Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus

The objective of this work was to determine the linear and non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus and to study the changes in mechanical properties throughout the thickness of the thrombus. Samples are gathered from thrombi of seven patients. Linear viscoelastic data from oscillatory shear experiments show that the change of properties throughout the thrombus is different for each thrombus. Furthermore the variations found within one thrombus are of the same order of magnitude as the variation between patients. To study the non-linear regime, stress relaxation experiments are performed. To describe the phenomena observed experimentally, a non-linear multimode model is presented. The parameters for this model are obtained by fitting this model successfully to the experiments. The model cannot only describe the average stress response for all thrombus samples but also the highest and lowest stress responses. To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.     

Viscoelastic evaluation of topical creams containing microcrystalline cellulose/sodium carboxymethyl cellulose as stabilizer

The purpose of this study was to examine the viscoelastic properties of topical creams containing various concentrations of microcrystalline cellulose and sodium carboxymethyl cellulose (Avicel(R) CL-611) as a stabilizer. Avicel CL-611 was used at 4 different levels (1%, 2%, 4%, and 6% dispersion) to prepare topical creams, and hydrocortisone acetate was used as a model drug. The viscoelastic properties such as loss modulus (G"), storage modulus (G'), and loss tangent (tan delta) of these creams were measured using a TA Instruments AR 1000 Rheometer and compared to a commercially available formulation. Continuous flow test to determine the yield stress and thixotropic behavior, and dynamic mechanical tests for determining the linear viscosity time sweep data, were performed. Drug release from the various formulations was studied using an Enhancer TM Cell assembly. Formulations containing 1% and 2% Avicel CL-611 had relative viscosity, yield stress, and thixotropic values that were similar to those of the commercial formulation. The elastic modulus (G') of the 1% and 2% formulation was relatively high and did not cross the loss modulus (G"), indicating that the gels were strong. In the commercial formulation, G' increased after preshearing and broke down after 600 seconds. The strain sweep tests showed that for all formulations containing Avicel CL-611, the G' was above G" with a good distance between them. The gel strength and the predominance of G' can be ranked 6% > 4% > 2%. The strain profiles for the 1% and 2% formulations were similar to those of the commercial formulation. The delta values for the 1% and 2% formulations were similar, and the formulations containing 4% Avicel CL-611 had lower delta values, indicating greater elasticity. Drug release from the commercial preparation was fastest compared to the formulations prepared using Avicel CL-611, a correlation with the viscoelastic properties. It was found that viscoelastic data, especially the strain sweep profiles of products containing Avicel CL-611 1% and 2%, correlated with the commercial formulation. Rheological tests that measure the viscosity, yield stress, thixotropic behavior, other oscillatory parameters such as G' and G" are necessary tools in predicting performance of semisolids.     

Microrheology of human lung epithelial cells measured by atomic force microscopy

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.     

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer.

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G'(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G'(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.     

Enhanced adhesion of dopamine methacrylamide elastomers via viscoelasticity tuning

We present a study on the effects of cross-linking on the adhesive properties of bio-inspired 3,4-dihydroxyphenylalanine (DOPA). DOPA has a unique catechol moiety found in adhesive proteins in marine organisms, such as mussels and polychaete, which results in strong adhesion in aquatic conditions. Incorporation of this functional group in synthetic polymers provides the basis for pressure-sensitive adhesives for use in a broad range of environments. A series of cross-linked DOPA-containing polymers were prepared by adding divinyl cross-linking agent ethylene glycol dimethacrylate (EGDMA) to monomer mixtures of dopamine methacrylamide (DMA) and 2-methoxyethyl acrylate (MEA). Samples were prepared using a solvent-free microwave-assisted polymerization reaction and compared to a similar series of cross-linked MEA materials. Cross-linking with EGDMA tunes the viscoelastic properties of the adhesive material and has the advantage of not reacting with the catechol group that is responsible for the excellent adhesive performance of this material. Adhesion strength was measured by uniaxial indentation tests, which indicated that 0.001 mol % of EGDMA-cross-linked copolymer showed the highest work of adhesion in dry conditions, but non-cross-linked DMA was the highest in wet conditions. The results suggest that there is an optimal cross-linking degree that displays the highest adhesion by balancing viscous and elastic behaviors of the polymer but this appears to depend on the conditions. This concentration of cross-linker is well below the theoretical percolation threshold, and we propose that subtle changes in polymer viscoelastic properties can result in significant improvements in adhesion of DOPA-based materials. The properties of lightly cross-linked poly(DMA-co-MEA) were investigated by measurement of the frequency dependence of the storage modulus (G') and loss modulus (G'). The frequency-dependence of G' and magnitude of G' showed gradual decreases with the fraction of EGDMA. Loosely cross-linked DMA copolymers, containing 0% and 0.001 mol % of EGDMA-cross-linked copolymers, displayed rheological behavior appropriate for pressure-sensitive adhesives characterized by a higher G' at high frequencies and lower G' at low frequencies. Our results indicate that dimethacrylate cross-linking of DMA copolymers can be used to enhance the adhesive properties of this unique material.     

Rheology and dynamic light scattering of silk fibroin solution extracted from the middle division of Bombyx mori silkworm

Dynamic light scattering (DLS) and rheological measurements were performed on aqueous silk fibroin solutions extracted from the middle division of Bombyx mori silkworm over a wide range of polymer concentration C from 0.08 to 27.5 wt %. DLS results obtained in the dilute region of C less than 1 wt % are consistent with a model that an elementary unit is a large protein complex consisting of silk fibroin and P25 with a 6:1 molar ratio. Rheological measurements in the dilute C region reveal that those units (or clusters) with the hydrodynamic radius of about 100 nm form a network extending over the whole sample volume with small pseudoplateau modulus mainly by ionic bonding between COO(-) ions of the fibroin molecules and divalent metallic ions such as Ca(2+) or Mg(2+) ions present in the sample and also that, after a yield stress is reached, steady plastic flow is induced with viscosity much lower than the zero-shear viscosity estimated from creep and creep recovery measurements by 4-6 orders of magnitude. Angular frequency omega dependencies of the storage and the loss shear moduli, G'(omega) and G' '(omega), measured in the linear viscoelastic region, indicate that all solutions possess the pseudoplateau modulus in the low omega region and samples become highly viscoleastic for C greater, similar 4.2 wt %. Above C = 11.2 wt % another plateau appears at the high omega end accompanied by a distinct maximum of G' ' in the intermediate omega region. The relaxation motion with tau = 0.5 s corresponding to the maximum of G' ' is one of characteristic properties of the fibroin solutions in the high C region. Thermorheological behaviors of the solution with C = 27.5 wt % show that the network structure formed in the MM part of the silk gland is susceptible to temperature and a more stable homogeneous network is realized by raising the temperature up to T = 65 degrees C.     

Characterizing viscoelastic properties of breast cancer tissue in a mouse model using indentation

Breast cancer is one of the leading cancer forms affecting females worldwide. Characterizing the mechanical properties of breast cancer tissue is important for diagnosis and uncovering the mechanobiology mechanism. Although most of the studies were based on human cancer tissue, an animal model is still describable for preclinical analysis. Using a custom-build indentation device, we measured the viscoelastic properties of breast cancer tissue from 4T1 and SKBR3 cell lines. A total of 7 samples were tested for each cancer tissue using a mouse model. We observed that a viscoelastic model with 2-term Prony series could best describe the ramp and stress relaxation of the tissue. For long-term responses, the SKBR3 tissues were stiffer in the strain levels of 4–10%, while no significant differences were found for the instantaneous elastic modulus. We also found tissues from both cell lines appeared to be strain-independent for the instantaneous elastic modulus and for the long-term elastic modulus in the strain level of 4–10%. In addition, by inspecting the cellular morphological structure of the two tissues, we found that SKBR3 tissues had a larger volume ratio of nuclei and a smaller volume ratio of extracellular matrix (ECM). Compared with prior cellular mechanics studies, our results indicated that ECM could contribute to the stiffening the tissue-level behavior. The viscoelastic characterization of the breast cancer tissue contributed to the scarce animal model data and provided support for the linear viscoelastic model used for in vivo elastography studies. Results also supplied helpful information for modeling of the breast cancer tissue in the tissue and cellular levels.     

Dynamic viscoelastic properties of cellulose carbamate dissolved in NaOH aqueous solution

Dynamic viscoelastic properties of cellulose carbamate (CC) dissolved in NaOH aqueous solution were systematically studied for the first time. CC was microwave-assisted synthesized from the mixture of cellulose and urea and then dissolved in 7 wt % NaOH aqueous solution precooled to -7 °C. The obtained CC solution is transparent and has good liquidity. To clarify the rheological behavior of the solution, the CC solutions were investigated by dynamic viscoelastic measurements. The shear storage modulus (G') and loss modulus (G') as a function of the angular frequency (ω), concentration (c), nitrogen content (N %), viscosity-average molecular weight (M(η)), temperature (T), and time (t) were analyzed and discussed in detail. The sol-gel transition temperature of CC (M(η) = 7.78 × 10(4)) solution decreased from 36.5 to 31.3 °C with an increase of the concentration from 3.0 to 4.3 wt % and decreased from 35.7 to 27.5 °C with an increase of the nitrogen content from 1.718 to 5.878%. The gelation temperature of a 3.8 wt % CC solution dropped from 38.2 to 34.4 °C with the M(η) of CC increased from 6.35 × 10(4) to 9.56 × 10(4). The gelation time of the CC solution was relatively short at 30 °C, but the solution was stable for a long time at about 15 °C. Moreover, the gels already formed at elevated temperature were irreversible; that is, after cooling to a lower temperature including the dissolution temperature (-7 °C), they could not be dissolved to become liquid.     

Shear linear behavior of brain tissue over a large frequency range

The literature review about the shear linear properties of brain tissue reveals both a large discrepancy in the existing data and a crucial lack of information at high frequencies associated with traffic road and non-penetrating ballistic impacts. The purpose of this study is to clarify and to complement the linear material characterisation of brain tissue. New data at small strains and high frequencies were obtained from oscillatory experiments. The tests were performed on thin porcine white matter samples (corona radiata) using an original custom-designed oscillatory shear testing device. At 37 degrees C, the results showed that the mean storage modulus (G') and the mean loss modulus (G') increased with the frequency (0.1 to 6310 Hz) from 2.1+/-0.9 kPa to 16.8+/-2.0 kPa and from 0.4+/-0.2 kPa to 18.7+/-2.3 kPa respectively. The reliability of these new dynamic data was checked over a partially common frequency range by conducting similar experiments using a standard rheometer (Bohlin C-VOR 150). Data were also compared in the time field. From these experiments, the relaxation modulus (G(t)) was found to decrease from 24.4+/-2.1 kPa to 1.0+/-0.3 kPa between 10(-5) s and 270 s.     

Viscoelastic properties of solutions of ovine submaxillary mucin

The linear viscoelastic and rheological properties of high molecular weight ovine submaxillary mucin (OSM) solution have been investigated in terms of the Newtonian steady-flow viscosity [eta(gamma)], the complex oscillatory viscosity [eta*(omega)], and the storage and loss shear moduli [G'(omega) and G"(omega)]. It was observed that tau(gamma), eta*(omega), and G'(omega) are always higher when OSM is dissolved in 0.1M NaCl than when at the same concentration in 6M GdnHCl. This is consistent with previous observations that submaxillary mucins self-associate in 0.1M NaCl to form large aggregates, which are disrupted in 6M GdnHCl. As the OSM concentration increases, the appearance of a plateau shear modulus indicates the formation of a gel network in both solvents. The results suggest gelation involves specific intermolecular interactions, perhaps due to hydrophobic forces between interdigitated oligosaccharide side chains. The viscoelastic behavior of OSM solution at high concentration is thus similar to that reported in the literature for porcine gastric mucin (PGM). However, the OSM gels are mechanically weaker, having moduli that are an order of magnitude lower than those for PGM gels of comparable concentration. The oligosaccharide side chains of OSM consist of only 1-2 sugar units compared to 10-15 for PGM, but it appears that this is sufficient to allow for intermolecular interaction and the formation of weak gels.     

Viscoelastic properties of single attached cells under compression

The viscoelastic properties of single, attached C2C12 myoblasts were measured using a recently developed cell loading device. The device allows global compression of an attached cell, while simultaneously measuring the associated forces. The viscoelastic properties were examined by performing a series of dynamic experiments over two frequency decades (0.1-10 Hz) and at a range of axial strains (approximately 10-40%). Confocal laser scanning microscopy was used to visualize the cell during these experiments. To analyze the experimentally obtained force-deformation curves, a nonlinear viscoelastic model was developed. The nonlinear viscoelastic model was able to describe the complete series of dynamic experiments using only a single set of parameters, yielding an elastic modulus of 2120 +/- 900 Pa for the elastic spring, an elastic modulus of 1960 +/- 1350 for the nonlinear spring, and a relaxation time constant of 0.3 +/- 0.12 s. To our knowledge, it is the first time that the global viscoelastic properties of attached cells have been quantified over such a wide range of strains. Furthermore, the experiments were performed under optimal environmental conditions and the results are, therefore, believed to reflect the viscoelastic mechanical behavior of cells, such as would be present in vivo.     

Viscoelastic behavior and in vivo release study of microgel dispersions with inverse thermoreversible gelation

The dispersion of microgels with two interpenetrating polymer networks of poly( N-isopropylacrylamide) and poly(acrylic acid) (PNIPAM-IPN-PAAc) has been studied for its viscoelastic behavior, biocompatibility, and in vivo release properties. The IPN microgels in water had an average hydrodynamic radius of about 85 nm at 21 degrees C, measured by dynamic light scattering method. The atomic force microscope image showed that the particles were much smaller after they were dried but remained spherical shape. The storage and loss moduli ( G' and G') of dispersions of IPN microgels were measured in the linear stress regime as functions of temperature and frequency at various polymer concentrations using a stress-controlled rheometer. For dispersions with polymer concentrations of 3.0 and 6.0 wt % above 33 degrees C, the samples behave as viscoelastic solids and the storage modulus was larger than the loss modulus over the entire frequency range. The loss tangent was measured at various frequencies as a function of temperature. The gelation temperature was determined to be 33 degrees C at the point where a frequency-independent value of the loss tangent was first observed. At pH 2.5, when heated above the gelation temperature, IPN microgels flocculate by pumping a large amount of water from the gel. When the pH value was adjusted to neutral, deprotonation of -COOH groups on PAAc made the microgel keep water even above the gelation temperature. Using an animal implantation model, the biocompatibility and drug release properties of the IPN microgel dispersion were evaluated. Fluorescein as a model drug was mixed into an aqueous microgel dispersion at ambient temperature. This drug-loaded liquid was then injected subcutaneously in Balb/C mice from Taconic Farms. The test results have shown that the IPN microgels did not adversely promote foreign body reactions in this acute implantation model and the presence of gelled microgel dispersion substantially slowed the release of fluorescein.     

Analysis of thromboelastogram on coagulation and fibrinolysis

Hartert's thromboelastography has been used in the diagnosis of abnormal blood clotting for more than 20 years. From a thromboelastogram three parameters are obtained, viz, the reaction time 'r', the rate of formation of fibrin clot 'k', the maximum elasticity of thrombus 'amax'. It is desirable, however, to know the equation that describes the thromboelastogram both in the period in which the complex modulus increases with time because of coagulation, and in the period in which the complex modulus decreases with time because of fibrinolysis. The parameters of the equation could then be used as a diagnostic criterion; yielding information on the mechanism of coagulation and fibrinolysis. Based on our experimental results on human blood in normal and abnormal subjects, we found that the complex modulus of thromboelastograms can be expressed by the sum of two terms, one describing the increase of the complex modulus during coagulation, G1 = G'1 Exp (-tau 1/t), the other describing the decrease of the complex modulus during fibrinolysis, G2 = G'2 Exp (-tau 2/(t-D) when t greater than D. G2 = 0 when t less than D. The compound complex modulus from coagulation to fibrinolysis is G = G1 - G2. Here t is the clotting time, and G'1, G'2, tau 1, tau 2, and D are five constants to be identified. These five constants can be used for diagnostic and prognostic purposes.     

Measurement of the dynamic shear modulus of mouse brain tissue in vivo by magnetic resonance elastography

In this study, the magnetic resonance (MR) elastography technique was used to estimate the dynamic shear modulus of mouse brain tissue in vivo. The technique allows visualization and measurement of mechanical shear waves excited by lateral vibration of the skull. Quantitative measurements of displacement in three dimensions during vibration at 1200 Hz were obtained by applying oscillatory magnetic field gradients at the same frequency during a MR imaging sequence. Contrast in the resulting phase images of the mouse brain is proportional to displacement. To obtain estimates of shear modulus, measured displacement fields were fitted to the shear wave equation. Validation of the procedure was performed on gel characterized by independent rheometry tests and on data from finite element simulations. Brain tissue is, in reality, viscoelastic and nonlinear. The current estimates of dynamic shear modulus are strictly relevant only to small oscillations at a specific frequency, but these estimates may be obtained at high frequencies (and thus high deformation rates), noninvasively throughout the brain. These data complement measurements of nonlinear viscoelastic properties obtained by others at slower rates, either ex vivo or invasively.     

Development of fibrinous thrombus analogue for in-vitro abdominal aortic aneurysm studies

PURPOSE: To develop different thrombus analogues, with mechanical properties similar to those of human fibrinous thrombus, for in-vitro aneurysm sac pressure studies. METHODS: Using dynamic mechanical analysis we determined the E-modulus (/E(*)/) at 0.8, 1.0, 1.5 and 3.9 Hz of ten different human fibrinous thrombus samples. We also determined loss and storage modulus to quantify the visco-elastic properties. For comparison, we measured the E-modulus (|E(*)|), loss and storage modulus of gelatin, Novalyse ST8, ST14 and ST20 with and without contrast agent. RESULTS: Mean E-modulus of the thrombus samples (SD) at 0.8, 1.0, 1.5 and 3.9 Hz was 39 (16), 37 (15), 37 (15) and 38 (14)kPa, respectively. Median (SD) storage and loss modulus were 35 (12) and 8 (4)kPa, respectively. Median (SD) tandelta was 0.25 (0.06). The E-modulus of gelatin, Novalyse ST8, ST14 and ST20 was 4, 27, 48 and 60 kPa, respectively. The E-modulus of Novalyse ST8, ST14 and ST20 mixed with contrast agent was 18, 23 and 33 kPa, respectively. Median (SD) storage, loss modulus and tan delta of the six Novalyse samples were 30 (15), 3 (1) and 0.087 (0.04), respectively. CONCLUSION: All the thrombus analogues, except gelatin, had an E-modulus in the range of human fibrinous thrombi. Novalyse samples are validated thrombus analogues for in-vitro aneurysm sac pressure studies. Gelatin is not appropriate to simulate fibrinous thrombus.     

Viscoelastic shear properties of the corneal stroma

The cornea is a highly specialized transparent tissue which covers the front of the eye. It is a tough tissue responsible for refracting the light and protecting the sensitive internal contents of the eye. The biomechanical properties of the cornea are primarily derived from its extracellular matrix, the stroma. The majority of previous studies have used strip tensile and pressure inflation testing methods to determine material parameters of the corneal stroma. Since these techniques do not allow measurements of the shear properties, there is little information available on transverse shear modulus of the cornea. The primary objectives of the present study were to determine the viscoelastic behavior of the corneal stroma in shear and to investigate the effects of the compressive strain. A thorough knowledge of the shear properties is required for developing better material models for corneal biomechanics. In the present study, torsional shear experiments were conducted at different levels of compressive strain (0–30%) on porcine corneal buttons. First, the range of linear viscoelasticity was determined from strain sweep experiments. Then, frequency sweep experiments with a shear strain amplitude of 0.2% (which was within the region of linear viscoelasticity) were performed. The corneal stroma exhibited viscoelastic properties in shear. The shear storage modulus, G′, and shear loss modulus, G″, were reported as a function of tissue compression. It was found that although both of these parameters were dependent on frequency, shear strain amplitude, and compressive strain, the average shear storage and loss moduli varied from 2 to 8 kPa, and 0.3 to 1.2 kPa, respectively. Therefore, it can be concluded that the transverse shear modulus is of the same order of magnitude as the out-of-plane Young's modulus and is about three orders of magnitude lower than the in-plane Young's modulus.     

Methylation of poloxamine for enhanced cell adhesion

Aiming at producing a synthetic collagen-mimetic material that is stiffer than collagen but that like collagen allows both cell encapsulation and cell growth on the surface, a positively charged poloxamine hydrogel was prepared by methylating the tertiary amine groups of a four-arm poly(ethylene oxide)-poly(propylene oxide) block copolymer derivative (Tetronic 1107). This derivative was subsequently reacted with methacryloyl isocyanate, rendering positively charged materials that are further cross-linkable by a photointiated free radical polymerization. Different hydrogels containing methylated poloxamine methacrylate concentrations between 6% and 18% were produced and characterized by means of water uptake and viscoelastic properties. A sharp increase in water content was observed in distilled water during the first week; some of the gels showed water uptakes as high as 2 times the initial wet weight. In PBS, this effect was less prominent due to the decrease in the osmotic gradient. Also, a gradual increase of both the storage modulus (G') and the loss modulus (G") resulted from increasing the polymer concentration: for example, G' values ranged between 70 and 23000 Pa for 6% and 18% methylated poloxamine methacrylate hydrogels (at 1 Hz, 100 Pa of oscillatory stress). HepG2 cells embedded in different compositions and exposed to UV light displayed good viability levels after the cross-linking, unlike a previously reported attempt at creating a synthetic collagen-mimetic material. A well-spread endothelial cell morphology was apparent on methylated poloxamine films after preincubation in serum-containing medium, while on unmodified poloxamine methacrylate hydrogels cells attached poorly. However, EC did not attach well to the same material when fabricated not as films but as cylindrical modules as needed for the modular construct for which this material was intended. Thus, for this apparently more challenging geometry, it was necessary to combine collagen with the methylated poloxamine to have good attachment of EC on the surface of modules as well as films. While the challenge of creating a synthetic alternative to collagen as a stiffer cell-compatible substrate remains, methylated poloxamine displays many of the attributes that make it a useful material for tissue engineering.     

Fluorescent in situ hybridization of the telomere repeat sequence in hamster sperm nuclear structures

The flat, hooked-shaped architecture of the hamster sperm nucleus makes this an excellent model for in situ hybridization studies of the three dimensional structure of the genome. We have examined the structure of the telomere repeat sequence (TTAGGG)_n with respect to the various nuclear structures present in hamster spermatozoa, using fluorescent in situ hybridization. In fully condensed, mature sperm nuclei, the telomere sequences appeared as discrete spots of various sizes interspersed throughout the volume of the nuclei. While the pattern of these signals was non-random, it varied significantly in different nuclei. These discrete telomere foci were seen to gradually lengthen into linear, beaded signals as sperm nuclei were decondensed, in vitro, and were not associated with the nuclear annulus. We also examined the relationship of telomeres to the sperm nuclear matrix, a residual nuclear structure that retains the original size and shape of the nucleus. In these structures the DNA extends beyond the perimeter of the nucleus to form a halo around it, representing the arrangement of the chromosomal DNA into loop domains attached at their bases to the nuclear matrix. Telomere signals in these structures were also linear and equal in length to those of the decondensed nuclei, and each signal represented part of a single DNA loop domain. The telomeres were attached at one end to the nuclear matrix and extended into the halo. Sperm nuclear matrices treated with Eco RI retained the telomere signals. These data support sperm DNA packaging models in which DNA is coiled into discrete foci, rather than spread out linearly along the length of the sperm nucleus.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.