Robust acoustic trapping and perturbation of single-cell microswimmers illuminate three-dimensional swimming and ciliary coordination.

We report a label-free acoustic microfluidic method to confine single, cilia-driven swimming cells in space without limiting their rotational degrees of freedom. Our platform integrates a surface acoustic wave (SAW) actuator and bulk acoustic wave (BAW) trapping array to enable multiplexed analysis with high spatial resolution and trapping forces that are strong enough to hold individual microswimmers. The hybrid BAW/SAW acoustic tweezers employ high-efficiency mode conversion to achieve submicron image resolution while compensating for parasitic system losses to immersion oil in contact with the microfluidic chip. We use the platform to quantify cilia and cell body motion for wildtype biciliate cells, investigating effects of environmental variables like temperature and viscosity on ciliary beating, synchronization, and three-dimensional helical swimming. We confirm and expand upon the existing understanding of these phenomena, for example determining that increasing viscosity promotes asynchronous beating. Motile cilia are subcellular organelles that propel microorganisms or direct fluid and particulate flow. Thus, cilia are critical to cell survival and human health. The unicellular alga Chlamydomonas reinhardtii is widely used to investigate the mechanisms underlying ciliary beating and coordination. However, freely swimming cells are difficult to image with sufficient resolution to capture cilia motion, necessitating that the cell body be held during experiments. Acoustic confinement is a compelling alternative to use of a micropipette, or to magnetic, electrical, and optical trapping that may modify the cells and affect their behavior. Beyond establishing our approach to studying microswimmers, we demonstrate a unique ability to mechanically perturb cells via rapid acoustic positioning.

Preoperative prolapse phenotype is predictive of surgical outcome with minimally invasive sacrocolpopexy.

BACKGROUND: The gold-standard treatment for advanced pelvic organ prolapse is sacrocolpopexy. However, the preoperative features of prolapse that predict optimal outcomes are unknown. OBJECTIVE: This study aimed to develop a clinical prediction model that uses preoperative scores on the Pelvic Organ Prolapse Quantification examination to predict outcomes after minimally invasive sacrocolpopexy for stages 2, 3, and 4 uterovaginal prolapse and vaginal vault prolapse. STUDY DESIGN: A 2-institution database of pre- and postoperative variables from 881 cases of minimally invasive sacrocolpopexy was analyzed. Data from patients were analyzed in the following 4 groups: stage 2 uterovaginal prolapse, stage 3 to 4 uterovaginal prolapse, stage 2 vaginal vault prolapse, and stage 3 to 4 vaginal vault prolapse. Unsupervised machine learning was used to identify clusters and investigate associations between clusters and outcome. The k-means clustering analysis was performed with preoperative Pelvic Organ Prolapse Quantification points and stratified by previous hysterectomy status. The "optimal" surgical outcome was defined as postoperative Pelvic Organ Prolapse Quantification stage <2. Demographic variables were compared by cluster with Student t and chi-square tests. Odds ratios were calculated to determine whether clusters could predict the outcome. Age at surgery, body mass index, and previous prolapse surgery were used for adjusted odds ratios. RESULTS: Five statistically distinct prolapse clusters (phenotypes C, A, A>P, P, and P>A) were found. These phenotypes reflected the predominant region of prolapse (apical, anterior, or posterior) and whether support was preserved in the nonpredominant region. Phenotype A (anterior compartment prolapse predominant, posterior support preserved) was found in all 4 groups of patients and was considered the reference in the analysis. In 111 patients with stage 2 uterovaginal prolapse, phenotypes A and A>P (greater anterior prolapse than posterior prolapse) were found, and patients with phenotype A were more likely than those with phenotype A>P to have an optimal surgical outcome. In 401 patients with stage 3 to 4 uterovaginal prolapse, phenotypes C (apical compartment predominant, prolapse in all compartments), A, and A>P were found, and patients with phenotype A>P were more likely than those with phenotype A to have ideal surgical outcome. In 72 patients with stage 2 vaginal vault prolapse, phenotypes A, A>P, and P (posterior compartment predominant, anterior support preserved) were found, and those with phenotype A>P were less likely to have an ideal outcome than patients with phenotype A. In 297 patients with stage 3 to 4 vaginal vault prolapse, phenotypes C, A, and P>A (prolapse greater in posterior than in anterior compartment) were found, but there were no significant differences in rate of ideal outcome between phenotypes. CONCLUSION: Five anatomic phenotypes based on preoperative Pelvic Organ Prolapse Quantification scores were present in patients with stages 2 and 3 to 4 uterovaginal prolapse and vaginal vault prolapse. These phenotypes are predictive of surgical outcome after minimally invasive sacrocolpopexy. Further work needs to confirm the presence and predictive nature of these phenotypes. In addition, whether the phenotypes represent a progression of prolapse or discrete prolapse presentations resulting from different anatomic and life course risk profiles is unknown. These phenotypes may be useful in surgical counseling and planning.

Shear wave speeds in a nearly incompressible fibrous material with two unequal fiber families.

The mechanical properties of soft biological tissues can be characterized non-invasively by magnetic resonance elastography (MRE). In MRE, shear wave fields are induced by vibration, imaged by magnetic resonance imaging, and inverted to estimate tissue properties in terms of the parameters of an underlying material model. Most MRE studies assume an isotropic material model; however, biological tissue is often anisotropic with a fibrous structure, and some tissues contain two or more families of fibers-each with different orientations and properties. Motivated by the prospect of using MRE to characterize such tissues, this paper describes the propagation of shear waves in soft fibrous material with two unequal fiber families. Shear wave speeds are expressed in terms of material parameters, and the effect of each parameter on the shear wave speeds is investigated. Analytical expressions of wave speeds are confirmed by finite element simulations of shear wave transmission with various polarization directions. This study supports the feasibility of estimating parameters of soft fibrous tissues with two unequal fiber families in vivo from local shear wave speeds and advances the prospects for the mechanical characterization of such biological tissues by MRE.

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig.

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development.

Effect of Direction and Frequency of Skull Motion on Mechanical Vulnerability of the Human Brain.

Strain energy and kinetic energy in the human brain were estimated by magnetic resonance elastography (MRE) during harmonic excitation of the head, and compared to characterize the effect of loading direction and frequency on brain deformation. In brain MRE, shear waves are induced by external vibration of the skull and imaged by a modified MR imaging sequence; the resulting harmonic displacement fields are typically "inverted" to estimate mechanical properties, like stiffness or damping. However, measurements of tissue motion from MRE also illuminate key features of the response of the brain to skull loading. In this study, harmonic excitation was applied in two different directions and at five different frequencies from 20 to 90 Hz. Lateral loading induced primarily left-right head motion and rotation in the axial plane; occipital loading induced anterior-posterior head motion and rotation in the sagittal plane. The ratio of strain energy to kinetic energy (SE/KE) depended strongly on both direction and frequency. The ratio of SE/KE was approximately four times larger for lateral excitation than for occipital excitation and was largest at the lowest excitation frequencies studied. These results are consistent with clinical observations that suggest lateral impacts are more likely to cause injury than occipital or frontal impacts, and also with observations that the brain has low-frequency (∼10 Hz) natural modes of oscillation. The SE/KE ratio from brain MRE is potentially a simple and powerful dimensionless metric of brain vulnerability to deformation and injury.

Comparison of Deformation Patterns Excited in the Human Brain In Vivo by Harmonic and Impulsive Skull Motion.

Noninvasive measurements of brain deformation in human participants in vivo are needed to develop models of brain biomechanics and understand traumatic brain injury (TBI). Tagged magnetic resonance imaging (tagged MRI) and magnetic resonance elastography (MRE) are two techniques to study human brain deformation; these techniques differ in the type of motion and difficulty of implementation. In this study, oscillatory strain fields in the human brain caused by impulsive head acceleration and measured by tagged MRI were compared quantitatively to strain fields measured by MRE during harmonic head motion at 10 and 50 Hz. Strain fields were compared by registering to a common anatomical template, then computing correlations between the registered strain fields. Correlations were computed between tagged MRI strain fields in six participants and MRE strain fields at 10 Hz and 50 Hz in six different participants. Correlations among strain fields within the same experiment type were compared statistically to correlations from different experiment types. Strain fields from harmonic head motion at 10 Hz imaged by MRE were qualitatively and quantitatively similar to modes excited by impulsive head motion, imaged by tagged MRI. Notably, correlations between strain fields from 10 Hz MRE and tagged MRI did not differ significantly from correlations between strain fields from tagged MRI. These results suggest that low-frequency modes of oscillation dominate the response of the brain during impact. Thus, low-frequency MRE, which is simpler and more widely available than tagged MRI, can be used to illuminate the brain's response to head impact.

Data-driven Uncertainty Quantification in Computational Human Head Models.

Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e., model geometry, material properties, and boundary conditions) are often associated with significant uncertainty and variability. As a result, uncertainty quantification (UQ), which involves quantification of the effect of this uncertainty and variability on the simulated response, becomes critical to ensure reliability of model predictions. Modern biofidelic head model simulations are associated with very high computational cost and high-dimensional inputs and outputs, which limits the applicability of traditional UQ methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input-output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of the strain fields highlights significant spatial variation in model uncertainty, and reveals key differences in uncertainty among commonly used strain-based brain injury predictor variables.

Dynamic patterns of cortical expansion during folding of the preterm human brain.

During the third trimester of human brain development, the cerebral cortex undergoes dramatic surface expansion and folding. Physical models suggest that relatively rapid growth of the cortical gray matter helps drive this folding, and structural data suggest that growth may vary in both space (by region on the cortical surface) and time. In this study, we propose a unique method to estimate local growth from sequential cortical reconstructions. Using anatomically constrained multimodal surface matching (aMSM), we obtain accurate, physically guided point correspondence between younger and older cortical reconstructions of the same individual. From each pair of surfaces, we calculate continuous, smooth maps of cortical expansion with unprecedented precision. By considering 30 preterm infants scanned two to four times during the period of rapid cortical expansion (28-38 wk postmenstrual age), we observe significant regional differences in growth across the cortical surface that are consistent with the emergence of new folds. Furthermore, these growth patterns shift over the course of development, with noninjured subjects following a highly consistent trajectory. This information provides a detailed picture of dynamic changes in cortical growth, connecting what is known about patterns of development at the microscopic (cellular) and macroscopic (folding) scales. Since our method provides specific growth maps for individual brains, we are also able to detect alterations due to injury. This fully automated surface analysis, based on tools freely available to the brain-mapping community, may also serve as a useful approach for future studies of abnormal growth due to genetic disorders, injury, or other environmental variables.

Shear wave speeds in nearly-incompressible fibrous materials with two fiber families.

An analytical and numerical investigation of shear wave behavior in nearly-incompressible soft materials with two fiber families was performed, focusing on the effects of material parameters and imposed pre-deformations on wave speed. This theoretical study is motivated by the emerging ability to image shear waves in soft biological tissues by magnetic resonance elastography (MRE). In MRE, the relationships between wave behavior and mechanical properties can be used to characterize tissue properties non-invasively. We demonstrate these principles in two material models, each with two fiber families. One model is a nearly-incompressible linear elastic model that exhibits both shear and tensile anisotropy; the other is a two-fiber-family version of the widely-used Holzapfel-Gasser-Ogden (HGO) model, which is nonlinear. Shear waves can be used to probe nonlinear material behavior using infinitesimal dynamic deformations superimposed on larger, quasi-static "pre-deformations." In this study, closed-form expressions for shear wave speeds in the HGO model are obtained in terms of the model parameters and imposed pre-deformations. Analytical expressions for wave speeds are confirmed by finite element simulations of shear waves with various polarizations and propagation directions. These studies support the feasibility of estimating the parameters of an HGO material model noninvasively from measured shear wave speeds.

Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material.

This paper describes the propagation of shear waves in a Holzapfel-Gasser-Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (predeformation) plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after imposed predeformations. These analytical expressions show that shear wave speeds are affected by the parameters (µ0, k1, k2, κ) of the HGO model and by the direction and amplitude of the predeformations. Simulations of corresponding finite element (FE) models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, the dependence of wave speeds on the parameters of the HGO model and imposed deformations could ultimately allow the noninvasive estimation of material parameters in vivo from experimental shear wave image data.

Multi-Excitation Magnetic Resonance Elastography of the Brain: Wave Propagation in Anisotropic White Matter.

Magnetic resonance elastography (MRE) has emerged as a sensitive imaging technique capable of providing a quantitative understanding of neural microstructural integrity. However, a reliable method for the quantification of the anisotropic mechanical properties of human white matter is currently lacking, despite the potential to illuminate the pathophysiology behind neurological disorders and traumatic brain injury. In this study, we examine the use of multiple excitations in MRE to generate wave displacement data sufficient for anisotropic inversion in white matter. We show the presence of multiple unique waves from each excitation which we combine to solve for parameters of an incompressible, transversely isotropic (ITI) material: shear modulus, µ, shear anisotropy, ϕ, and tensile anisotropy, ζ. We calculate these anisotropic parameters in the corpus callosum body and find the mean values as µ = 3.78 kPa, ϕ = 0.151, and ζ = 0.099 (at 50 Hz vibration frequency). This study demonstrates that multi-excitation MRE provides displacement data sufficient for the evaluation of the anisotropic properties of white matter.

Estimation of Anisotropic Material Properties of Soft Tissue by MRI of Ultrasound-Induced Shear Waves.

This paper describes a new method for estimating anisotropic mechanical properties of fibrous soft tissue by imaging shear waves induced by focused ultrasound (FUS) and analyzing their direction-dependent speeds. Fibrous materials with a single, dominant fiber direction may exhibit anisotropy in both shear and tensile moduli, reflecting differences in the response of the material when loads are applied in different directions. The speeds of shear waves in such materials depend on the propagation and polarization directions of the waves relative to the dominant fiber direction. In this study, shear waves were induced in muscle tissue (chicken breast) ex vivo by harmonically oscillating the amplitude of an ultrasound beam focused in a cylindrical tissue sample. The orientation of the fiber direction relative to the excitation direction was varied by rotating the sample. Magnetic resonance elastography (MRE) was used to visualize and measure the full 3D displacement field due to the ultrasound-induced shear waves. The phase gradient (PG) of radially propagating "slow" and "fast" shear waves provided local estimates of their respective wave speeds and directions. The equations for the speeds of these waves in an incompressible, transversely isotropic (TI), linear elastic material were fitted to measurements to estimate the shear and tensile moduli of the material. The combination of focused ultrasound and MR imaging allows noninvasive, but comprehensive, characterization of anisotropic soft tissue.

How Does Cilium Length Affect Beating?

The effects of cilium length on the dynamics of cilia motion were investigated by high-speed video microscopy of uniciliated mutants of the swimming alga, Chlamydomonas reinhardtii. Cells with short cilia were obtained by deciliating cells via pH shock and allowing cilia to reassemble for limited times. The frequency of cilia beating was estimated from the motion of the cell body and of the cilium. Key features of the ciliary waveform were quantified from polynomial curves fitted to the cilium in each image frame. Most notably, periodic beating did not emerge until the cilium reached a critical length between 2 and 4 µm. Surprisingly, in cells that exhibited periodic beating, the frequency of beating was similar for all lengths with only a slight decrease in frequency as length increased from 4 µm to the normal length of 10-12 µm. The waveform average curvature (rad/µm) was also conserved as the cilium grew. The mechanical metrics of ciliary propulsion (force, torque, and power) all increased in proportion to length. The mechanical efficiency of beating appeared to be maximal at the normal wild-type length of 10-12 µm. These quantitative features of ciliary behavior illuminate the biophysics of cilia motion and, in future studies, may help distinguish competing hypotheses of the underlying mechanism of oscillation.

How Forces Fold the Cerebral Cortex.

Improved understanding of the factors that govern folding of the cerebral cortex is desirable for many reasons. The existence of consistent patterns in folding within and between species suggests a fundamental role in brain function. Abnormal folding patterns found in individuals affected by a diverse array of neurodevelopmental disorders underline the clinical relevance of understanding the folding process. Recent experimental and computational efforts to elucidate the biomechanical forces involved in cerebral cortical folding have converged on a consistent approach. Brain growth is modeled with two components: an expanding outer zone, destined to become the cerebral cortex, is mechanically coupled to an inner zone, destined to become white matter, that grows at a slower rate, perhaps in response to stress induced by expansion from the outer layer. This framework is consistent with experimentally observed internal forces in developing brains, and with observations of the folding process in physical models. In addition, computational simulations based on this foundation can produce folding patterns that recapitulate the characteristics of folding patterns found in gyroencephalic brains. This perspective establishes the importance of mechanical forces in our current understanding of how brains fold, and identifies realistic ranges for specific parameters in biophysical models of developing brain tissue. However, further refinement of this approach is needed. An understanding of mechanical forces that arise during brain development and their cellular-level origins is necessary to interpret the consequences of abnormal brain folding and its role in functional deficits as well as neurodevelopmental disease.Dual Perspectives Companion Paper: How Cells Fold the Cerebral Cortex, by Víctor Borrell.

Acoustic trap-and-release for rapid assessment of cell motility.

Functional cilia and flagella are crucial to the propulsion of physiological fluids, motile cells, and microorganisms. Motility assessment of individual cells allows discrimination of normal from dysfunctional behavior, but cell-scale analysis of individual trajectories to represent a population is laborious and impractical for clinical, industrial, and even research applications. We introduce an assay that quantifies swimming capability as a function of the variation in polar moment of inertia of cells released from an acoustic trap. Acoustic confinement eliminates the need to trace discrete trajectories and enables automated analysis of hundreds of cells in minutes. The approach closely approximates the average speed estimated from the mean squared displacement of individual cells for wild-type Chlamydomonas reinhardtii and two mutants (ida3 and oda5) that display aberrant swimming behaviors. Large-population acoustic trap-and-release rapidly differentiates these cell types based on intrinsic motility, which provides a highly sensitive and efficient alternative to conventional particle tracing.

Quantifying Ciliary Dynamics during Assembly Reveals Stepwise Waveform Maturation in Airway Cells.

Motile cilia are essential for clearance of particulates and pathogens from airways. For effective transport, ciliary motor proteins and axonemal structures interact to generate the rhythmic, propulsive bending, but the mechanisms that produce a dynamic waveform remain incompletely understood. Biomechanical measures of human ciliary motion and their relationships to ciliary assembly are needed to illuminate the biophysics of normal ciliary function and to quantify dysfunction in ciliopathies. To these ends, we analyzed ciliary motion by high-speed video microscopy of ciliated cells sampled from human lung airways compared with primary culture cells that undergo ciliogenesis in vitro. Quantitative assessment of waveform parameters showed variations in waveform shape between individual cilia; however, general trends in waveform parameters emerged, associated with progression of cilia length and stage of differentiation. When cilia emerged from cultured cells, beat frequency was initially elevated, then fell and remained stable as cilia lengthened. In contrast, the average bending amplitude and the ability to generate force gradually increased and eventually approached values observed in ex vivo samples. Dynein arm motor proteins DNAH5, DNAH9, DNAH11, and DNAH6 were localized within specific regions of the axoneme in the ex vivo cells; however, distinct stages of in vitro waveform development identified by biomechanical features were associated with the progressive movement of dyneins to the appropriate proximal or distal sections of the cilium. These observations suggest that the stepwise variation in waveform development during ciliogenesis is dependent on cilia length and potentially on outer dynein arm assembly.

Multimodal surface matching with higher-order smoothness constraints.

In brain imaging, accurate alignment of cortical surfaces is fundamental to the statistical sensitivity and spatial localisation of group studies, and cortical surface-based alignment has generally been accepted to be superior to volume-based approaches at aligning cortical areas. However, human subjects have considerable variation in cortical folding, and in the location of functional areas relative to these folds. This makes alignment of cortical areas a challenging problem. The Multimodal Surface Matching (MSM) tool is a flexible, spherical registration approach that enables accurate registration of surfaces based on a variety of different features. Using MSM, we have previously shown that driving cross-subject surface alignment, using areal features, such as resting state-networks and myelin maps, improves group task fMRI statistics and map sharpness. However, the initial implementation of MSM's regularisation function did not penalize all forms of surface distortion evenly. In some cases, this allowed peak distortions to exceed neurobiologically plausible limits, unless regularisation strength was increased to a level which prevented the algorithm from fully maximizing surface alignment. Here we propose and implement a new regularisation penalty, derived from physically relevant equations of strain (deformation) energy, and demonstrate that its use leads to improved and more robust alignment of multimodal imaging data. In addition, since spherical warps incorporate projection distortions that are unavoidable when mapping from a convoluted cortical surface to the sphere, we also propose constraints that enforce smooth deformation of cortical anatomies. We test the impact of this approach for longitudinal modelling of cortical development for neonates (born between 31 and 43 weeks of post-menstrual age) and demonstrate that the proposed method increases the biological interpretability of the distortion fields and improves the statistical significance of population-based analysis relative to other spherical methods.

Statistical Characterization of Human Brain Deformation During Mild Angular Acceleration Measured In Vivo by Tagged Magnetic Resonance Imaging.

Understanding of in vivo brain biomechanical behavior is critical in the study of traumatic brain injury (TBI) mechanisms and prevention. Using tagged magnetic resonance imaging, we measured spatiotemporal brain deformations in 34 healthy human volunteers under mild angular accelerations of the head. Two-dimensional (2D) Lagrangian strains were examined throughout the brain in each subject. Strain metrics peaked shortly after contact with a padded stop, corresponding to the inertial response of the brain after head deceleration. Maximum shear strain of at least 3% was experienced at peak deformation by an area fraction (median±standard error) of 23.5±1.8% of cortical gray matter, 15.9±1.4% of white matter, and 4.0±1.5% of deep gray matter. Cortical gray matter strains were greater in the temporal cortex on the side of the initial contact with the padded stop and also in the contralateral temporal, frontal, and parietal cortex. These tissue-level deformations from a population of healthy volunteers provide the first in vivo measurements of full-volume brain deformation in response to known kinematics. Although strains differed in different tissue type and cortical lobes, no significant differences between male and female head accelerations or strain metrics were found. These cumulative results highlight important kinematic features of the brain's mechanical response and can be used to facilitate the evaluation of computational simulations of TBI.

The Relationship of Three-Dimensional Human Skull Motion to Brain Tissue Deformation in Magnetic Resonance Elastography Studies.

In traumatic brain injury (TBI), membranes such as the dura mater, arachnoid mater, and pia mater play a vital role in transmitting motion from the skull to brain tissue. Magnetic resonance elastography (MRE) is an imaging technique developed for noninvasive estimation of soft tissue material parameters. In MRE, dynamic deformation of brain tissue is induced by skull vibrations during magnetic resonance imaging (MRI); however, skull motion and its mode of transmission to the brain remain largely uncharacterized. In this study, displacements of points in the skull, reconstructed using data from an array of MRI-safe accelerometers, were compared to displacements of neighboring material points in brain tissue, estimated from MRE measurements. Comparison of the relative amplitudes, directions, and temporal phases of harmonic motion in the skulls and brains of six human subjects shows that the skull-brain interface significantly attenuates and delays transmission of motion from skull to brain. In contrast, in a cylindrical gelatin "phantom," displacements of the rigid case (reconstructed from accelerometer data) were transmitted to the gelatin inside (estimated from MRE data) with little attenuation or phase lag. This quantitative characterization of the skull-brain interface will be valuable in the parameterization and validation of computer models of TBI.

Flexural Rigidity and Shear Stiffness of Flagella Estimated from Induced Bends and Counterbends.

Motile cilia and flagella are whiplike cellular organelles that bend actively to propel cells or move fluid in passages such as airways, brain ventricles, and the oviduct. Efficient motile function of cilia and flagella depends on coordinated interactions between active forces from an array of motor proteins and passive mechanical resistance from the complex cytoskeletal structure (the axoneme). However, details of this coordination, including axonemal mechanics, remain unclear. We investigated two major mechanical parameters, flexural rigidity and interdoublet shear stiffness, of the flagellar axoneme in the unicellular alga Chlamydomonas reinhardtii. Combining experiment, theory, and finite element models, we demonstrate that the apparent flexural rigidity of the axoneme depends on both the intrinsic flexural rigidity (EI) and the elastic resistance to interdoublet sliding (shear stiffness, ks). We estimated the average intrinsic flexural rigidity and interdoublet shear stiffness of wild-type Chlamydomonas flagella in vivo, rendered immotile by vanadate, to be EI = 840 ± 280 pN⋅µm(2) and ks = 79.6 ± 10.5 pN/rad, respectively. The corresponding values for the pf3; cnk11-6 double mutant, which lacks the nexin-dynein regulatory complex (N-DRC), were EI = 1011 ± 183 pN·µm(2) and ks = 39.3 ± 6.0 pN/rad under the same conditions. Finally, in the pf13A mutant, which lacks outer dynein arms and inner dynein arm c, the estimates were EI = 777 ± 184 pN·µm(2) and ks = 43.3 ± 7.7 pN/rad. In the two mutant strains, the flexural rigidity is not significantly different from wild-type (p > 0.05), but the lack of N-DRC (in pf3; cnk11-6) or dynein arms (in pf13A) significantly reduces interdoublet shear stiffness. These differences may represent the contributions of the N-DRCs (∼40 pN/rad) and residual dynein interactions (∼35 pN/rad) to interdoublet sliding resistance in these immobilized Chlamydomonas flagella.