An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Thermal model for optimization of vascular laser tissue soldering

Laser tissue soldering (LTS) is a promising technique for tissue fusion based on a heat-denaturation process of proteins. Thermal damage of the fused tissue during the laser procedure has always been an important and challenging problem. Particularly in LTS of arterial blood vessels strong heating of the endothelium should be avoided to minimize the risk of thrombosis. A precise knowledge of the temperature distribution within the vessel wall during laser irradiation is inevitable. The authors developed a finite element model (FEM) to simulate the temperature distribution within blood vessels during LTS. Temperature measurements were used to verify and calibrate the model. Different parameters such as laser power, solder absorption coefficient, thickness of the solder layer, cooling of the vessel and continuous vs. pulsed energy deposition were tested to elucidate their impact on the temperature distribution within the soldering joint in order to reduce the amount of further animal experiments. A pulsed irradiation with high laser power and high absorbing solder yields the best results.

Histological evidence of delayed ischemic brain tissue damage in the rat double-hemorrhage model

The rat double-SAH model is one of the standard models to simulate delayed cerebral vasospasm (CVS) in humans. However, the proof of delayed ischemic brain damage is missing so far. Our objective was, therefore, to determine histological changes in correlation with the development of symptomatic and perfusion weighted imaging (PWI) proven CVS in this animal model. CVS was induced by injection of autologous blood in the cisterna magna of 22 Sprague-Dawley rats. Histological changes were analyzed on day 3 and day 5. Cerebral blood flow (CBF) was assessed by PWI at 3 tesla magnetic resonance (MR) tomography. Neuronal cell count did not differ between sham operated and SAH rats in the hippocampus and the cerebral cortex on day 3. In contrast, on day 5 after SAH the neuronal cell count was significantly reduced in the hippocampus (p<0.001) and the inner cortical layer (p=0.03). The present investigation provides quantitative data on brain tissue damage in association with delayed CVS for the first time in a rat SAH model. Accordingly, our data suggest that the rat double-SAH model may be suitable to mimic delayed ischemic brain damage due to CVS and to investigate the neuroprotective effects of drugs.

Continuous intrathecal glyceryl trinitrate prevents delayed cerebral vasospasm in the single-SAH rabbit model in vivo

Delayed cerebral vasospasm after aneurysmal subarachnoid hemorrhage (SAH) is a major cause of high morbidity and mortality. The reduced availability of nitric oxide (NO) in blood and cerebrospinal fluid (CSF) is well established as a key mechanism of vasospasm. Systemic administration of glyceryl trinitrate (GTN), an NO donor also known as nitroglycerin, has failed to be established in clinical settings to prevent vasospasm because of its adverse effects, particularly hypotension. The purpose of this study was to analyze the effect of intrathecally administered GTN on vasospasm after experimental SAH in the rabbit basilar artery.

Cortical reorganization after brain damage: the oculomotor model

Recovery from eye movement deficits after cortical lesions is amazingly rapid and almost complete, which is in sharp contrast to most other neurological deficits of cerebral lesions. The underlying mechanisms of this successful recovery remain uncertain. We had the rare opportunity to examine two patients with recovery from saccade deficits after a lesion restricted to the frontal eye field (FEF) by means of transcranial magnetic stimulation (TMS). The results provide direct evidence that recovery depended on the integrity of the oculomotor regions of the nonlesioned contralesional hemisphere, and that the compensatory network is task-specific.

Effects of local continuous release of brain derived neurotrophic factor (BDNF) on peripheral nerve regeneration in a rat model

The purpose of this study was to evaluate the effect of continuously released BDNF on peripheral nerve regeneration in a rat model. Initial in vitro evaluation of calcium alginate prolonged-release-capsules (PRC) proved a consistent release of BDNF for a minimum of 8 weeks. In vivo, a worst case scenario was created by surgical removal of a 20-mm section of the sciatic nerve of the rat. Twenty-four autologous fascia tubes were filled with calcium alginate spheres and sutured to the epineurium of both nerve ends. The animals were divided into 3 groups. In group 1, the fascial tube contained plain calcium alginate spheres. In groups 2 and 3, the fascial tube contained calcium alginate spheres with BDNF alone or BDNF stabilized with bovine serum albumin, respectively. The autocannibalization of the operated extremity was clinically assessed and documented in 12 additional rats. The regeneration was evaluated histologically at 4 weeks and 10 weeks in a blinded manner. The length of nerve fibers and the numbers of axons formed in the tube was measured. Over a 10-week period, axons have grown significantly faster in groups 2 and 3 with continuously released BDNF compared to the control. The rats treated with BDNF (groups 2 and 3) demonstrated significantly less autocannibalization than the control group (group 1). These results suggest that BDNF may not only stimulate faster peripheral nerve regeneration provided there is an ideal, biodegradable continuous delivery system but that it significantly reduces the neuropathic pain in the rat model.

Systemically transferred hematopoietic stem cells home to the subretinal space and express RPE-65 in a mouse model of retinal pigment epithelium damage

Stem cell regeneration of damaged tissue has recently been reported in many different organs. Since the loss of retinal pigment epithelium (RPE) in the eye is associated with a major cause of visual loss - specifically, age-related macular degeneration - we investigated whether hematopoietic stem cells (HSC) given systemically can home to the damaged subretinal space and express markers of RPE lineage. Green fluorescent protein (GFP) cells of bone marrow origin were used in a sodium iodate (NaIO(3)) model of RPE damage in the mouse. The optimal time for adoptive transfer of bone marrow-derived stem cells relative to the time of injury and the optimal cell type [whole bone marrow, mobilized peripheral blood, HSC, facilitating cells (FC)] were determined by counting the number of GFP(+) cells in whole eye flat mounts. Immunocytochemistry was performed to identify the bone marrow origin of the cells in the RPE using antibodies for CD45, Sca-1, and c-kit, as well as the expression of the RPE-specific marker, RPE-65. The time at which bone marrow-derived cells were adoptively transferred relative to the time of NaIO(3) injection did not significantly influence the number of cells that homed to the subretinal space. At both one and two weeks after intravenous (i.v.) injection, GFP(+) cells of bone marrow origin were observed in the damaged subretinal space, at sites of RPE loss, but not in the normal subretinal space. The combined transplantation of HSC+FC cells appeared to favor the survival of the homed stem cells at two weeks, and RPE-65 was expressed by adoptively transferred HSC by four weeks. We have shown that systemically injected HSC homed to the subretinal space in the presence of RPE damage and that FC promoted survival of these cells. Furthermore, the RPE-specific marker RPE-65 was expressed on adoptively transferred HSC in the denuded areas.

Characterization of retinal damage in the episcleral vein cauterization rat glaucoma model

Episcleral vein cauterization (EVC) is used in rats to generate a glaucoma model with high intraocular pressure (IOP). The long-term retinal damage in this glaucoma model, however, has not been accurately quantified. We report the location and amount of retinal ganglion cell (RGC) damage caused by (EVC) induced IOP elevation in two rat strains. IOP was raised in one eye of Wistar (N = 5) and Brown-Norway(B-N)(N = 7) rats by EVC and monitored monthly until IOP in contralateral eyes equalized at 5 months post-surgery. Animals were maintained for 3.5-4.5 additional months. B-N rats (N = 7) that had no EVC served as controls for this strain. Scotopic flash ERGs were recorded at baseline and just prior to euthanasia. Automated counts of all retrogradely labeled RGCs in retinal flat-mounts were determined and compared between contralateral eyes. RGC density maps were constructed and RGC size distribution was determined. Oscillatory potentials in the group of eyes which had elevated IOP were decreased at the time of euthanasia, when IOP had returned to normal. The group of normal B-N rats had similar RGC counts between contralateral eyes. In the experimental group the mean number of RGCs was not significantly different between control and experimental eyes, but 1 of 5 Wistar and 2 of 7 B-N experimental eyes had at least 30% fewer RGCs than contralateral control eyes. Total retinal area in B-N experimental eyes was higher compared to contralateral eyes. Cumulative IOP exposure of the experimental eyes was modestly correlated with RGC loss while oscillatory potentials appeared to be inversely related to RGC loss. In retinas with extensive (> 30% RGC loss) but not complete damage, smaller cells were preserved better than larger ones. The above results indicate that RGC loss in both Wistar and B-N strains is variable after a prolonged elevation of IOP via EVC. Such variability despite equivalent IOP levels and ERG abnormalities, suggests unknown factors that can protect IOP-stressed RGCs. Identification and enhancement of such factors could prove useful for glaucoma therapy.

An infant mouse model of brain damage in pneumococcal meningitis

Bacterial meningitis due to Streptococcus pneumoniae is associated with an significant mortality rate and persisting neurologic sequelae including sensory-motor deficits, seizures, and impairments of learning and memory. The histomorphological correlate of these sequelae is a pattern of brain damage characterized by necrotic tissue damage in the cerebral cortex and apoptosis of neurons in the hippocampal dentate gyrus. Different animal models of pneumococcal meningitis have been developed to study the pathogenesis of the disease. To date, the infant rat model is unique in mimicking both forms of brain damage documented in the human disease. In the present study, we established an infant mouse model of pneumococcal meningitis. Eleven-days-old C57BL/6 (n = 299), CD1 (n = 42) and BALB/c (n = 14) mice were infected by intracisternal injection of live Streptococcus pneumoniae. Sixteen hours after infection, all mice developed meningitis as documented by positive bacterial cultures of the cerebrospinal fluid. Sixty percent of infected C57BL/6 mice survived more than 40 h after infection (50% of CD1, 0% of BALB/c). Histological evaluations of brain sections revealed apoptosis in the dentate gyrus of the hippocampus in 27% of infected C57BL/6 and in 5% of infected CD1 mice. Apoptosis was confirmed by immunoassaying for active caspase-3 and by TUNEL staining. Other forms of brain damage were found exclusively in C57BL/6, i.e. caspase-3 independent (pyknotic) cell death in the dentate gyrus in 2% and cortical damage in 11% of infected mice. This model may prove useful for studies on the pathogenesis of brain injury in childhood bacterial meningitis.

A genetically explicit model of speciation by sensory drive within a continuous population in aquatic environments

BACKGROUND: The sensory drive hypothesis predicts that divergent sensory adaptation in different habitats may lead to premating isolation upon secondary contact of populations. Speciation by sensory drive has traditionally been treated as a special case of speciation as a byproduct of adaptation to divergent environments in geographically isolated populations. However, if habitats are heterogeneous, local adaptation in the sensory systems may cause the emergence of reproductively isolated species from a single unstructured population. In polychromatic fishes, visual sensitivity might become adapted to local ambient light regimes and the sensitivity might influence female preferences for male nuptial color. In this paper, we investigate the possibility of speciation by sensory drive as a byproduct of divergent visual adaptation within a single initially unstructured population. We use models based on explicit genetic mechanisms for color vision and nuptial coloration. RESULTS: We show that in simulations in which the adaptive evolution of visual pigments and color perception are explicitly modeled, sensory drive can promote speciation along a short selection gradient within a continuous habitat and population. We assumed that color perception evolves to adapt to the modal light environment that individuals experience and that females prefer to mate with males whose nuptial color they are most sensitive to. In our simulations color perception depends on the absorption spectra of an individual's visual pigments. Speciation occurred most frequently when the steepness of the environmental light gradient was intermediate and dispersal distance of offspring was relatively small. In addition, our results predict that mutations that cause large shifts in the wavelength of peak absorption promote speciation, whereas we did not observe speciation when peak absorption evolved by stepwise mutations with small effect. CONCLUSION: The results suggest that speciation can occur where environmental gradients create divergent selection on sensory modalities that are used in mate choice. Evidence for such gradients exists from several animal groups, and from freshwater and marine fishes in particular. The probability of speciation in a continuous population under such conditions may then critically depend on the genetic architecture of perceptual adaptation and female mate choice.

Prevention of delayed cerebral vasospasm by continuous intrathecal infusion of glyceroltrinitrate and nimodipine in the rabbit model in vivo

OBJECTIVE: Intrathecal bolus administration of nitric oxide donors and calcium channel antagonists has been proposed to reduce cerebral vasospasm (CVS) in animal subarachnoid hemorrhage (SAH) models. Intrathecal continuous administration of these substances for CVS prevention has not been extensively evaluated. This study compared the efficacy of continuous intrathecal infusions of the NO donor glyceroltrinitrate and nimodipine in preventing delayed CVS associated with SAH in an animal model in vivo. METHODS: New Zealand White rabbits were randomly assigned to six groups: no SAH/NaCl, no SAH/NO, no SAH/nimodipine, SAH/NaCl, SAH/NO, or SAH/nimodipine. Glyceroltrinitrate (GTN) at 0.5 microg/microl (0.5 microl/h) or nimodipine at 0.2 microg/microl (10 microl/h) or NaCl was continuously infused into the cisterna magna via an Alzet osmotic pump from day 0 to day 5 after injection of 1.0 ml autologous blood. The magnitude of spasm in the basilar artery was determined by comparison of pre- and posttreatment angiography and was calculated as proportional change in intraluminal diameter based on automatic measurements. RESULTS: A total of 55 experiments and 110 angiograms were performed. SAH was associated with vasoconstriction of the basilar artery (SAH/NaCl group 19.85+/-2.94%). Continuous intrathecal injection of GTN and nimodipine prevented SAH-induced CVS. There was significant prevention of CVS in animals treated with GTN (SAH/NO group 5.93+/-5.2%, n=11) and nimodipine (SAH/nimodipine group: 0.55+/-2.66%, n=9). There was no significant difference between the treatment groups and controls in prevention of CVS. CONCLUSIONS: This study demonstrates that prophylactic continuous intrathecal administration of either GTN or nimodipine equally prevents SAH-associated CVS in an animal model.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.