loss in glaucoma.

Financial Disclosures

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Long-term Remodeling Response in the Lamina Cribrosa Years after Intraocular Pressure Lowering by Suturelysis after Trabeculectomy

OBJECTIVE

To measure the remodeling of the lamina cribrosa (LC) years after intraocular pressure (IOP) lowering by suturelysis.

DESIGN

Cohort study.

PARTICIPANTS

Glaucoma patients were imaged 20 minutes after laser suturelysis after trabeculectomy surgery and at their follow-up appointment 1 to 4 years later (16 image pairs; 15 persons).

INTERVENTION

Noninvasive OCT imaging of the eye.

MAIN OUTCOME MEASURES

Deformation calculated by correlating OCT scans of the LC immediately after IOP lowering by suturelysis and those acquired years later (defined as remodeling strain).

RESULTS

The LC anterior border moved 60.9 ± 54.6 μm into the eye (P = 0.0007), and the LC exhibited regions of large local stretch in the anterior-posterior direction on long-term, maintained IOP lowering, resulting in a mean anterior-posterior remodeling strain of 14.0% ± 21.3% (P = 0.02). This strain and the LC border movement was 14 times and 124 times larger, respectively, than the direct response to IOP lowering by suturelysis. A larger anterior LC border movement was associated with greater mean anterior-posterior remodeling strain (P = 0.004). A thinner retinal nerve fiber layer at suturelysis was also associated with greater mean anterior-posterior remodeling strain at follow-up (P = 0.05). Worsening visual field indexes during follow-up were associated with a greater mean circumferential remodeling strain (P = 0.02), due to regions of large local circumferential stretch of the LC. Eyes with a more compliant LC torsional shear strain response at lysis were associated with worse mean deviation at follow-up (P = 0.03).

CONCLUSIONS

Strains and LC border position changes measured years after IOP lowering are far larger than the immediate response to IOP lowering and indicate dramatic remodeling of the LC anatomical structure caused by IOP lowering and glaucoma progression. The remodeling strains indicate substantial local stretch in the anterior-posterior direction and are associated with movement of the LC anterior border into the eye. Eyes with greater direct strain response to IOP lowering, greater glaucoma damage at suturelysis, and greater worsening of visual field at follow-up experienced greater remodeling.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT03267849.

FINANCIAL DISCLOSURE(S)

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Comparison of two contrast-enhancing staining agents for use in X-ray imaging and digital volume correlation measurements across the cartilage-bone interface

OBJECTIVE

The pathogenesis of osteoarthritis (OA) is associated with subchondral bone changes, which is linked to abnormal strain distribution in the overlying articular cartilage. This highlights the importance of understanding mechanical interaction at the cartilage-bone interface. The aim of this study is to compare solutions of two contrast-enhancing staining agents (CESA) for combining high-resolution Contrast-Enhanced X-ray microfocus Computed Tomography (CECT) with Digital Volume Correlation (DVC) for full-field strain measurements at the cartilage-bone interface.

DESIGN

Bovine osteochondral plugs were stained with phosphotungstic acid (PTA) in 70% ethanol or 1:2 hafnium-substituted Wells-Dawson polyoxometalate (Hf-WD POM) in PBS. Mechanical properties were assessed using micromechanical probing and nanoindentation. Strain uncertainties (from CECT data) were evaluated following two consecutive unloaded scans. Residual strains were computed following unconfined compression (ex situ) testing.

RESULTS

PTA and Hf-WD POM enabled the visualisation of structural features in cartilage, allowing DVC computation on the CECT data. Residual strains up to ∼10,000 μɛ were detected up to the tidemark. Nanoindentation showed that PTA-staining caused an average ∼6-fold increase in articular cartilage stiffness, a ∼19-fold increase in reduced modulus and ∼7-fold increase in hardness, whereas Hf-WD POM-stained specimens had mechanical properties similar to pre-stain tissue. Micromechanical probing showed a 77% increase in cartilage surface stiffness after PTA-staining, in comparison to a 16% increase in stiffness after staining with Hf-WD POM.

CONCLUSION

Hf-WD POM is a more suitable CESA solution compared to PTA for CECT imaging combined with DVC as it allowed visualisation of structural features in the cartilage tissue whilst more closely maintaining tissue mechanical properties.

Full-field strain distribution in hierarchical electrospun nanofibrous poly-L(lactic) acid/collagen scaffolds for tendon and ligament regeneration: A multiscale study

Regeneration of injured tendons and ligaments (T/L) is a worldwide need. In this study electrospun hierarchical scaffolds made of a poly-L (lactic) acid/collagen blend were developed reproducing all the multiscale levels of aggregation of these tissues. Scanning electron microscopy, microCT and tensile mechanical tests were carried out, including a multiscale digital volume correlation analysis to measure the full-field strain distribution of electrospun structures. The principal strains (εp1 and εp3) described the pattern of strains caused by the nanofibers rearrangement, while the deviatoric strains (εD) revealed the related internal sliding of nanofibers and bundles. The results of this study confirmed the biomimicry of such electrospun hierarchical scaffolds, paving the way to further tissue engineering and clinical applications.

Quantifying the immediate post-implantation strain field of cadaveric tibiae implanted with cementless tibial trays: A time-elapsed micro-CT and digital volume correlation analysis during stair descent

Primary stability, the mechanical fixation between implant and bone prior to osseointegration, is crucial for the long-term success of cementless tibial trays. However, little is known about the mechanical interplay between the implant and bone internally, as experimental studies quantifying internal strain are limited. This study employed digital volume correlation (DVC) to quantify the immediate post-implantation strain field of five cadaveric tibiae implanted with a commercially available cementless titanium tibial tray (Attune, DePuy Synthes). The tibiae were subjected to a five-step loading sequence (0-2.5 bodyweight, BW) replicating stair descent, with concomitant time-elapsed micro-CT imaging. With progressive loads, increased compression of trabecular bone was quantified, with the highest strains directly under the posterior region of the tibial tray implant, dissipating with increasing distance from the bone-implant interface. After load removal of the last load step (2.5BW), residual strains were observed in all of the five tibiae, with residual strains confined within 3.14 mm from the bone-implant interface. The residual strain is reflective of the observed initial migration of cementless tibial trays reported in clinical studies. The presence of strains above the yield strain of bone accepted in literature suggests that inelastic properties should be included within finite element models of the initial mechanical environment. This study provides a means to experimentally quantify the internal strain distribution of human tibia with cementless trays, increasing the understanding of the mechanical interaction between bone and implant.

In vivo strain measurements in the human buttock during sitting using MR-based digital volume correlation

Advancements in systems for prevention and management of pressure ulcers require a more detailed understanding of the complex response of soft tissues to compressive loads. This study aimed at quantifying the progressive deformation of the buttock based on 3D measurements of soft tissue displacements from MR scans of 10 healthy subjects in a semi-recumbent position. Measurements were obtained using digital volume correlation (DVC) and released as a public dataset. A first parametric optimisation of the global registration step aimed at aligning skeletal elements showed acceptable values of Dice coefficient (around 80%). A second parametric optimisation on the deformable registration method showed errors of 0.99mm and 1.78mm against two simulated fields with magnitude 7.30±3.15mm and 19.37±9.58mm, respectively, generated with a finite element model of the buttock under sitting loads. Measurements allowed the quantification of the slide of the gluteus maximus away from the ischial tuberosity (IT, average 13.74 mm) that was only qualitatively identified in the literature, highlighting the importance of the ischial bursa in allowing sliding. Spatial evolution of the maximus shear strain on a path from the IT to the seating interface showed a peak of compression in the fat, close to the interface with the muscle. Obtained peak values were above the proposed damage threshold in the literature. Results in the study showed the complexity of the deformation of the soft tissues in the buttock and the need for further investigations aimed at isolating factors such as tissue geometry, duration and extent of load, sitting posture and tissue properties.

3D strain pattern in additively manufactured AlSi10Mg from digital volume correlation

Although much research has focused on AlSi10Mg processed via laser-based powder bed fusion, the material deformation mechanisms at the microscale are still unclear. To improve the current understanding, 3D measurements of the strain field at the microstructural scale are needed to complement surface-based SEM observations. This work demonstrates that X-ray tomography combined with digital volume correlation can be used to measure the strain in the bulk of AlSi10Mg using the Si-rich particles contained in the heat-treated microstructure as markers. The method allows for measuring strains larger than 0.5 % with a spatial resolution of 35 μm and it can thus be used to study the impact of factors like porosity distribution or crystallographic texture on the material deformation and damage mechanisms.

On the material dependency of peri-implant morphology and stability in healing bone

The microstructural architecture of remodeled bone in the peri-implant region of screw implants plays a vital role in the distribution of strain energy and implant stability. We present a study in which screw implants made from titanium, polyetheretherketone and biodegradable magnesium-gadolinium alloys were implanted into rat tibia and subjected to a push-out test four, eight and twelve weeks after implantation. Screws were 4 mm in length and with an M2 thread. The loading experiment was accompanied by simultaneous three-dimensional imaging using synchrotron-radiation microcomputed tomography at 5 μm resolution. Bone deformation and strains were tracked by applying optical flow-based digital volume correlation to the recorded image sequences. Implant stabilities measured for screws of biodegradable alloys were comparable to pins whereas non-degradable biomaterials experienced additional mechanical stabilization. Peri-implant bone morphology and strain transfer from the loaded implant site depended heavily on the biomaterial utilized. Titanium implants stimulated rapid callus formation displaying a consistent monomodal strain profile whereas the bone volume fraction in the vicinity of magnesium-gadolinium alloys exhibited a minimum close to the interface of the implant and less ordered strain transfer. Correlations in our data suggest that implant stability benefits from disparate bone morphological properties depending on the biomaterial utilized. This leaves the choice of biomaterial as situational depending on local tissue properties.

Development of a method to investigate strain distribution across the cartilage-bone interface in guinea pig model of spontaneous osteoarthritis using lab-based contrast enhanced X-ray-computed tomography and digital volume correlation

OBJECTIVE

Strain changes at the cartilage-bone interface play a crucial role in osteoarthritis (OA) development. Contrast-Enhanced X-ray Computed Tomography (CECT) and Digital Volume Correlation (DVC) can measure 3D strain changes at the osteochondral interface. Using lab-based CT systems it is often difficult to visualise soft tissues such as articular cartilage without staining to enhance contrast. Contrast-Enhancing Staining Agents (CESAs), such as Phosphotungstic Acid (PTA) in 70% ethanol, can cause tissue shrinkage and alter tissue mechanics. The aims of this study were, firstly, to assess changes to the mechanical properties of osteochondral tissue after staining with a PTA/PBS solution, and secondly, to visualise articular cartilage during loading and with CECT imaging in order to compare strain across the interface in both healthy and OA joints using DVC.

DESIGN

Nanoindentation was used to assess changes to mechanical properties in articular cartilage and subchondral bone before and after staining. Hindlimbs from Dunkin-Hartley guinea pigs were stained with 1% PTA/PBS at room temperature for 6 days. Two consecutive CECT datasets were acquired for DVC error analysis. In-situ compression with a load corresponding to 2x body weight was applied, the specimen was re-imaged, and DVC was performed between the pre- and post-load tomograms.

RESULTS

Nanoindentation before and after PTA/PBS staining showed similar cartilage stiffness (p < 0.05), however, staining significantly decreased the stiffness of subchondral bone (∼9-fold; p = 0.0012). In severe OA specimens, third principal/compressive (εp3) strain was 141.7% higher and shear strain (γ) was 98.2% higher in tibial articular cartilage compared to non-OA (2 - month) specimens. A 23.1% increase in third principal stain strain and a 54.5% significant increase in the shear (γ) strain (p = 0.0027) was transferred into the mineralised regions of calcified cartilage and subchondral bone in severe OA specimens.

CONCLUSIONS

These results indicate the suitability of PTA in PBS as a contrast agent for the visualisation of cartilage during CECT imaging and allowed DVC computation of strain across the cartilage-bone interface. However, further research is needed to address the reduction in stiffness of subchondral bone after incubation in PBS.

In vivo evaluation of ankle kinematics and tibiotalar joint contact strains using digital volume correlation and 3 T clinical MRI

BACKGROUND

In vivo evaluation of ankle joint biomechanics is key to investigating the effect of injuries on the mechanics of the joint and evaluating the effectiveness of treatments. The objectives of this study were to 1) investigate the kinematics and contact strains of the ankle joint and 2) to investigate the correlation between the tibiotalar joint contact strains and the prevalence of osteochondral lesions of the talus distribution.

METHODS

Eight healthy human ankle joints were subjected to compressive load and 3 T MRIs were obtained before and after applying load. The MR images in combination with digital volume correlation enabled non-invasive measurement of ankle joint kinematics and tibiotalar joint contact strains in three dimensions.

FINDINGS

The total translation of the calcaneus was smaller (0.48 ± 0.15 mm, p < 0.05) than the distal tibia (0.93 ± 0.16 mm) and the talus (1.03 ± 0.26 mm). These movements can produce compressive and shear joint contact strains (approaching 9%), which can cause development of lesions on joints. 87.5% of peak tensile, compressive, and shear strains in the tibiotalar joint took place in the medial and lateral zones.

INTERPRETATION

The findings suggested that ankle bones translate independently from each other, and in some cases in opposite directions. These findings help explain the distribution of osteochondral lesions of the talus which have previously been observed to be in medial and lateral regions of the talar dome in 90% of cases. They also provide a reason for the central region of talar dome being less susceptible to developing osteochondral lesions.

Mapping internal strain fields of fused filament fabrication metal filled polylactic acid structure using digital volume correlation

With the advancement in Fused Filament Fabrication (FFF), its application is increasing widely across different industries such as aeronautical, biomedical, robotics, etc. The internal structure is becoming more complex and intricate with varying materials of reinforcement which are used to improve mechanical properties. Current measurement techniques like Digital Image Correlation (DIC) are non-destructive testing methods that do not provide enough information on the behaviour of internal microstructure for anisotropic FFF materials. Digital Volume Correlation (DVC) is non-destructive testing technique which provides full field internal 3D deformation and strain fields. Copper particle filled PLA samples manufactured using FFF method with 20, 40, 60 and 80 infill percentages were loaded in tension inside Micro-CT. X-rays were passed through the sample to get a volumetric dataset for different loadings. Using DVC method on the dataset, internal displacement and strain fields were generated for 20, 40, 60 and 80 infill percentage FFF sample.

The role of bone metastases on the mechanical competence of human vertebrae

Spine is the most common site for bone metastases. The evaluation of the mechanical competence and failure location in metastatic vertebrae is a biomechanical and clinical challenge. Little is known about the failure behaviour of vertebrae with metastatic lesions. The aim of this study was to use combined micro-Computed Tomography (microCT) and time-lapsed mechanical testing to reveal the failure location in metastatic vertebrae. Fifteen spine segments, each including a metastatic and a radiologically healthy vertebra, were tested in compression up to failure within a microCT. Volumetric strains were measured using Digital Volume Correlation. The images of undeformed and deformed specimens were overlapped to identify the failure location. Vertebrae with lytic metastases experienced the largest average compressive strains (median ± standard deviation: -8506 ± 4748microstrain), followed by the vertebrae with mixed metastases (-7035 ± 15605microstrain), the radiologically healthy vertebrae (-5743 ± 5697microstrain), and the vertebrae with blastic metastases (-3150 ± 4641microstrain). Strain peaks were localised within and nearby the lytic lesions or around the blastic tissue. Failure between the endplate and the metastasis was identified in vertebrae with lytic metastases, whereas failure localised around the metastasis in vertebrae with blastic lesions. This study showed for the first time the role of metastases on the vertebral internal deformations. While lytic lesions lead to failure of the metastatic vertebra, vertebrae with blastic metastases are more likely to induce failure in the adjacent vertebrae. Nevertheless, every metastatic lesion affects the vertebral deformation differently, making it essential to assess how the lesion affects the bone microstructure. These results suggest that the properties of the lesion (type, size, location within the vertebral body) should be considered when developing clinical tools to predict the risk of fracture in patients with metastatic lesions.

Comparison of linear and nonlinear stepwise μFE displacement predictions to digital volume correlation measurements of trabecular bone biopsies

Digital volume correlation (DVC) enables to evaluate the ability of μFE models in predicting experimental results on the mesoscale. In this study predicted displacement fields of three different linear and materially nonlinear μFE simulation methods were compared to DVC measured displacement fields at specific load steps in the elastic regime (Step_El) and after yield (Step_Ult). Five human trabecular bone biopsies from a previous study were compressed in several displacement steps until failure. At every compression step, μCT images (resolution: 36 μm) were recorded. A global DVC algorithm was applied to compute the displacement fields at all loading steps. The unloaded 3D images were then used to generate homogeneous, isotropic, linear and materially nonlinear μFE models. Three different μFE simulation methods were used: linear (L), nonlinear (NL), and nonlinear stepwise (NLS). Regarding L and NL, the boundary conditions were derived from the interpolated displacement fields at Step_El and Step_Ult, while for the NLS method nonlinear changes of the boundary conditions of the experiments were captured using the DVC displacement field of every available load step until Step_El and Step_Ult. The predicted displacement fields of all μFE simulation methods were in good agreement with the DVC measured displacement fields (individual specimens: R²>0.83 at Step_El and R²>0.59 at Step_Ult; pooled data: R²>0.97 at Step_El and R²>0.92 at Step_Ult). At Step_El, all three simulation methods showed similar intercepts, slopes, and coefficients of determination while the nonlinear μFE models improved the prediction of the displacement fields slightly in all Cartesian directions at Step_Ult (individual specimens: L: R²>0.59 and NL, NLS: R²>0.68; pooled data: L: R²>0.92 and NL, NLS: R²>0.94). Damaged/overstrained elements in L, NL, and NLS occurred at similar locations but the number of overstrained elements was overestimated when using the L simulation method. Considering the increased solving time of the nonlinear μFE models as well as the acceptable performance in displacement prediction of the linear μFE models, one can conclude that for similar use cases linear μFE models represent the best compromise between computational effort and accuracy of the displacement field predictions.

Measurement of bone damage caused by quasi-static compressive loading-unloading to explore dental implants stability: Simultaneous use of in-vitro tests, μ-CT images, and digital volume correlation

Primary stability of dental implants is the initial mechanical engagement of the implant with its adjacent bone. Implantation and the subsequent loading may cause mechanical damage in the peripheral bone, which ultimately reduces the stability of the implant. This study aimed at evaluating primary stability of dental implants through applying stepwise compressive displacement-controlled, loading-unloading cycles to obtain overall stiffness and dissipated energy of the bone-implant structure; and quantifying induced plastic strains in surrounding bone using digital volume correlation (DVC) method, through comparing μCT images in different loading steps. To this end, dental implants were inserted into the cylindrical trabecular bones, then the bone-implant structure was undergone step-wise loading-unloading cycles, and μCT images were taken in some particular steps, then comparison was made between undeformed and deformed configurations using DVC to quantify plastic strain within the trabecular bone. Comparing stiffness reduction and dissipated energy values in different loading steps, obtained from the force-displacement curve in each loading step, revealed that the maximum displacement of 0.16 mm can be deemed as a safe threshold above which damages in peri-implant bone started to increase considerably (p < 0.05). In addition, it was found here that peri-implant bone strain linearly increased with decreasing bone-implant stiffness (p < 0.05). Moreover, strain concentration in peri-implant bone region showed that the plastic strain in trabecular bone spread up to a distance of about 2.5 mm away from the implant surface. Research of this kind can be used to optimize the design of dental implants, with the ultimate goal of improving their stability, also to validate in-silico models, e.g., micro-finite element models, which can help gain a deeper understanding of bone-implant construct behavior.

The Strain Response to Intraocular Pressure Decrease in the Lamina Cribrosa of Patients with Glaucoma

OBJECTIVE

To measure biomechanical strains in the lamina cribrosa (LC) of living human eyes with intraocular pressure (IOP) lowering.

DESIGN

Cohort study.

PARTICIPANTS

Patients with glaucoma underwent imaging before and after laser suturelysis after trabeculectomy surgery (29 image pairs; 26 persons).

INTERVENTION

Noninvasive imaging of the eye.

MAIN OUTCOME MEASURES

Strains in optic nerve head tissue and changes in depths of the anterior border of the LC.

RESULTS

Intraocular pressure decreases caused the LC to expand in thickness in the anterior-posterior strain (Ezz = 0.94 ± 1.2%; P = 0.00020) and contract in radius in the radial strain (Err = - 0.19 ± 0.33%; P = 0.0043). The mean LC depth did not significantly change with IOP lowering (1.33 ± 6.26 μm; P = 0.26). A larger IOP decrease produced a larger, more tensile Ezz (P < 0.0001), greater maximum principal strain (Emax; P < 0.0001), and greater maximum shear strain (Γmax; P < 0.0001). The average LC depth change was associated with the Γmax and radial-circumferential shear strain (Erθ; P < 0.02) but was not significantly related to tensile or compressive strains. An analysis by clock hour showed that in temporal clock hours 3 to 6, a more anterior LC movement was associated with a more positive Emax, and in clock hours 3, 5, and 6, it was associated with a more positive Γmax. At 10 o'clock, a more posterior LC movement was related to a more positive Emax (P < 0.004). Greater compliance (strain/ΔIOP) of Emax (P = 0.044), Γmax (P = 0.052), and Erθ (P = 0.018) was associated with a thinner retinal nerve fiber layer. Greater compliance of Emax (P = 0.041), Γmax (P = 0.021), Erθ (P = 0.024), and in-plane shear strain (Erz; P = 0.0069) was associated with more negative mean deviations. Greater compliance of Γmax (P = 0.055), Erθ (P = 0.040), and Erz (P = 0.015) was associated with lower visual field indices.

CONCLUSIONS

With IOP lowering, the LC moves either into or out of the eye but, on average, expands in thickness and contracts in radius. Shear strains are nearly as substantial as in-plane strains. Biomechanical strains are more compliant in eyes with greater glaucoma damage. This work was registered at ClinicalTrials.gov as NCT03267849.

Application of phase-field fracture theories and digital volume correlation to synchrotron X-ray monitored fractures in human trabecular bone: A case study

Fracture processes of trabecular bone have been studied using various approaches over the years. However, reliable methods to analyse fracture at the single trabecula level are limited. In this study, a digital volume correlation (DVC) and a phase-field fracture model are applied and contrasted for human trabecular bone to analyse its failure under global compression at high resolution. A human trabecular bone sample was fractured in situ under synchrotron-based X-ray micro computed tomography (CT). Reconstructed CT data was then used in DVC algorithms to obtain high-resolution displacement fields in the bone at different load steps. A high-resolution specimen-specific structural mesh was discretized from the CT data and used for the phase-field simulation of the fracturing bone. The DVC analysis showed opening mode cracks as well as shear mode cracks. Strains in cracked regions were analysed. The load distribution in the trabecular structure resulted in two completely separated fracture regions in the sample body. A phenomenon that was also captured in the phase-field model. The results encourage us to believe improvements in boundary conditions and material models are worthwhile pursuing. Findings in this study support further development of a phase-field method to analyse fracture in samples with complex morphology, such as trabecular bone, and the capacity of DVC to quantify strains and slowly growing stable fractures during step-wise loading of trabecular bone.

A practical guide for in situ mechanical testing of musculoskeletal tissues using synchrotron tomography

Musculoskeletal tissues are complex hierarchical materials where mechanical response is linked to structural and material properties at different dimensional levels. Therefore, high-resolution three-dimensional tomography is very useful for assessing tissue properties at different scales. In particular, Synchrotron Radiation micro-Computed Tomography (SR-microCT) has been used in several applications to analyze the structure of bone and biomaterials. In the past decade the development of digital volume correlation (DVC) algorithms applied to SR-microCT images and its combination with in situ mechanical testing (four-dimensional imaging) have allowed researchers to visualise, for the first time, the deformation of musculoskeletal tissues and their interaction with biomaterials under different loading scenarios. However, there are several experimental challenges that make these measurements difficult and at high risk of failure. Challenges relate to sample preparation, imaging parameters, loading setup, accumulated tissue damage for multiple tomographic acquisitions, reconstruction methods and data processing. Considering that access to SR-microCT facilities is usually associated with bidding processes and long waiting times, the failure of these experiments could notably slow down the advancement of this research area and reduce its impact. Many of the experimental failures can be avoided with increased experience in performing the tests and better guidelines for preparation and execution of these complex experiments; publication of negative results could help interested researchers to avoid recurring mistakes. Therefore, the goal of this article is to highlight the potential and pitfalls in the design and execution of in situ SR-microCT experiments, involving multiple scans, of musculoskeletal tissues for the assessment of their structural and/or mechanical properties. The advice and guidelines that follow should improve the success rate of this type of experiment, allowing the community to reach higher impact more efficiently.

Micro-CT scan optimisation for mechanical loading of tibia with titanium tibial tray: A digital volume correlation zero strain error analysis

Primary stability of press-fit tibial trays is achieved by introducing an interference fit between bone and implant. The internal cancellous bone strains induced during this process and during loading have yet to be quantified experimentally. Advancements in large-gantry micro-CT imaging and digital volume correlation (DVC) allow quantification of such strains. However, before undertaking such a test, experimental requirements and DVC performance need to be examined, particularly considering the presence of a large orthopaedic implant (tibial tray). The aim of this study was to assess the DVC zero-strain accuracy (mean absolute error: MAER) and precision (standard deviation of error: SDER) on a cadaveric human tibia implanted with a titanium press-fit tray across four plausible scanning configurations, using a cabinet micro-CT system (Nikon XT H 225 ST). These varied in rotation step and resulting scanning time (106 min vs. 66 min), presence or absence of a 2 mm-thick aluminium cylinder for mechanical testing, and X-ray tube voltage (150 kVp vs. 215 kVp). One proximal tibia was implanted and micro-CT scanned (42 μm/pixel), with repeated scanning and specimen repositioning in between. DVC (DaVis, LaVision, direct correlation) was performed on nine cubic volumes of interest (VOIs: 13.4 mm-side) and across the entire proximal tibia. Strain errors were comparable across the four scanning configurations and sufficiently low for assessing bone within its elastic region in VOIs (MAER=223-540 με; SDER=88-261 με) and at organ level (MAER=536 με; SDER=473 με). Whilst the investigated experimental conditions, including a large titanium implant, present added complexity for DVC analysis, scans of sufficient quality can be achieved, reaching a compromise between the DVC requirements and the wanted application. The approach used for choosing the X-ray source settings considering the transmitted X-ray signal intensity and source power, is also discussed.

Nonlinear micro finite element models based on digital volume correlation measurements predict early microdamage in newly formed bone

Bone regeneration in critical-sized defects is a clinical challenge, with biomaterials under constant development aiming at enhancing the natural bone healing process. The delivery of bone morphogenetic proteins (BMPs) in appropriate carriers represents a promising strategy for bone defect treatment but optimisation of the spatial-temporal release is still needed for the regeneration of bone with biological, structural, and mechanical properties comparable to the native tissue. Nonlinear micro finite element (μFE) models can address some of these challenges by providing a tool able to predict the biomechanical strength and microdamage onset in newly formed bone when subjected to physiological or supraphysiological loads. Yet, these models need to be validated against experimental data. In this study, experimental local displacements in newly formed bone induced by osteoinductive biomaterials subjected to in situ X-ray computed tomography compression in the apparent elastic regime and measured using digital volume correlation (DVC) were used to validate μFE models. Displacement predictions from homogeneous linear μFE models were highly correlated to DVC-measured local displacements, while tissue heterogeneity capturing mineralisation differences showed negligible effects. Nonlinear μFE models improved the correlation and showed that tissue microdamage occurs at low apparent strains. Microdamage seemed to occur next to large cavities or in biomaterial-induced thin trabeculae, independent of the mineralisation. While localisation of plastic strain accumulation was similar, the amount of damage accumulated in these locations was slightly higher when including material heterogeneity. These results demonstrate the ability of the nonlinear μFE model to capture local microdamage in newly formed bone tissue and can be exploited to improve the current understanding of healing bone and mechanical competence. This will ultimately aid the development of BMPs delivery systems for bone defect treatment able to regenerate bone with optimal biological, mechanical, and structural properties.

A high-accuracy and high-efficiency digital volume correlation method to characterize in-vivo optic nerve head biomechanics from optical coherence tomography

In-vivo optic nerve head (ONH) biomechanics characterization is emerging as a promising way to study eye physiology and pathology. We propose a high-accuracy and high-efficiency digital volume correlation (DVC) method to characterize the in-vivo ONH deformation from optical coherence tomography (OCT) volumes. Using a combination of synthetic tests and analysis of OCTs from monkey ONHs subjected to acutely elevated intraocular pressure, we demonstrate that our proposed methodology overcame several challenges for conventional DVC methods: First, a pre-registration technique was used to remove large ONH rigid body motion in OCT volumes which could lead to analysis failure; second, a modified 3D inverse-compositional Gaussian Newton method was used to ensure sub-voxel accuracy of displacement calculations despite high noise and low image contrast of some OCT volumes; third, a tricubic B-spline interpolation method was applied to improve computational efficiency; fourth, a confidence parameter was introduced to guide the searching path in the displacement calculation; fifth, a confidence-weighted strain calculation method was applied to further improve the accuracy. The proposed DVC method had displacement errors smaller than 0.037 and 0.028 voxels with Gaussian and speckle noises, respectively. The strain errors in the three directions were less than 0.0045 and 0.0018 with Gaussian and speckle noises, respectively. Compared with the conventional DVC method, the proposed method reduced the errors of displacement and strain calculations by up to 70% under large body motions, with 75% lower computation time, while saving about 30% memory. Our study demonstrates the potential of the proposed technique to investigate ONH biomechanics. STATEMENT OF SIGNIFICANCE: The biomechanics of the optic nerve head (ONH) in the posterior pole of the globe play a central role in eye physiology and pathology. The application of digital volume correlation (DVC) to the analysis of optical coherence tomography (OCT) images of the ONH has emerged as a promising way to quantify ONH biomechanics. Conventional DVC methods, however, face several important challenges when analyzing OCT images of the ONH. We introduce a high-accuracy and high-efficiency DVC method to characterize in vivo ONH deformations from OCT volumes. We demonstrate the new method using synthetic tests and actual OCT data from monkey ONHs. The new method also has the potential to be used to study other tissues, as OCT applications continue to expand.

Mechanical strain in the mouse astrocytic lamina increases after exposure to recombinant trypsin

The responses of astrocytes in the optic nerve head (ONH) to mechanical and biochemical stimuli are important to understanding the degeneration of retinal ganglion cell axons in glaucoma. The ONH in glaucoma is vulnerable to stress produced by the intraocular pressure (IOP). Notably, after three days of elevated IOP in a mouse model, the junctions between the astrocytic processes and the peripapillary sclera were altered and the structural compliance of the ONH increased. In order to simulate this aspect of glaucomatous remodeling, explanted mouse eyes were treated with TrypLE, a recombinant trypsin enzyme. Treatment with TrypLE caused the periphery of the astrocytic lamina to contract radially by 0.044 ± 0.038. Transmission electron microscopy showed that TrypLE caused a separation of the end-feet of the astrocyte processes from the basement membrane at the junction with the sclera. Inflation testing after treatment with TrypLE caused an increased strain response in the astrocytic lamina compared to the strain response before treatment. The greatest increase was in the radial Green-Lagrange strain, E_rr = 0.028 ± 0.009, which increased by 340%. The alterations in the microstructure and in the strain response of the astrocytic lamina reported in mouse experimental glaucoma were partially reproduced by experimental treatment of mouse eyes with TrypLE. The results herein suggest that separation of junctions between the astrocyte processes and the sclera may be instrumental in increasing the structural compliance of the ONH after a period of elevated IOP. STATEMENT OF SIGNIFICANCE: Astrocytes of the optic nerve of the eye spread out from edge to edge across the optic nerve in a region referred to as the astrocytic lamina. In an experimental model of glaucoma caused by elevated eye-pressure, there is disruption of the connections between astrocytes and the edge of the astrocytic lamina. We caused a similar event in the lamina by incubating explanted mouse eyes with an enzyme. Disruption of the astrocyte connections to the edge of their tissue caused the tissue to stretch more when we increased the eye-pressure, compared to the control tissue. This work is the first on the tissue of the optic nerve to demonstrate the importance of cell connections in preventing the over-stretching of the astrocytic lamina.

MicroFE models of porcine vertebrae with induced bone focal lesions: Validation of predicted displacements with digital volume correlation

The evaluation of the local mechanical behavior as a result of metastatic lesions is fundamental for the characterization of the mechanical competence of metastatic vertebrae. Micro finite element (microFE) models have the potential of addressing this challenge through laboratory studies but their predictions of local deformation due to the complexity of the bone structure compromized by the lesion must be validated against experiments. In this study, the displacements predicted by homogeneous, linear and isotropic microFE models of vertebrae were validated against experimental Digital Volume Correlation (DVC) measurements. Porcine spine segments, with and without mechanically induced focal lesions, were tested in compression within a micro computed tomography (microCT) scanner. The displacement within the bone were measured with an optimized global DVC approach (BoneDVC). MicroFE models of the intact and lesioned vertebrae, including or excluding the growth plates, were developed from the microCT images. The microFE and DVC boundary conditions were matched. The displacements measured by the DVC and predicted by the microFE along each Cartesian direction were compared. The results showed an excellent agreement between the measured and predicted displacements, both for intact and metastatic vertebrae, in the middle of the vertebra, in those cases where the structure was not loaded beyond yield (0.69 < R² < 1.00). Models with growth plates showed the worst correlations (0.02 < R² < 0.99), while a clear improvement was observed if the growth plates were excluded (0.56 < R² < 1.00). In conclusion, these simplified models can predict complex displacement fields in the elastic regime with high reliability, more complex non-linear models should be implemented to predict regions with high deformation, when the bone is loaded beyond yield.

Microstructure and mechanical behaviors of tibia for collagen-induced arthritic mice treated with gingiva-derived mesenchymal stem cells

Rheumatoid arthritis (RA) is a systemic polyarticular arthritis that primarily affects the small joints but also causes bone erosion in large joints. None of the currently existing treatment approaches is curable. In this study, the effects of human gingiva-derived mesenchymal stem cells (GMSCs) on collagen-induced arthritis (CIA) mice are examined by experimentally assessing the microstructure and mechanical behaviors of tibia. Bone morphology and mineral density of mouse tibiae were assessed using micro-X-ray computed tomography (micro-CT). Compression testing was performed on mouse tibia to access its stiffness. The deformation and strain localized inside proximal tibia were mapped using mechanical testing coupled with micro-CT and digital volume correlation of micro-CT images. The results show that CIA disease caused bone erosion in epiphyseal cortical bone, which manifested into the adjacent epiphyseal trabecular bone, and also affected the metaphyseal cortical bone. CIA disease also weakened the load-bearing function of proximal tibia. GMSC treatment interfered with the progress of CIA, attenuated the bone erosion in epiphyseal and metaphyseal trabecular bone and resulted in improved load-bearing function of proximal tibia. GMSCs provide a promising potential treatment of autoimmune arthritis.

A combined experimental and numerical method to estimate the elastic modulus of single trabeculae

The elastic modulus at the single trabecular level is an important parameter for the understanding of the mechanical behavior of trabecular bone. Current methods are commonly limited by the irregular trabecular shape and the accuracy of displacement measurement. The aim of this study was to propose a method to estimate the trabecular modulus overcoming some of these limitations. For high-precision displacement measurements, in-situ compression within a synchrotron radiation based X-ray tomograph was used. Trabecular displacements were subsequently estimated by a global digital volume correlation algorithm, followed by high-resolution finite element analyses to account for the irregular geometry. The trabecular elastic moduli were then estimated by comparing the loads from the finite element analyses with those of the experiments. With this strategy, the average elastic modulus was estimated to 3.83 ± 0.54 GPa for three human trabeculae samples. Though limited by the sample size, the demonstrated method shows a potential to estimate the mechanical properties at the single trabecular level.

High resolution three-dimensional strain measurements in human articular cartilage

An unresolved challenge in osteoarthritis research is characterising the localised intra-tissue mechanical response of articular cartilage. The aim of this study was to explore whether laboratory micro-computed tomography (micro-CT) and digital volume correlation (DVC) permit non-destructive quantification of three-dimensional (3D) strain fields in human articular cartilage. Human articular cartilage specimens were harvested from the knee, mounted into a loading device and imaged in the unloaded and loaded states using a micro-CT scanner. Strain was measured throughout the cartilage volume using the micro-CT image data and DVC analysis. The volumetric DVC-measured strain was within 5% of the known applied strain. Variation in strain distribution between the superficial, middle and deep zones was observed, consistent with the different architecture of the material in these locations. These results indicate DVC method may be suitable for calculating strain in human articular cartilage.

Time-resolved in situ synchrotron-microCT: 4D deformation of bone and bone analogues using digital volume correlation

Digital volume correlation (DVC) in combination with high-resolution micro-computed tomography (microCT) imaging and in situ mechanical testing is gaining popularity for quantifying 3D full-field strains in bone and biomaterials. However, traditional in situ time-lapsed (i.e., interrupted) mechanical testing cannot fully capture the dynamic strain mechanisms in viscoelastic biological materials. The aim of this study was to investigate the time-resolved deformation of bone structures and analogues via continuous in situ synchrotron-radiation microCT (SR-microCT) compression and DVC to gain a better insight into their structure-function relationships. Fast SR-microCT imaging enabled the deformation behaviour to be captured with high temporal and spatial resolution. Time-resolved DVC highlighted the relationship between local strains and damage initiation and progression in the different biostructures undergoing plastic deformation, bending and/or buckling of their main microstructural elements. The results showed that SR-microCT continuous mechanical testing complemented and enhanced the information obtained from time-lapsed testing, which may underestimate the 3D strain magnitudes as a result of the stress relaxation occurring in between steps before image acquisition in porous biomaterials. Altogether, the findings of this study highlight the importance of time-resolved in situ experiments to fully characterise the time-dependent mechanical behaviour of biological tissues and biomaterials and to further explore their micromechanics under physiologically relevant conditions. STATEMENT OF SIGNIFICANCE: Time-resolved synchrotron X-ray tomography in combination with in situ mechanical testing provided the first four-dimensional analysis of the mechanical deformation of bone and bone analogues. To unravel the interplay of damage initiation and progression with local deformation, digital volume correlation was used to map the local strain field while microstructural changes were tracked with high temporal and spatial resolution. The results highlighted the importance of fast imaging and time-resolved in situ experiments to capture the real deformation of complex porous materials to fully characterize the local strain-damage relationship. The findings are notably improving the understanding of time-dependent mechanical behaviour of bone tissue, with the potential to be extend to highly viscoelastic biomaterials and soft tissues.

Functional adaptation of interradicular alveolar bone to reduced chewing loads on dentoalveolar joints in rats

OBJECTIVES

The effects of reduced chewing loads on load bearing integrity of interradicular bone (IB) within dentoalveolar joints (DAJ) in rats were investigated.

METHODS

Four-week-old Sprague Dawley rats (N = 60) were divided into two groups; rats were either fed normal food, which is hard-pellet food (HF) (N = 30), or soft-powdered chow (SF) (N = 30). Biomechanical testing of intact DAJs and mapping of the resulting mechanical strains within IBs from 8- through 24-week-old rats fed HF or SF were performed. Tension- and compression-based mechanical strain profiles were mapped by correlating digital volumes of IBs at no load with the same IBs under load. Heterogeneity within IB was identified by mapping cement lines and TRAP-positive multinucleated cells using histology, and mechanical properties using nanoindentation technique.

RESULTS

Significantly decreased interradicular functional space, IB volume fraction, and elastic modulus of IB in the SF group compared with the HF group were observed, and these trends varied with an increase in age. The elastic modulus values illustrated significant heterogeneity within IB from HF or SF groups. Both compression- and tension-based strains were localized at the coronal portion of the IB and the variation in strain profiles complemented the observed material heterogeneity using histology and nanoindentation.

SIGNIFICANCE

Interradicular space and IB material-related mechanoadaptations in a DAJ are optimized to meet soft food related chewing demands. Results provided insights into age-specific regulation of chewing loads as a plausible "therapeutic dose" to reverse adaptations within the periodontal complex as an attempt to regain functional competence of a dynamic DAJ.

Full-field comparisons between strains predicted by QCT-derived finite element models of the scapula and experimental strains measured by digital volume correlation

Subject-specific finite element models (FEMs) of the shoulder can be used to evaluate joint replacement designs preclinically. However, to ensure accurate conclusions are drawn, experimental validation is critical. The objective of the current study was to evaluate the accuracy of strain predictions generated by subject-specific scapula FEMs through comparisons against full-field experimental strains measured using digital volume correlation (DVC). Three cadaveric scapulae were mechanically loaded using a custom-hexapod robot within a micro-CT scanner. BoneDVC was used to quantify resultant experimental full-field strains. Scapula FEMs were generated using three different density-modulus relationships to assign material properties. Two types of boundary conditions (BCs) were simulated: DVC-displacement-driven or applied-force-driven. Third principal strains were compared between the DVC measurements and FEM predictions. With applied-force BCs, poor agreement was observed between the predicted and measured strains (slope range: 0.16-0.19, r² range: 0.04-0.30). Agreement was improved with the use of DVC-displacement BCs (slope range: 0.54-0.59, r² range: 0.73-0.75). Strain predictions were independent of the density-modulus relationship used for DVC-displacement BCs, but differences were observed in the correlation coefficient and intercept for applied-force BCs. Overall, this study utilized full-field DVC-derived experimental strains for comparison with FEM predicted strains in models with varying material properties and BCs. It was found that fair agreement can be achieved in localized strain measurements between DVC measurements and FEM predictions when DVC-displacement BCs are used. However, performance suffered with use of applied-force BCs.

Glenoid bone strain after anatomical total shoulder arthroplasty: In vitro measurements with micro-CT and digital volume correlation

Glenoid implant loosening remains a major source of failure and concern after anatomical total shoulder arthroplasty (aTSA). It is assumed to be associated with eccentric loading and excessive bone strain, but direct measurement of bone strain after aTSA is not available yet. Therefore, our objective was to develop an in vitro technique for measuring bone strain around a loaded glenoid implant. A custom loading device (1500 N) was designed to fit within a micro-CT scanner, to use digital volume correlation for measuring displacement and calculating strain. Errors were evaluated with three pairs of unloaded scans. The average displacement random error of three pairs of unloaded scans was 6.1 µm. Corresponding systematic and random errors of strain components were less than 806.0 µε and 2039.9 µε, respectively. The average strain accuracy (MAER) and precision (SDER) were 694.3 µε and 440.3 µε, respectively. The loaded minimum principal strain (8738.9 µε) was 12.6 times higher than the MAER (694.3 µε) on average, and was above the MAER for most of the glenoid bone volume (98.1%). Therefore, this technique proves to be accurate and precise enough to eventually compare glenoid implant designs, fixation techniques, or to validate numerical models of specimens under similar loading.

Vertebral stiffness measured via tomosynthesis-based digital volume correlation is strongly correlated with reference values from micro-CT-based DVC

Digital tomosynthesis (DTS) is a clinically available modality that allows imaging of a patient's spine in supine and standing positions. The purpose of this study was to establish the extent to which vertebral displacement and stiffness derived from DTS-based digital volume correlation (DTS-DVC) are correlated with those from a reference method, i.e., microcomputed tomography-based DVC (μCT-DVC). T11 vertebral bodies from 11 cadaveric donors were DTS imaged twice in a nonloaded state and once under a fixed load level approximating upper body weight. The same vertebrae were µCT imaged in nonloaded and loaded states (40 μm voxel size). Vertebral displacements were calculated at each voxel using DVC with pairs of nonloaded and loaded images, from which endplate-to-endplate axial displacement (D_DVC) and vertebral stiffness (S_DVC) were calculated. Both D_DVC and S_DVC demonstrated strong positive correlations between DTS-DVC and μCT-DVC, with correlations being stronger when vertebral displacement was calculated using the median (R²=0.80; p<0.0002 and R²=0.93; p<0.0001, respectively) rather than average displacement (R²=0.63; p<0.004 and R²=0.69; p<0.002, respectively). In conclusion, the demonstrated relationship of DTS-DVC with the μCT standard supports further development of a biomechanics-based clinical assessment of vertebral bone quality using the DTS-DVC technique.

The Application of Digital Volume Correlation (DVC) to Evaluate Strain Predictions Generated by Finite Element Models of the Osteoarthritic Humeral Head

Continuum-level finite element models (FEMs) of the humerus offer the ability to evaluate joint replacement designs preclinically; however, experimental validation of these models is critical to ensure accuracy. The objective of the current study was to quantify experimental full-field strain magnitudes within osteoarthritic (OA) humeral heads by combining mechanical loading with volumetric microCT imaging and digital volume correlation (DVC). The experimental data was used to evaluate the accuracy of corresponding FEMs. Six OA humeral head osteotomies were harvested from patients being treated with total shoulder arthroplasty and mechanical testing was performed within a microCT scanner. MicroCT images (33.5 µm isotropic voxels) were obtained in a pre- and post-loaded state and BoneDVC was used to quantify full-field experimental strains (≈ 1 mm nodal spacing, accuracy = 351 µstrain, precision = 518 µstrain). Continuum-level FEMs with two types of boundary conditions (BCs) were simulated: DVC-driven and force-driven. Accuracy of the FEMs was found to be sensitive to the BC simulated with better agreement found with the use of DVC-driven BCs (slope = 0.83, r² = 0.80) compared to force-driven BCs (slope = 0.22, r² = 0.12). This study quantified mechanical strain distributions within OA trabecular bone and demonstrated the importance of BCs to ensure the accuracy of predictions generated by corresponding FEMs.

A method for fracture toughness measurement in trabecular bone using computed tomography, image correlation and finite element methods

The fracture resistance of load-bearing trabecular bone is adversely affected by diseases such as osteoporosis. However, there are few published measurements of trabecular bone fracture toughness due to the difficulty of conducting reliable tests in small specimens of this highly porous material. A new approach is demonstrated that uses digital volume correlation of X-ray computed tomographs to measure 3D displacement fields in which the crack shape and size can be objectively identified using a phase congruency analysis. The criteria for crack propagation, i.e. fracture toughness, can then be derived by finite element simulation, with knowledge of the elastic properties.

3D full-field strain in bone-implant and bone-tooth constructs and their morphological influential factors

The biomechanics of bone-tooth and bone-implant interfaces affects the outcomes of several dental treatments, such as implant placement, because bone, tooth and periodontal ligament are living tissues that adapt to the changes in mechanical stimulations. In this work, mechanical testing coupled with micro-CT was performed on human cadaveric mandibular bone-tooth and bone-implant constructs. Using digital volume correlation, the 3D full-field strain in bone under implant loading and tooth loading was measured. Concurrently, bone morphology and bone-implant and bone-tooth contact were also measured through the analysis of micro-CT images. The results show that strain in bone increased when a tooth was replaced by a dental implant. Strain concentration was observed in peri-implant bone, as well as in the buccal bone plate, which is also the clinically-observed bone resorption area after implant placement. Decreasing implant stability measurements (resonance frequency analysis and torque test) indicated increased peri-implant strain, but their relationships may not be linear. Peri-implant bone strain linearly increased with decreasing bone-implant contact (BIC) ratio. It also linearly decreased with increasing bone-tooth/bone-implant contact ratio. The high strain in the buccal bone plate linearly increased with decreasing buccal bone plate thickness. The results of this study revealed 3D full-field strain in bone-tooth and bone-implant constructs, as well as their several morphological influential factors.

The inflation response of the human lamina cribrosa and sclera: Analysis of deformation and interaction

This study investigated the inflation response of the lamina cribrosa (LC) and adjacent peripapillary sclera (PPS) in post-mortem human eyes with no history of glaucoma. The posterior sclera of 13 human eyes from 7 donors was subjected to controlled pressurization between 5-45 mmHg. A laser-scanning microscope (LSM) was used to image the second harmonic generation (SHG) response of collagen and the two-photon fluorescent (TPF) response of elastin within the volume of the LC and PPS at each pressure. Image volumes were analyzed using digital volume correlation (DVC) to calculate the three-dimensional (3D) deformation field between pressures. The LC exhibited larger radial strain, Err, and maximum principal strain, Emax, (p < 0.0001) and greater posterior displacement (p=0.0007) compared to the PPS between 5-45 mmHg, but had similar average circumferential strain, Eθθ, and maximum shear strain, Γmax. The Emax and Γmax were highest near the LC-PPS interface and lowest in the nasal quadrant of both tissues. Larger LC area was associated with smaller Emax in the peripheral LC and larger Emax in the central LC (p ≤ 0.01). The Emax, Γmax, and Eθθ in the inner PPS increased with increasing strain in adjacent LC regions (p ≤ 0.001). Smaller strains in the PPS were associated with a larger difference in the posterior displacement between the PPS and central LC (p < 0.0001 for Emax and Err), indicating that a stiffer pressure-strain response of the PPS is associated with greater posterior bowing of the LC. STATEMENT OF SIGNIFICANCE: Glaucoma causes vision loss through progressive damage of the retinal ganglion axons at the lamina cribrosa (LC), a connective tissue structure that supports the axons as they pass through the eye wall. It is hypothesized that strains caused by intraocular pressure may initiate this damage and that these strains are modulated by the combined deformation of the LC and adjacent peripapillary sclera (PPS). In this study we present a method to measure the pressure-induced 3D displacement and strain field in the LC and PPS simultaneously. Regional strain variation in the LC and PPS was investigated and compared and strains were analyzed for associations with age, LC area, LC strain magnitude, and LC posterior motion relative to the PPS.

Characterization of chemoelastic effects in arteries using digital volume correlation and optical coherence tomography

Understanding stress-strain relationships in arteries is important for fundamental investigations in mechanobiology. Here we demonstrate the essential role of chemoelasticity in determining the mechanical properties of arterial tissues. Stepwise stress-relaxation uniaxial tensile tests were carried out on samples of porcine thoracic aortas immersed in a hyperosmotic solution. The tissue deformations were tracked using optical coherence tomography (OCT) during the tensile tests and digital volume correlation (DVC) was used to obtain measurements of depth-resolved strains across the whole thickness of the tested aortas. The hyperosmotic solution exacerbated chemoelastic effects, and we were able to measure different manifestations of these chemoelastic effects: swelling of the media inducing a modification of its optical properties, and existence of a transverse tensile strain. For the first time ever to our best knowledge, 3D strains induced by chemoelastic effects in soft tissues were quantified thanks to the OCT-DVC method. Without doubt, chemoelasticity plays an essential role in arterial mechanobiology in vivo and future work should focus on characterizing chemoelastic effects in arterial walls under physiological and disease conditions. STATEMENT OF SIGNIFICANCE: Chemoelasticity, coupling osmotic phenomena and mechanical stresses, is essential in soft tissue mechanobiology. For the first time ever, we measure and analyze 3D strain fields induced by these chemoelastic effects thanks to the unique combination of OCT imaging and digital volume correlation.

Polymerization shrinkage of resin-based composites for dental restorations: A digital volume correlation study

OBJECTIVE

Resin-based composites are widely used in dental restorations; however, their volumetric shrinkage during polymerization leads to several issues that reduce the restoration survival rates. For overcoming this problem, a deep study of shrinkage phenomena is necessary.

METHODS

In this study, micro-tomography (μ-CT) is combined with digital volume correlation (DVC) to investigate the effect of several factors on the polymerization strain of dental composites in model cavities: the presence/absence of an adhesive, the use of transparent/blackened cavities, and irradiation times between 1 and 40s.

RESULTS

The results indicate that the presence of an adhesive at the interface between the cavity and composite does not reduce the total strain but instead limits it to a preferential direction. In addition, regardless of the conditions, the main strain is generated along the axis parallel to the polymerization irradiation (the vertical axis). Finally, the total strain appears to occur in the first 5s of irradiation, with no further evolution observed for longer irradiation times.

SIGNIFICANCE

This work provides new insight into resin-based composite shrinkage and demonstrates the benefit of coupling DVC and μ-CT to better understand the degradation mechanisms of these materials.

In vivo characterization of the deformation of the human optic nerve head using optical coherence tomography and digital volume correlation

We developed a method to measure the 3-dimensional (3D) strain field in the optic nerve head (ONH) in vivo between two intraocular pressures (IOP). Radial optical coherence tomography (OCT) scans were taken of the ONH of 5 eyes from 5 glaucoma patients before and after IOP-lowering surgery and from 5 eyes from 3 glaucoma suspect patients before and after raising IOP by wearing tight-fitting swimming goggles. Scans taken at higher and lower IOP were compared using a custom digital volume correlation (DVC) algorithm to calculate strains in the anterior lamina cribrosa (ALC), retina, and choroid. Changes in anterior lamina depth (ALD) relative to Bruch's membrane were also analyzed. Average displacement error was estimated to be subpixel and strain errors were smaller than 0.37%. Suturelysis decreased IOP by 9-20 mmHg and decreased compressive anterior-posterior strain Ezz in the ALC by 0.76% (p=0.002,n=5). Goggle-wearing increased IOP by 3-4 mmHg and produced compressive Ezz in the ALC (-0.32%,p=0.001,n=5). Greater IOP decrease was associated with greater ALD change (p=0.047,n=10) and greater strains in the ALC (Ezz:p=0.002,n=10). A deepening of ALD was associated with lower IOP and greater ALC strains (p⩽0.045,n=10). A DVC-based method to measure strains from OCT images caused by IOP changes as small as 2.3 mmHg provides preliminary evidence that ALD is shallower and ALC strains are less compressive at higher IOP and that ALD change is associated with ALC strains. STATEMENT OF SIGNIFICANCE: Glaucoma causes vision loss through progressive damage of the retinal ganglion axons at the lamina cribrosa, a connective tissue structure in the optic nerve head that supports the axons as they pass through the eye wall. It is hypothesized that strains caused by intraocular pressure (IOP) may initiate this damage, but few studies have measured the strain response to pressure of the optic nerve head in patients. We present a method to measure the 3D displacement and strain field in the optic nerve head caused by IOP alteration in glaucoma patients using clinically available images. We used this method to measure strain within the optic nerve head from IOP changes caused by glaucoma surgery and wearing tight-fitting swimming goggles.

Synchrotron tomography of intervertebral disc deformation quantified by digital volume correlation reveals microstructural influence on strain patterns

The intervertebral disc (IVD) has a complex and multiscale extracellular matrix structure which provides unique mechanical properties to withstand physiological loading. Low back pain has been linked to degeneration of the disc but reparative treatments are not currently available. Characterising the disc's 3D microstructure and its response in a physiologically relevant loading environment is required to improve understanding of degeneration and to develop new reparative treatments. In this study, techniques for imaging the native IVD, measuring internal deformation and mapping volumetric strain were applied to an in situ compressed ex vivo rat lumbar spine segment. Synchrotron X-ray micro-tomography (synchrotron CT) was used to resolve IVD structures at microscale resolution. These image data enabled 3D quantification of collagen bundle orientation and measurement of local displacement in the annulus fibrosus between sequential scans using digital volume correlation (DVC). The volumetric strain mapped from synchrotron CT provided a detailed insight into the micromechanics of native IVD tissue. The DVC findings showed that there was no slipping at lamella boundaries, and local strain patterns were of a similar distribution to the previously reported elastic network with some heterogeneous areas and maximum strain direction aligned with bundle orientation, suggesting bundle stretching and sliding. This method has the potential to bridge the gap between measures of macro-mechanical properties and the local 3D micro-mechanical environment experienced by cells. This is the first evaluation of strain at the micro scale level in the intact IVD and provides a quantitative framework for future IVD degeneration mechanics studies and testing of tissue engineered IVD replacements. STATEMENT OF SIGNIFICANCE: Synchrotron in-line phase contrast X-ray tomography provided the first visualisation of native intact intervertebral disc microstructural deformation in 3D. For two annulus fibrosus volumes of interest, collagen bundle orientation was quantified and local displacement mapped as strain. Direct evidence of microstructural influence on strain patterns could be seen such as no slipping at lamellae boundaries and maximum strain direction aligned with collagen bundle orientation. Although disc elastic structures were not directly observed, the strain patterns had a similar distribution to the previously reported elastic network. This study presents technical advances and is a basis for future X-ray microscopy, structural quantification and digital volume correlation strain analysis of soft tissue.

Effect of SR-microCT radiation on the mechanical integrity of trabecular bone using in situ mechanical testing and digital volume correlation

The use of synchrotron radiation micro-computed tomography (SR-microCT) is becoming increasingly popular for studying the relationship between microstructure and bone mechanics subjected to in situ mechanical testing. However, it is well known that the effect of SR X-ray radiation can considerably alter the mechanical properties of bone tissue. Digital volume correlation (DVC) has been extensively used to compute full-field strain distributions in bone specimens subjected to step-wise mechanical loading, but tissue damage from sequential SR-microCT scans has not been previously addressed. Therefore, the aim of this study is to examine the influence of SR irradiation-induced microdamage on the apparent elastic properties of trabecular bone using DVC applied to in situ SR-microCT tomograms obtained with different exposure times. Results showed how DVC was able to identify high local strain levels (> 10,000 µε) corresponding to visible microcracks at high irradiation doses (~ 230 kGy), despite the apparent elastic properties remained unaltered. Microcracks were not detected and bone plasticity was preserved for low irradiation doses (~ 33 kGy), although image quality and consequently, DVC performance were reduced. DVC results suggested some local deterioration of tissue that might have resulted from mechanical strain concentration further enhanced by some level of local irradiation even for low accumulated dose.

Novel image analysis methods for quantification of in situ 3-D tendon cell and matrix strain

Macroscopic tendon loads modulate the cellular microenvironment leading to biological outcomes such as degeneration or repair. Previous studies have shown that damage accumulation and the phases of tendon healing are marked by significant changes in the extracellular matrix, but it remains unknown how mechanical forces of the extracellular matrix are translated to mechanotransduction pathways that ultimately drive the biological response. Our overarching hypothesis is that the unique relationship between extracellular matrix strain and cell deformation will dictate biological outcomes, prompting the need for quantitative methods to characterize the local strain environment. While 2-D methods have successfully calculated matrix strain and cell deformation, 3-D methods are necessary to capture the increased complexity that can arise due to high levels of anisotropy and out-of-plane motion, particularly in the disorganized, highly cellular, injured state. In this study, we validated the use of digital volume correlation methods to quantify 3-D matrix strain using images of naïve tendon cells, the collagen fiber matrix, and injured tendon cells. Additionally, naïve tendon cell images were used to develop novel methods for 3-D cell deformation and 3-D cell-matrix strain, which is defined as a quantitative measure of the relationship between matrix strain and cell deformation. The results support that these methods can be used to detect strains with high accuracy and can be further extended to an in vivo setting for observing temporal changes in cell and matrix mechanics during degeneration and healing.

The pressure-induced deformation response of the human lamina cribrosa: Analysis of regional variations

The objective of this study was to measure the pressure-induced deformation response of the human lamina cribrosa (LC) and analyze for variations with age and anatomical region. The posterior scleral cup of 8 eyes from 6 human donors was mounted onto a custom inflation chamber. A laser-scanning microscope was used for second harmonic generation (SHG) imaging of the collagen structure in the posterior volume of the LC at pressures from 5mmHg to 45mmHg. The SHG volumes were analyzed by the Fast-Fourier Iterative Digital Volume Correlation (DVC) algorithm for the three dimensional (3D) displacement field. The components of the Green-Lagrange strain tensor and the in-plane principal and maximum shear strains were evaluated from the DVC displacement field for the central and peripheral regions of the LC and the nasal, temporal, inferior, and superior quadrants surrounding the central retinal artery and vein. Among the major findings were that older age was associated with lower strains, the maximum shear strain was larger in the peripheral than central region, and the maximum principal strain was lower in the nasal quadrant. The elliptical shape of the LC was also predictive of the biaxial strain ratio. Age-related and structure-related variations in the pressure-induced strains of the LC may contribute to the susceptibility and severity of optic nerve damage in glaucoma, and regional variations may explain the progression of axonal damage and tissue remodeling observed in the LC in glaucoma.

STATEMENT OF SIGNIFICANCE

Glaucoma causes vision loss through progressive damage of the retinal ganglion axons at the lamina cribrosa (LC), the connective tissue structure that supports the axons as they leave the eye. Mechanical characterization of the LC is challenging because of the complex 3D shape and inaccessibility of the tissue. We present a new method using digital volume correlation to map the 3D displacement and strain fields in the LC under inflation. We report for the first time significant regional variations in the strains that are consistent with the pattern of optic nerve damage in early glaucoma. Thus regional strain variations may be predictive of the progression of axonal damage in glaucoma.

Trabecular deformations during screw pull-out: a micro-CT study of lapine bone

The mechanical fixation of endosseous implants, such as screws, in trabecular bone is challenging because of the complex porous microstructure. Development of new screw designs to improve fracture fixation, especially in high-porosity osteoporotic bone, requires a profound understanding of how the structural system implant/trabeculae interacts when it is subjected to mechanical load. In this study, pull-out tests of screw implants were performed. Screws were first inserted into the trabecular bone of rabbit femurs and then pulled out from the bone inside a computational tomography scanner. The tests were interrupted at certain load steps to acquire 3D images. The images were then analysed with a digital volume correlation technique to estimate deformation and strain fields inside the bone during the tests. The results indicate that the highest shear strains are concentrated between the inner and outer thread diameter, whereas compressive strains are found at larger distances from the screw. Tensile strains were somewhat smaller. Strain concentrations and the location of trabecular failures provide experimental information that could be used in the development of new screw designs and/or to validate numerical simulations.

Application of digital volume correlation to study the efficacy of prophylactic vertebral augmentation

BACKGROUND

Prophylactic augmentation is meant to reinforce the vertebral body, but in some cases it is suspected to actually weaken it. Past studies only investigated structural failure and the surface strain distribution. To elucidate the failure mechanism of the augmented vertebra, more information is needed about the internal strain distribution. This study aims to measure, for the first time, the full-field three-dimensional strain distribution inside augmented vertebrae in the elastic regime and to failure.

METHODS

Eight porcine vertebrae were prophylactically-augmented using two augmentation materials. They were scanned with a micro-computed tomography scanner (38.8μm voxel resolution) while undeformed, and loaded at 5%, 10%, and 15% compressions. Internal strains (axial, antero-posterior and lateral-lateral components) were computed using digital volume correlation.

FINDINGS

For both augmentation materials, the highest strains were measured in the regions adjacent to the injected cement mass, whereas the cement-interdigitated-bone was less strained. While this was already visible in the elastic regime (5%), it was a predictor of the localization of failure, which became visible at higher degrees of compression (10% and 15%), when failure propagated across the trabecular bone. Localization of high strains and failure was consistent between specimens, but different between the cement types.

INTERPRETATION

This study indicated the potential of digital volume correlation in measuring the internal strain (elastic regime) and failure in augmented vertebrae. While the cement-interdigitated region becomes stiffer (less strained), the adjacent non-augmented trabecular bone is affected by the stress concentration induced by the cement mass. This approach can help establish better criteria to improve vertebroplasty.

Strain mapping and correlative microscopy of the alveolar bone in a bone-periodontal ligament-tooth fibrous joint

This study details a method to calculate strains within interradicular alveolar bone using digital volume correlation on X-ray tomograms of intact bone-periodontal ligament-tooth fibrous joints. The effects of loading schemes (concentric and eccentric) and optical magnification on the resulting strain in alveolar bone will be investigated with an intent to correlate deformation gradients with data sets from other complementary techniques. Strain maps will be correlated with structural and site-specific mechanical properties obtained on the same specimen using atomic force microscopy and atomic force microscopy-based nanoindentation technique. Specimens include polydimethylsiloxane as a standard material and intact hemi-mandibles harvested from rats. X-ray tomograms were taken at no-load and loaded conditions using an in situ load cell coupled to a micro X-ray computed tomography unit. Digital volume correlation was used to calculate deformations within alveolar bone. Comparison of strain maps was made as a result of different loading schemes (concentric vs eccentric) and at different magnifications (4× vs 10×). Virtual sections and strain maps from digital volume correlation solutions were aligned with structure and reduced elastic modulus to correlate datasets of the same region within a specimen. Strain distribution between concentrically and eccentrically loaded complexes was different but illustrated a similar range. Strain maps of homogeneous materials (polydimethylsiloxane) resulting from digital volume correlation at different magnifications were similar. However, strain maps of heterogeneous materials at lower and higher magnification differed. The digital volume correlation technique illustrated a dependence on optical magnification specifically for heterogeneous materials such as bone. The results at a higher optical magnification highlight the potential for extracting deformation at higher resolutions. Correlation of data spaces from different complementary techniques is plausible and could provide insights into biological and physicochemical processes that lead to functional adaptation of tissues and joints.

Measurement of lacunar bone strains and crack formation during tensile loading by digital volume correlation of second harmonic generation images

The maintenance of healthy bone tissue depends upon the ability of osteocytes to respond to mechanical cues on the cellular level. The combination of digital volume correlation and second harmonic generation microscopy offers the opportunity to investigate the mechanical microenvironment of intact bone on the scale of individual osteocytes. Adult human femurs were imaged under tensile loads of 5 and 15MPa and volumes of approximately 492×429×31μm(3) were analyzed, along with an image of a bone microcrack under the same loading conditions. Principal strains were significantly higher in three-dimensional digital volume correlation when compared to two-dimensional digital image correlation. The average maximum principal strain magnitude was 5.06-fold greater than the applied global strain, with peak strains of up to 23.14-fold over global strains measured at the borders of osteocyte lacunae. Finally, a microcrack that initiated at an osteocyte lacunae had its greatest tensile strain magnitudes at the crack expansion front in the direction of a second lacunae, but strain at the crack border was reduced to background strain magnitudes upon breaching the second lacunae. This serveed to demonstrate the role of lacunae in initiating, mediating and terminating microcrack growth.

Accuracy of finite element analyses of CT scans in predictions of vertebral failure patterns under axial compression and anterior flexion

Finite element (FE) models built from quantitative computed tomography (QCT) scans can provide patient-specific estimates of bone strength and fracture risk in the spine. While prior studies demonstrate accurate QCT-based FE predictions of vertebral stiffness and strength, the accuracy of the predicted failure patterns, i.e., the locations where failure occurs within the vertebra and the way in which the vertebra deforms as failure progresses, is less clear. This study used digital volume correlation (DVC) analyses of time-lapse micro-computed tomography (μCT) images acquired during mechanical testing (compression and anterior flexion) of thoracic spine segments (T7-T9, n=28) to measure displacements occurring throughout the T8 vertebral body at the ultimate point. These displacements were compared to those simulated by QCT-based FE analyses of T8. We hypothesized that the FE predictions would be more accurate when the boundary conditions are based on measurements of pressure distributions within intervertebral discs of similar level of disc degeneration vs. boundary conditions representing rigid platens. The FE simulations captured some of the general, qualitative features of the failure patterns; however, displacement errors ranged 12-279%. Contrary to our hypothesis, no differences in displacement errors were found when using boundary conditions representing measurements of disc pressure vs. rigid platens. The smallest displacement errors were obtained using boundary conditions that were measured directly by DVC at the T8 endplates. These findings indicate that further work is needed to develop methods of identifying physiological loading conditions for the vertebral body, for the purpose of achieving robust, patient-specific FE analyses of failure mechanisms.

Biomechanics and strain mapping in bone as related to immediately-loaded dental implants

The effects of alveolar bone socket geometry and bone-implant contact on implant biomechanics, and resulting strain distributions in bone were investigated. Following extraction of lateral incisors on a cadaver mandible, implants were placed immediately and bone-implant contact area, stability implant biomechanics and bone strain were measured. In situ biomechanical testing coupled with micro X-ray microscopy (µ-XRM) illustrated less stiff bone-implant complexes (701-822 N/mm) compared with bone-periodontal ligament (PDL)-tooth complexes (791-913 N/mm). X-ray tomograms illustrated that the cause of reduced stiffness was due to limited bone-implant contact. Heterogeneous elemental composition of bone was identified by using energy dispersive X-ray spectroscopy (EDS). The novel aspect of this study was the application of a new experimental mechanics method, that is, digital volume correlation, which allowed mapping of strains in volumes of alveolar bone in contact with a loaded implant. The identified surface and subsurface strain concentrations were a manifestation of load transferred to bone through bone-implant contact based on bone-implant geometry, quality of bone, implant placement, and implant design. 3D strain mapping indicated that strain concentrations are not exclusive to the bone-implant contact regions, but also extend into bone not directly in contact with the implant. The implications of the observed strain concentrations are discussed in the context of mechanobiology. Although a plausible explanation of surgical complications for immediate implant treatment is provided, extrapolation of results is only warranted by future systematic studies on more cadaver specimens and/or in vivo models.

Digital volume correlation and micro-CT: An in-vitro technique for measuring full-field interface micromotion around polyethylene implants

Micromotion around implants is commonly measured using displacement-sensor techniques. Due to the limitations of these techniques, an alternative approach (DVC-μCT) using digital volume correlation (DVC) and micro-CT (μCT) was developed in this study. The validation consisted of evaluating DVC-μCT based micromotion against known micromotions (40, 100 and 150 μm) in a simplified experiment. Subsequently, a more clinically realistic experiment in which a glenoid component was implanted into a porcine scapula was carried out and the DVC-μCT measurements during a single load cycle (duration 20 min due to scanning time) was correlated with the manual tracking of micromotion at 12 discrete points across the implant interface. In this same experiment the full-field DVC-μCT micromotion was compared to the full-field micromotion predicted by a parallel finite element analysis (FEA). It was found that DVC-μCT micromotion matched the known micromotion of the simplified experiment (average/peak error=1.4/1.7 μm, regression line slope=0.999) and correlated with the micromotion at the 12 points tracked manually during the realistic experiment (R(2)=0.96). The DVC-μCT full-field micromotion matched the pattern of the full-field FEA predicted micromotion. This study showed that the DVC-μCT technique provides sensible estimates of micromotion. The main advantages of this technique are that it does not damage important parts of the specimen to gain access to the bone-implant interface, and it provides a full-field evaluation of micromotion as opposed to the micromotion at just a few discrete points. In conclusion the DVC-μCT technique provides a useful tool for investigations of micromotion around plastic implants.

Combining micro computed tomography and three-dimensional registration to evaluate local strains in shape memory scaffolds

Appropriate mechanical stimulation of bony tissue enhances osseointegration of load-bearing implants. Uniaxial compression of porous implants locally results in tensile and compressive strains. Their experimental determination is the objective of this study. Selective laser melting is applied to produce open-porous NiTi scaffolds of cubic units. To measure displacement and strain fields within the compressed scaffold, the authors took advantage of synchrotron radiation-based micro computed tomography during temperature increase and non-rigid three-dimensional data registration. Uniaxial scaffold compression of 6% led to local compressive and tensile strains of up to 15%. The experiments validate modeling by means of the finite element method. Increasing the temperature during the tomography experiment from 15 to 37°C at a rate of 4 K h(-1), one can locally identify the phase transition from martensite to austenite. It starts at ≈ 24°C on the scaffolds bottom, proceeds up towards the top and terminates at ≈ 34°C on the periphery of the scaffold. The results allow not only design optimization of the scaffold architecture, but also estimation of maximal displacements before cracks are initiated and of optimized mechanical stimuli around porous metallic load-bearing implants within the physiological temperature range.

Cell and tissue deformation measurements: texture correlation with third-order approximation of displacement gradients

Cells remarkably are capable of large deformations during motility and when subjected to mechanical force. Measurement of mechanical deformation (i.e. displacements, strain) is critical to understand functional changes in cells and biological tissues following disease, and to elucidate basic relationships between applied force and cellular biosynthesis. Microscopy-based imaging modalities provide the ability to noninvasively visualize small cell or tissue structures and track their motion over time, often using two-dimensional (2D) digital image (texture) correlation algorithms. For the measurement of complex and nonlinear motion in cells and tissues, implementation of texture correlation algorithms with high order approximations of displacement mapping terms are needed to minimize error. Here, we extend a texture correlation algorithm with up to third-order approximation of displacement mapping terms for the measurement of cell and tissue deformation. We additionally investigate relationships between measurement error and image texture, defined by subset entropy. Displacement measurement error is significantly reduced when the order of displacement mapping terms in the texture correlation algorithm matches or exceeds the order of the deformation observed. Displacement measurement error is also inversely proportional to subset entropy, with well-defined cell and tissue structures leading to high entropy and low error. For cell and tissue studies where complex or nonlinear displacements are expected, texture correlation algorithms with high order terms are required to best characterize the observed deformation.