The effect of perfusion on soft tissue mechanical properties: a computational model

The Networking Brain: How Extracellular Matrix, Cellular Networks, and Vasculature Shape the In Vivo Mechanical Properties of the Brain

Mechanically, the brain is characterized by both solid and fluid properties. The resulting unique material behavior fosters proliferation, differentiation, and repair of cellular and vascular networks, and optimally protects them from damaging shear forces. Magnetic resonance elastography (MRE) is a noninvasive imaging technique that maps the mechanical properties of the brain in vivo. MRE studies have shown that abnormal processes such as neuronal degeneration, demyelination, inflammation, and vascular leakage lead to tissue softening. In contrast, neuronal proliferation, cellular network formation, and higher vascular pressure result in brain stiffening. In addition, brain viscosity has been reported to change with normal blood perfusion variability and brain maturation as well as disease conditions such as tumor invasion. In this article, the contributions of the neuronal, glial, extracellular, and vascular networks are discussed to the coarse-grained parameters determined by MRE. This reductionist multi-network model of brain mechanics helps to explain many MRE observations in terms of microanatomical changes and suggests that cerebral viscoelasticity is a suitable imaging marker for brain disease.

Post-mortem changes of anisotropic mechanical properties in the porcine brain assessed by MR elastography

Knowledge of the mechanical properties of brain tissue in vivo is essential to understanding the mechanisms underlying traumatic brain injury (TBI) and to creating accurate computational models of TBI and neurosurgical simulation. Brain white matter, which is composed of aligned, myelinated, axonal fibers, is structurally anisotropic. White matter in vivo also exhibits mechanical anisotropy, as measured by magnetic resonance elastography (MRE), but measurements of anisotropy obtained by mechanical testing of white matter ex vivo have been inconsistent. The minipig has a gyrencephalic brain with similar white matter and gray matter proportions to humans and therefore provides a relevant model for human brain mechanics. In this study, we compare estimates of anisotropic mechanical properties of the minipig brain obtained by identical, non-invasive methods in the live (in vivo) and dead animals (in situ). To do so, we combine wave displacement fields from MRE and fiber directions derived from diffusion tensor imaging (DTI) with a finite element-based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal alive and at specific times post-mortem. These maps show that white matter is stiffer, more dissipative, and more anisotropic than gray matter when the minipig is alive, but that these differences largely disappear post-mortem, with the exception of tensile anisotropy. Overall, brain tissue becomes stiffer, less dissipative, and less mechanically anisotropic post-mortem. These findings emphasize the importance of testing brain tissue properties in vivo.

Statement of Significance

In this study, MRE and DTI in the minipig were combined to estimate, for the first time, anisotropic mechanical properties in the living brain and in the same brain after death. Significant differences were observed in the anisotropic behavior of brain tissue post-mortem. These results demonstrate the importance of measuring brain tissue properties in vivo as well as ex vivo, and provide new quantitative data for the development of computational models of brain biomechanics.

Ex vivo bovine liver nonlinear viscoelastic properties: MR elastography and rheological measurements

INTRODUCTION

Knowledge of the nonlinear viscoelastic properties of the liver is important, but the complex tissue behavior outside the linear viscoelastic regime has impeded their characterization, particularly in vivo. Combining static compression with magnetic resonance (MR) elastography has the potential to be a useful imaging method for assessing large deformation mechanical properties of soft tissues in vivo. However, this remains to be verified. Therefore this study aims first to determine whether MR elastography can measure the nonlinear mechanical properties of ex vivo bovine liver tissue under varying levels of uniform and focal preloads (up to 30%), and second to compare MR elastography-derived complex shear modulus with standard rheological measurements.

METHOD

Nine fresh bovine livers were collected from a local abattoir, and experiments were conducted within 12hr of death. Two cubic samples (∼10 × 10 × 10 cm³) were dissected from each liver and imaged using MR elastography (60 Hz) under 4 levels of uniform and focal preload (1, 10, 20, and 30% of sample width) to investigate the relationship between MR elastography-derived complex shear modulus (G∗) and the maximum principal Right Cauchy Green Strain (C₁₁). Three tissue samples from each of the same 9 livers underwent oscillatory rheometry under the same 4 preloads (1, 10, 20, and 30% strain). MR elastography-derived complex shear modulus (G∗) from the uniform preload was validated against rheometry by fitting the frequency dependence of G∗ with a power-law and extrapolating rheometry-derived G∗ to 60 Hz.

RESULTS

MR elastography-derived G∗ increased with increasing compressive large deformation strain, and followed a power-law curve (G∗ = 1.73 × C₁₁^-0.38, R² = 0.96). Similarly, rheometry-derived G∗ at 1 Hz, increasing from 0.66 ± 1.03 kPa (1% strain) to 1.84 ± 1.65 kPa (30% strain, RM one-way ANOVA, P < 0.001), and the frequency dependence of G∗ followed a power-law with the exponent decreasing from 0.13 to 0.06 with increasing preload. MR elastography-derived G∗ was 1.4-3.1 times higher than the extrapolated rheometry-derived G∗ at 60 Hz, but the strain dependence was consistent between rheometry and MR elastography measurements.

CONCLUSIONS

This study demonstrates that MR elastography can detect changes in ex vivo bovine liver complex shear modulus due to either uniform or focal preload and therefore can be a useful technique to characterize nonlinear viscoelastic properties of soft tissue, provided that strains applied to the tissue can be quantified. Although MR elastography could reliably characterize the strain dependence of the ex vivo bovine liver, MR elastography overestimated the complex shear modulus of the tissue compared to rheological measurements, particularly at lower preload (<10%). That is likely to be important in clinical hepatic MR elastography diagnosis studies if preload is not carefully considered. A limitation is the absence of overlapping frequency between rheometry and MR elastography for formal validation.

Assessment of alternative techniques to quantify the effect of injury on soft tissue in closed ankle and pilon fractures

INTRODUCTION

Local soft tissue status (STS) guides the timing for definitive surgical treatment strategies of fracture fixation around the ankle joint. The aim of this study was to assess different types of new technical devices in relation to the surgical treatment in closed ankle and pilon fractures.

METHODS

This study was designed as a cohort study. Adult patients admitted between February 1, 2019 and December 31, 2020 presenting with closed ankle fracture requiring surgical treatment were eligible. The exclusion criteria were previous injuries to the lower extremity, acute deep venous thrombosis, skin diseases, and delayed presentation (admission >24 hours after injury). Moderate-energy trauma includes injuries sustained during team sports, biking, and running. The primary outcome was the assessment of the degree of soft tissue involvement following closed fractures by comparing different techniques focusing on the ankle region and including ankle and pilon fractures. The variables of interest included the circumference of soft tissue swelling around the ankle, determined within a 5-mm range in the area of the medial and lateral malleolus and the bone-skin distance on a plain radiograph, determined by the largest distance from the malleolus to the border of the soft-tissue shadow. STS assessment included optical measures of local perfusion (O2C, Lea Inc. Germany) and tactile measures of mechanical characteristics (Myoton® tensiometer AS, Estonia). Measurements of Group Temp (temporary stabilization) and Group Def (definitive surgery) were taken on admission and prior to the treatment strategy decision. The contralateral non-injured ankle served as a control. The quality of assessment tools was quantified by calculating the smallest detectable change (SDC).

RESULTS

In total, 38 patients with a mean age of 40.4 (SD 17.8) years were included. The SDC was 3.2% (95%CI 2.5 to 3.8) for local blood flow and 1.1% (95%CI 0.4 to 1.7) for soft tissue stiffness. The circumference of the injured area at admission was significantly higher than that of the healthy site (28.2 [SD 3.4] cm versus 23.9 [SD 2.4] cm, p < 0.001). The local perfusion (blood flow 107.5 (SD 40.79 A.U. vs. 80.1 [SD 13.8] A.U., p = 0.009), and local dynamic stiffness of the skin (668.1 (SD 148.0) N/m vs 449.5 (SD 87.7) N/m, p < 0.001) were significantly higher at the injured site. In Group Temp, the local blood flow was significantly higher when compared with Group Def (109.6 [SD 39.8] vs. 94.5 [SD 13.0], p = 0.023). The dynamic stiffness of the soft tissue was significantly higher in Group Temp (679.4 N/m [SD 147.0] N/m vs. 573.0 N/m (SD 93.8) N/m, p < 0.001). The physical properties of STS were comparable among the fracture types. None of the included patients had local soft tissue complications.

CONCLUSION

Closed fractures of the ankle and the pilon are associated with an increase in local circulation and local soft tissue stiffness and tension. These changes of the STS following injury can be quantified in a standardized and reproducible manner.

Real-Time Multifrequency MR Elastography of the Human Brain Reveals Rapid Changes in Viscoelasticity in Response to the Valsalva Maneuver

Modulation of cerebral blood flow and vascular compliance plays an important role in the regulation of intracranial pressure (ICP) and also influences the viscoelastic properties of brain tissue. Therefore, magnetic resonance elastography (MRE), the gold standard for measuring in vivo viscoelasticity of brain tissue, is potentially sensitive to cerebral autoregulation. In this study, we developed a multifrequency MMRE technique that provides serial maps of viscoelasticity at a frame rate of nearly 6 Hz without gating, i.e., in quasi-real time (rt-MMRE). This novel method was used to monitor rapid changes in the viscoelastic properties of the brains of 17 volunteers performing the Valsalva maneuver (VM). rt-MMRE continuously sampled externally induced vibrations comprising three frequencies of 30.03, 30.91, and 31.8 Hz were over 90 s using a steady-state, spiral-readout gradient-echo sequence. Data were processed by multifrequency dual elasto-visco (MDEV) inversion to generate maps of magnitude shear modulus | G^∗| (stiffness) and loss angle φ at a frame rate of 5.4 Hz. As controls, the volunteers were examined to study the effects of breath-hold following deep inspiration and breath-hold following expiration. We observed that | G^∗| increased while φ decreased due to VM and, less markedly, due to breath-hold in inspiration. Group mean VM values showed an early overshoot of | G^∗| 2.4 ± 1.2 s after the onset of the maneuver with peak values of 6.7 ± 4.1% above baseline, followed by a continuous increase in stiffness during VM. A second overshoot of | G^∗| occurred 5.5 ± 2.0 s after the end of VM with peak values of 7.4 ± 2.8% above baseline, followed by 25-s sustained recovery until the end of image acquisition. φ was constantly reduced by approximately 2% during the entire VM without noticeable peak values. This is the first report of viscoelasticity changes in brain tissue induced by physiological maneuvers known to alter ICP and detected by clinically applicable rt-MMRE. Our results show that apnea and VM slightly alter brain properties toward a more rigid-solid behavior. Overshooting stiffening reactions seconds after onset and end of VM reveal rapid autoregulatory processes of brain tissue viscoelasticity.

Time-Resolved Response of Cerebral Stiffness to Hypercapnia in Humans

Cerebral blood flow, cerebral stiffness (CS) and intracranial pressure are tightly linked variables of cerebrovascular reactivity and cerebral autoregulation. Transtemporal ultrasound time-harmonic elastography was used for rapid measurement of CS changes in 10 volunteers before, during and after administration of a gas mixture of 95% O₂ and 5% CO₂ (carbogen). Within the first 2.2 ± 2.0 min of carbogen breathing, shear wave speed determined as a surrogate parameter of CS increased from 1.57 ± 0.04 to 1.66 ± 0.05 m/s (p < 0.01) in synchrony with end-tidal CO₂ while post-hypercapnic CS recovery was delayed by 2.7 ± 1.4 min in relation to end-tidal CO₂. Our results indicate that CS is highly sensitive to changes in CO₂ levels of inhaled air. Possible mechanisms underlying the observed CS changes might be associated with cerebrovascular reactivity, cerebral blood flow adaptation and intracranial regulation, all of which are potentially relevant for future diagnostic applications of transtemporal time-harmonic elastography in a wide spectrum of neurologic diseases.

Soft tissue rheology and its implications for elastography: Challenges and opportunities

Magnetic resonance elastography and related shear wave ultrasound elastography techniques can be used to estimate the mechanical properties of soft tissues in vivo by using the relationships between wave propagation and the elastic properties of materials. These techniques have found numerous clinical and research applications, tracking changes in tissue properties as a result of disease or other interventions. Most dynamic elastography approaches estimate tissue elastic (or viscoelastic) properties from a simplified version of the equations for the propagation of acoustic waves through a homogeneous linear (visco)elastic medium. However, soft tissue rheology is complex and departs significantly from this idealized picture. In particular, soft tissues are nonlinearly viscoelastic, inhomogeneous and often anisotropic, and their apparent stiffness can vary with the current loading state. All of these features have implications for the reliability and reproducibility of elastography measurements, from data acquisition to analysis and interpretation. New developments in inversion algorithms for elastography are beginning to offer solutions to account for the complex rheology of tissues, including inhomogeneity and anisotropy. There remains considerable potential to further refine elastography to capture the full spectrum of tissue rheology, and thus to better understand the underlying tissue microstructural changes in a broad range of clinical disorders.

Constitutive Relations for Pressure-Driven Stiffening in Poroelastic Tissues

Vascularized biological tissue has been shown to increase in stiffness with increased perfusion pressure. The interaction between blood in the vasculature and other tissue components can be modeled with a poroelastic, biphasic approach. The ability of this model to reproduce the pressure-driven stiffening behavior exhibited by some tissues depends on the choice of the mechanical constitutive relation, defined by the Helmholtz free energy density of the skeleton. We analyzed the behavior of a number of isotropic poroelastic constitutive relations by applying a swelling pressure, followed by homogeneous uniaxial or simple-shear deformation. Our results demonstrate that a strain-stiffening constitutive relation is required for a material to show pressure-driven stiffening, and that the strain-stiffening terms must be volume-dependent.

Characterising soft tissues under large amplitude oscillatory shear and combined loading

Characterising soft biological tissues outside the linear viscoelastic regime is challenging due to their complex behaviour. In addition, the viscoelastic properties of tissues have been shown to be sensitive to sample preparation and loading regime resulting in inconsistent data varying by orders magnitude in the literature. This paper presents a novel technique to characterise the non-linear behaviour of tissues which uses Fourier Transformation to decompose the stress output waveform under large amplitude oscillatory shear (LAOS) into harmonic contributions. The effect of varying preload, the compressive strain exerted on a liver tissue specimen prior to shear testing to minimise slip, was also investigated. Results showed that in the linear regime, preload affects the viscoelastic response of liver. Histological analysis indicated that there were structural changes as a result of the preload that may be linked to the differences in observed behaviour. Fourier analysis was used to extract the first and third harmonic components of the shear moduli at large strain. At 50% shear strain, a change in the third harmonic component of the shear moduli was accompanied by a marked change in the micro-structural arrangement of the sinusoids. This paper demonstrates a method of efficiently characterising soft biological tissues under large amplitude oscillatory shear under combined loading.

MR elastography of liver tumours: value of viscoelastic properties for tumour characterisation

OBJECTIVES

To assess the value of the viscoelastic parameters in the characterisation of liver tumours at MR elastography.

PATIENTS AND METHODS

Ninety-four patients with liver tumours >1 cm prospectively underwent MR elastography using 50-Hz mechanical waves and a full three-directional motion-sensitive sequence. The model-free viscoelastic parameters (the complex shear modulus and its real and imaginary parts, i.e. the storage and loss moduli) were calculated in 72 lesions after exclusion of cystic, treated or histopathologically undetermined tumours.

RESULTS

We observed higher absolute shear modulus and loss modulus in malignant versus benign tumours (3.38 ± 0.26 versus 2.41 ± 0.15 kPa, P < 0.01 and 2.25 ± 0.26 versus 1.05 ± 0.13 kPa, P < 0.001, respectively). Moreover, the loss modulus of hepatocellular carcinomas was significantly higher than in benign hepatocellular tumours. The storage modulus did not differ significantly between malignant and benign tumours. The area under the receiver-operating characteristic curve of loss modulus was significantly larger than that of the absolute shear modulus and storage modulus when comparing malignant and benign lesions.

CONCLUSIONS

The increased loss modulus is a better discriminator between benign and malignant tumours than the increased storage modulus or absolute value of the shear modulus.

KEY POINTS

• Magnetic Resonance elastography is a new method of assessing the liver. • Increased loss modulus is an indicator of malignancy in hepatic tumours. • Loss modulus is a better discriminator than absolute shear modulus values. • The viscoelastic properties of lesions offer promise for characterising liver tumours.

Identification of capillary blood pressure levels at which capillary collapse is likely in a tissue subjected to large compressive and shear deformations

Pressure ulcers (PU) are localised damage to skin and underlying tissues, caused by sustained tissue deformations and ischaemia. PU typically appear in insensitive or immobile patients, e.g. those with spinal cord injury (SCI) or geriatric patients. As these patients often experience fluctuations in blood pressure, and are also exposed to high-shear loads in their weight-bearing soft tissues during wheelchair sitting or bed rest, we used an inverse finite element method to determine the effects of capillary blood pressure (CBP) and shear deformations on occurrence of mechanical collapse in capillaries. We studied collapse in straight, U-shaped and bifurcated capillaries. All model configurations were consistent in demonstrating that the level of CBP has a considerable influence on the likelihood of capillary collapse in the physiological CBP range, particularly if shear is present. Our modelling therefore suggests that low CBP is a 'suspect' risk factor for PU in SCI and geriatric patients.

Computational model of the cerebral ventricles in hydrocephalus

Understanding the mechanisms of tissue injury in hydrocephalus is important to shed light on the pathophysiology of this neurostructural disorder. To date, most of the finite element models created to study hydrocephalus have been two-dimensional (2D). This may not be adequate as the geometry of the cerebral ventricles is unique. In this study, a three-dimensional (3D) finite element model of the cerebral ventricles during hydrocephalus is presented. Results from this model show that during hydrocephalus, the periventricular regions experience the highest stress, and stress magnitude is approximately 80 times higher than the cerebral mantle. This suggests that functional deficits observed in hydrocephalic patients could therefore be more related to the damage to periventricular white matter. In addition, the stress field simulated in the tissues based on the 3D model was found to be approximately four times lower than on the 2D model.

The effect of bone fragment size and cerebrospinal fluid on spinal cord deformation during trauma: an ex vivo study

Object

The purpose of the study was to assess the effect of CSF and the size of the impacting bone fragment area on spinal cord deformation during trauma.

Methods

A transverse impact rig was used to produce repeated impacts on bovine and surrogate cord models. Tests were recorded with high-speed video and performed on specimens with and without CSF and/or dura mater and with 3 different impactor areas.

Results

The CSF layer was found to reduce the maximum cord deformation significantly. A 50% reduction in impact area significantly increased the maximum cord deformation by 20–30%. The surrogate model showed similar trends to the bovine model but with lower absolute deformation values.

Conclusions

Cerebrospinal fluid protects the cord during impact by reducing its deformation. A smaller bone fragment impact area increases the deformation of the cord, in agreement with clinical results, where a higher impact energy—possibly giving rise to smaller fragments—results in a worse neurological deficit.

Assessment of in vivo and post-mortem mechanical behavior of brain tissue using magnetic resonance elastography

The knowledge of in vivo brain tissue mechanical properties is essential in several biomedical engineering fields, such as injury biomechanics and neurosurgery simulation. Almost all existing available data have been obtained in vitro by invasive experimental protocols. However, the difference between in vivo and post-mortem mechanical properties remains poorly known, essentially due to the lack of a common method that could measure them both in vivo and ex vivo. In this study, we report the use of magnetic resonance elastography (MRE) for the non-invasive assessment of in vivo brain tissue viscoelastic properties and for the investigation of their evolution after the death. Experiments were performed on seven adult male rats. Shear storage and loss moduli were measured in vivo, just after death and at post-mortem time of approximately 24h. A significant increase in shear storage modulus G(') of approximately 100% was found to occur just after death (p=0.002), whereas no significant difference was found between in vivoG(') and G(') at 24h post-mortem time. No significant difference was found between shear loss modulus G('')in vivo and just after death, whereas a decrease of about 50% was found to occur after 24h (p=0.02). These results illustrate the ability of MRE to investigate some of the critical soft tissue biomechanics-related issues, as it can be used as a non-invasive tool for measuring soft tissue viscoelastic properties.

The effect of cerebrospinal fluid on the biomechanics of spinal cord: an ex vivo bovine model using bovine and physical surrogate spinal cord

STUDY DESIGN

A biomechanical study using ex vivo bovine spinal cord and dura, and a synthetic surrogate spinal cord with bovine dura.

OBJECTIVE

To investigate the effect of cerebrospinal fluid (CSF) on spinal cord deformation characteristics and to evaluate the biofidelity of a new surrogate spinal cord using an ex vivo bovine model of the burst fracture process.

SUMMARY OF BACKGROUND DATA

Spinal cord injury is associated with significant personal, economic and social costs. The role of CSF during the injury event and its effect on the spinal cord deformation and neurologic injury is not well understood. Such knowledge could inform preventative strategies and clinical interventions and aid the development and validation of experimental and computational models.

METHODS

The transverse impact of a propelled bone fragment analogue with bovine and surrogate cord models was recorded with high speed video and the images analyzed to determine deformation trajectories. Each cord specimen was tested in 3 states: with dura and CSF, with dura only, and without dura. The effect of these states on deformation magnitude, duration, and energy loss parameters was assessed. RESULTS.: The estimated spinal cord deformation was significantly reduced, although not eliminated, in the presence of CSF when compared to the bare state. The duration of deformation was generally increased in the presence of CSF, though this difference was not statistically significant. This may indicate a reduction in the cord-fragment interaction force for a given impulse. The dura was found to have no significant effect on deformation parameters for the bovine spinal cord. The deformation of the surrogate cord gave similar trends for the different states in comparison to the bovine cord, but was significantly less than the bovine spinal cord for all conditions.

CONCLUSION

The results indicate that the protective mechanism of CSF may not eliminate cord deformationunder the high energy transverse impact characteristic of a burst fracture. However, CSF may contribute to a lessening of cord deformation and applied force.

The effects of pressure and shear on capillary closure in the microstructure of skeletal muscles

Deep tissue injury (DTI) is a severe pressure ulcer, which initiates in muscle tissue under a bony prominence, and progresses outwards. It is associated with mechanical pressure and shear that may cause capillaries to collapse and thus, induce ischemic conditions. Recently, some investigators stipulated that ischemia alone cannot explain the etiology of DTI, and other mechanisms, particularly excessive cellular deformations may be involved. The goal of this study was to evaluate the functioning of capillaries in loaded muscle tissue, using animal and finite element (FE) models. Pressures of 12, 37, and 78 kPa were applied directly to one gracilis muscle of 11 rats for 2 h. Temperatures of the loaded and contralateral muscles were recorded with time using infrared thermography (IRT) as a measure of the ischemic level. In addition, a non-linear large deformation muscle-fascicle-level FE model was developed and subjected to pressures of 12-120 kPa without and with simultaneous shear strain of up to 8%. For each simulation case, the accumulative percentage of open capillary cross-sectional area and the number of completely closed capillaries were determined. After 2 h, temperature of the loaded muscles was 2.4 +/- 0.3 degrees C (mean +/- standard deviation) lower than that of the unloaded contralateral limbs (mean of plateau temperature values across all pressure groups). Temperature of the loaded muscles dropped within 10 min but then remained stable and significantly higher than room temperature for at least 30 additional minutes in all pressure groups, indicating that limbs were not completely ischemic within the first 40 min of the trials. Our FE model showed that in response to pressures of 12-120 kPa and no shear, the accumulative percentage of open capillary cross-sectional area decreased by up to 71%. When shear strains were added, the open capillary cross-sectional area decreased more rapidly, but even for maximal loading, only 46% of the capillaries were completely closed. Taken together, the animal and FE model results suggest that acute ischemia does not develop in skeletal muscles under physiological load levels within a timeframe of 40 min. Since there is evidence that DTI develops within a shorter time, ischemia is unlikely to be the only factor causing DTI.

Interstitial fluid pressure in soft tissue as a result of an externally applied contact pressure

Manipulation of interstitial fluid pressure (IFP) has a clinical potential when used in conjunction with near-infrared spectroscopy for the detection of breast cancer. In order to better interpret how the applied pressure alters the vascular space and interstitial water volumes in breast tissue, a study on tissue-mimicking, gelatin phantoms was carried out to mimic the translation of external force into internal pressures. A complete set of three-dimensional (3D) pressure maps were obtained for the interior volumes of phantoms as an external force of 10 mmHg was applied, using mixtures of elastic moduli 19 and 33 kPa to simulate adipose and fibroglandular values of breast tissue. Corresponding linear elastic finite element analysis (FEA) cases were formulated. Shear stress, nonlinear mechanical properties, gravity and tissue geometry were all observed to contribute to internal pressure distribution, with surface shear stresses increasing internal pressures near the surface to greater than twice the applied external pressure. Average pressures by depth were predicted by the linear elastic FEA models. FEA models were run for cases mimicking a 93 kPa tumor inclusion within regions of adipose, fibroglandular tissue, and a composite of the two tissue types to illustrate the localized high fluid pressures caused by a tumor when an external force is applied. The conclusion was that external contact forces can generate potentially clinically useful fluid pressure magnitudes in regions of sharp effective elastic modulus gradients, such as tumor boundaries.

Spinal cord–fragment interactions following burst fracture: an in vitro model

Object

The purpose of the study was to develop an in vitro model of the bone fragment and spinal cord interactions that occur during a burst fracture and further the understanding of how the velocity of the bone fragment and the status of the posterior longitudinal ligament (PLL) affect the deformation of the cord.

Methods

An in vitro model was developed such that high-speed video and pressure measurements recorded the impact of a simulated bone fragment on sections of explanted bovine spinal cord. The model simulated the PLL and the posterior elements.

The status of the PLL had a significant effect on both the maximum occlusion of the spinal cord and the time for occlusion to occur. Raising the fragment velocity led to an overall increase in the spinal cord deformation. Interestingly the dura mater appeared to have little or no effect on the extent of occlusion.

Conclusions

These findings may indicate the importance of the dura’s interaction with the cerebrospinal fluid in protecting the cord during this type of impact.

The biomechanical response of spinal cord tissue to uniaxial loading

The spinal cord is an integral component of the spinal column and is prone to physical injury during trauma or more long-term pathological insults. The development of computational models to simulate the cord-column interaction during trauma is important in developing a proper understanding of the injury mechanism. Such models would be invaluable in seeking both preventive strategies that reduce the propensity for injury and identifying specific treatment regimes. However, these developments are hampered by the limited information available on the structural and mechanical properties of this soft tissue owing to the difficulty in handling this material in a cadaveric situation. The purpose of the present paper is to report the rapid deterioration in the quality of the tissues once excised, which provides a further challenge to the successful elucidation of the structural properties of the tissue. In particular, the tangent modulus of the tissue is seen to increase sharply over a period of 72 h.

Application of soft tissue modelling to image-guided surgery

The deformation of soft tissue compromises the accuracy of image-guided surgery based on preoperative images, and restricts its applicability to surgery on or near bony structures. One way to overcome these limitations is to combine biomechanical models with sparse intraoperative data, in order to realistically warp the preoperative image to match the surgical situation. We detail the process of biomechanical modelling in the context of image-guided surgery. We focus in particular on the finite element method, which is shown to be a promising approach, and review the constitutive relationships which have been suggested for representing tissue during surgery. Appropriate intraoperative measurements are required to constrain the deformation, and we discuss the potential of the modalities which have been applied to this task. This technology is on the verge of transition into clinical practice, where it promises to increase the guidance accuracy and facilitate less invasive interventions. We describe here how soft tissue modelling techniques have been applied to image-guided surgery applications.

The mechanical properties of rat spinal cord in vitro

Freshly excised rat spinal cords were tested in uniaxial tension, in vitro, at strain rates ranging from 0.002 to 0.2 s-1. Stress relaxation tests were performed for a range of strains from 2% to 5%, with the relaxation behaviour being recorded for a period of at least 30 min. Samples exhibited a characteristic "J" shaped non-linear stress-strain response, with stiffness increasing with applied strain. The cords were labelled with rows of small markers and the uniaxial tension tests were recorded via video. Subsequent image analysis enabled the distribution of strain on the cord surface to be determined. Viscoelastic models were developed to model the mechanical behaviour of the specimens and were found to adequately describe the material behaviour.

Are in vivo and in situ brain tissues mechanically similar?

Brain tissue mechanical properties have been well-characterized in vitro, and were found to be inhomogeneous, nonlinear anisotropic and influenced by neurological development and postmortem time interval prior to testing. However, brain in vivo is a vascularized tissue, and there is a paucity of information regarding the effect of perfusion on brain mechanical properties. Furthermore, mechanical properties are often extracted from preconditioned tissue, and it remains unclear if these properties are representative of non-preconditioned tissue. We present non-preconditioned (NPC) and preconditioned (PC) relaxation responses of porcine brain (N = 10) obtained in vivo, in situ and in vitro, at anterior, mid and posterior regions of the cerebral cortex during 4mm indentations at either 3 or 1 mm/s. Material property characteristics showed no dependency on the site tested, thus revealing that cortical gray matter on the parietal and frontal lobes can be considered homogenous. In most cases, preconditioning decreased the shear moduli, with a more pronounced effect in the dead (in situ and in vitro) brain. For most conditions, it was found that only the long-term time constant of relaxation (tau > 20 s) significantly decreased from in vivo to in situ modes (p < 0.02), and perfusion had no effect on any other property. These findings support the concept that perfusion does not affect the stiffness of living cortical tissue.