The Concept of a Rupture Risk Envelope for the Cochleo-Saccular Membranes

Abstract Introduction Alterations in endolymphatic pressure have long been suspected of being associated with the development of endolymphatic hydrops and rupture of the membranous labyrinth. More recently, there has been a focus on how membrane mechanics might contribute to membrane rupture. This is suspected to involve the viscoelastoplastic properties of these membranes. Objective To construct a rupture risk envelope for the cochleo-saccular membranes based on viscoelastoplasticity to provide insight into lesion behavior in Meniere disease. Methods Reported deformation data from a collagen model of the cochleo-saccular membranes was utilized. Yield stress was defined as 80% of ultimate failure stress. The yield points at various strain rates were used to construct a rupture risk envelope for the membranes. Results The rupture risk envelope was found to be downward sloping in configuration. At the highest strain rate of 385% per minute, the membrane yield was associated with greater stress (7.0 kPa) and lesser strain (30%); while at the lowest strain rate of 19.2% per minute, there was substantially less membrane yield stress (4.3 kPa) but it was associated with greater strain (44%). Conclusion The concept of a rupture risk envelope based on viscoelastoplasticity provides insight into hydropic lesion behavior in Meniere disease. This concept helps to explain how variations in membrane distensibility might occur as suspected in the double hit theory of lesion generation in Meniere disease. Slowly developing lesions would appear have a lower rupture risk while rapidly developing lesions would appear to have a greater risk of early membrane rupture.

The Concept of a Rupture Risk Envelope for the Cochleo-Saccular Membranes.

Introduction Alterations in endolymphatic pressure have long been suspected of being associated with the development of endolymphatic hydrops and rupture of the membranous labyrinth. More recently, there has been a focus on how membrane mechanics might contribute to membrane rupture. This is suspected to involve the viscoelastoplastic properties of these membranes. Objective To construct a rupture risk envelope for the cochleo-saccular membranes based on viscoelastoplasticity to provide insight into lesion behavior in Meniere disease. Methods Reported deformation data from a collagen model of the cochleo-saccular membranes was utilized. Yield stress was defined as 80% of ultimate failure stress. The yield points at various strain rates were used to construct a rupture risk envelope for the membranes. Results The rupture risk envelope was found to be downward sloping in configuration. At the highest strain rate of 385% per minute, the membrane yield was associated with greater stress (7.0 kPa) and lesser strain (30%); while at the lowest strain rate of 19.2% per minute, there was substantially less membrane yield stress (4.3 kPa) but it was associated with greater strain (44%). Conclusion The concept of a rupture risk envelope based on viscoelastoplasticity provides insight into hydropic lesion behavior in Meniere disease. This concept helps to explain how variations in membrane distensibility might occur as suspected in the double hit theory of lesion generation in Meniere disease. Slowly developing lesions would appear have a lower rupture risk while rapidly developing lesions would appear to have a greater risk of early membrane rupture.

The Effect of Collagen Viscoelastoplasiticty on Reissner's Membrane Displacement: A Graphic Analysis.

BACKGROUND: The aim of this study is to analyze the effect of collagen viscoelastoplasticity on the bulge displacement of Reissner's membrane that is observed in endolymphatic hydrops and Meniere's disease. METHODS: Viscoelastoplastic load-deformation characteristics for Reissner's membrane were based on a reported collagen polymer model of the cochleo-saccular membranes. The projected bulge displacements of Reissner's model membrane at key distention points were quantified trigonometrically and plotted graphically. RESULTS: Initial deformation is characterized by a membrane laxity with substantial stretch at low tension with projected bulge displacement of Reissner's membrane approaching 30%. Intermediate deformation is characterized by a linear membrane stiffness with projected bulge displacement of Reissner's membrane in the range of 30-40%. Terminal deformation is characterized by reduced stiffness with a disproportionate increase in membrane stretch with projected bulge displacement of Reissner's membrane reaching a critical value of 50%, indicating a hemi-circular profile with imminent risk of rupture. CONCLUSION: This collagen model of membrane viscoelastoplasticity demonstrates that at low pressure significant degrees of bulge displacement up to 30% can occur that may be reversible. The narrower 30-40% range of membrane displacement is one of the increasing deformity but without risk of rupture. Greater displacements approaching 50% indicate that the membrane is reaching a critical hemi-circular configuration with impending rupture.

The Biomechanics of Lesion Formation in Endolymphatic Hydrops: Single and Double Hit Mechanisms.

BACKGROUND: The vestibular membranes of the cochlea and saccule are subject to two simultaneous constraints as they deform in endolymphatic hydrops. Boundary tethers impose a bulge-type constraint during pressure-induced transverse membrane displacement, while inherent elasticity imposes a stretch-type constraint during stress-induced longitudinal membrane distention. OBJECTIVE: The aim of this study is to reconcile the effect of these dual constraints on membrane deformation. It is hypothesized that it is the interaction of these constraints that determines whether a stable membrane configuration can be achieved or progression to endolymphatic hydrops will occur. METHODS: Reissner's membrane was modeled as a flat elastic ribbon that was bound along its lateral edges and subject to trans-mural pressure. The bulge and stretch constraints on membrane deformation were formulated mathematically. A graphic solution of the constraint functions was used to examine the nature of the interaction and determine how pressure and elasticity influence the hydropic process. RESULTS: The graphic analysis shows how bulge and stretch phenomena interact to achieve an equilibrium point that satisfies both physical requirements. Nominal values of pressure and elasticity are projected to result in a stable membrane equilibrium in the precritical zone with the modest isolated increases in either parameter alone compatible with stability. However, a sufficiently large increase in either pressure or elasticity alone can constitute a single hit mechanism to exceed the critical point and destabilize the membrane. Moreover, simultaneous modest increases in both pressure and elasticity, neither of which would be sufficient in its own right, can be additive and constitute a double hit mechanism to destabilize the membranes as well. Finally, extreme values of pressure and elasticity that fail to intersect imply that no solution is feasible and that the affected membranes will fail immediately. CONCLUSIONS: Sufficiently large increases in either endolymphatic pressure or membrane elasticity alone can destabilize the membranes and constitute single hit mechanisms for inducing hydrops. Combined moderate increases in both trans-mural pressure and membrane elasticity can also destabilize the membranes and constitute a double hit mechanism for hydrops induction.

A model of viscoelastoplasticity in the cochleo-saccular membranes.

INTRODUCTION: Variations in the distensile behavior of the cochleo-saccular vestibular membranes may contribute to lesion evolution of endolymphatic hydrops in Meniere's disease. Such variation may be mediated through membrane viscoelastoplasticity. This feature may provide insight into the distensile process at work in these membranes. HYPOTHESIS: A precipitated collagen matrix can provide a suitable in vitro model of viscoelastoplasticity in cochleo-saccular vestibular membranes. METHODS: An in vitro extra-cellular matrix of precipitated collagen was evaluated as a model of suspected viscoelastoplastic behavior in the cochleo-saccular vestibular membranes. The structure of the precipitated collagen was assessed for its similarity to that of the basal lamina of the pars inferior vestibular membranes. The biomechanics of this matrix were scrutinized for evidence of viscoelastoplastic distensile properties. RESULTS: A matrix of precipitated collagen was found to exhibit a mesh-like fibrous structure similar to that of collagen found in the basilar lamina of the cochleo-saccular vestibular membranes. This matrix was also found to exhibit a sigmoid distensile response as well as strain rate sensitivity, both of which are characteristic properties of polymer viscoelastoplasticity. CONCLUSIONS: An in vitro matrix of precipitated collagen appears to provide a suitable model that can account for variations in the distensile behavior of the cochleo-saccular vestibular membranes. The model exhibits viscoelastoplasticity and may have heuristic value in the analysis of lesion evolution in Meniere's disease. LEVEL OF EVIDENCE: 6.

Suspensory Tethers and Critical Point Membrane Displacement in Endolymphatic Hydrops.

Introduction Grossly displaced membranes are characteristic of endolymphatic hydrops. The process whereby physiological membrane displacement becomes pathological may be mediated by stress, but the membrane biomechanics underlying this transition are unclear. Objective This study seeks to determine the role of suspensory tethers during pressure-induced membrane displacement in the generation of the membranous lesions seen in this disease entity using a biomechanical model approach. Methods The location of membrane suspensory tethers was identified histologically. The influence of tethers on model membrane configuration during displacement was assessed graphically. The relationship of membrane configuration during displacement to curvature radius was quantified trigonometrically. The relationship of curvature radius to stress susceptibility was determined mathematically. The net effect of suspensory tethers on membrane stress levels for various degrees of membrane distention and displacement was then calculated numerically. Results In the inferior labyrinth, suspensory tethers are found to occur on the membranes' boundaries. Such tethering is found to impose a biphasic effect on membrane curvature with increasing degrees of displacement. As a consequence, tensile stress susceptibility is found to decline with initial membrane displacement to a critical point nadir beyond which stress then increases monotonically. No such effect was found for the superior labyrinth. Conclusion Boundary tethers in the inferior labyrinth are associated with significant tensile stress reductions until a critical point of membrane displacement is reached. Displacements short of the critical point may be physiological and even reversible, whereas such displacements beyond the critical point are apt to be overtly hydropic and irreversible.

Suspensory Tethers and Critical Point Membrane Displacement in Endolymphatic Hydrops

Abstract Introduction Grossly displaced membranes are characteristic of endolymphatic hydrops. The process whereby physiological membrane displacement becomes pathological may be mediated by stress, but the membrane biomechanics underlying this transition are unclear. Objective This study seeks to determine the role of suspensory tethers during pressure-induced membrane displacement in the generation of the membranous lesions seen in this disease entity using a biomechanical model approach. Methods The location of membrane suspensory tethers was identified histologically. The influence of tethers on model membrane configuration during displacement was assessed graphically. The relationship of membrane configuration during displacement to curvature radius was quantified trigonometrically. The relationship of curvature radius to stress susceptibility was determined mathematically. The net effect of suspensory tethers on membrane stress levels for various degrees of membrane distention and displacement was then calculated numerically. Results In the inferior labyrinth, suspensory tethers are found to occur on the membranes' boundaries. Such tethering is found to impose a biphasic effect on membrane curvature with increasing degrees of displacement. As a consequence, tensile stress susceptibility is found to decline with initial membrane displacement to a critical point nadir beyond which stress then increases monotonically. No such effect was found for the superior labyrinth. Conclusion Boundary tethers in the inferior labyrinth are associated with significant tensile stress reductions until a critical point of membrane displacement is reached. Displacements short of the critical pointmay be physiological and even reversible,whereas such displacements beyond the critical point are apt to be overtly hydropic and irreversible.

The Progressive Nature of Menière's Disease: Stress Projections and Lesion Analysis.

HYPOTHESIS: An engineering model of the labyrinth can provide a mechanism that accounts for the pattern of lesion development observed in Menière's disease. BACKGROUND: Membrane lesions in Menière's disease can occur in virtually every part of the membranous labyrinth. How these lesions are induced is unclear and their mode of distribution uncertain. Pressure induced stress in the membranous labyrinth may play a mechanistic role in lesion formation and distribution. METHODS: An engineering model of the labyrinth was used to provide membrane stress formulations and projections for lesion induction in the several chambers using membrane theory. These were compared with an analysis of actual lesions observed in Menière's disease to evaluate the model's accuracy. RESULTS: The model projects that lesions in the membranous labyrinth will be induced progressively because of stress differentials among the chambers, with a chain of lesion pattern that follows the serial anatomic order and occurs with a frequency commensurate with chamber stress level. An analysis of lesions observed in actual cases of Menière's disease reveals a pattern of lesion development that is progressive, sequential, commensurate, and concordant with the model's stress projections. CONCLUSIONS: The concordance between the stress projections and the lesion analysis strengthens the hypothesis that Menière's is a progressive disease that follows a chain of lesions paradigm based on pressure-induced stress differentials in the variously configured chambers of the membranous labyrinth.

Membrane Stress in the Human Labyrinth and Meniere Disease: A Model Analysis

Introduction The nature and extent of membrane damage encountered in Meniere disease remains unexplained. Pressure-induced membrane stress may underlie the characteristic hydropic distention. Analysis of stress in the several vestibular chambers may offer insight into the nature and progression of Meniere disease. Objective Membrane stress levels will be assessed by constructing a specific model of the human membranous labyrinth through the application of human dimensions to an existing generic model of the mammalian labyrinth. Methods Nominal dimensions for a model of the human membranous labyrinth were obtained from fixed human tissue. Stress proclivities were calculated and normalized based on shell theory applied to the various geometric figures comprising the model. Results Normalized peak stress levels were projected to be highest in the saccule (38.8), followed by the utricle (5.4), then ampulla (2.4), and lowest in the canal system (1.0). These results reflect macrostructural variations in membrane shape, size, and thickness among the several chambers of the labyrinth. These decreasing stress proclivities parallel the decreasing frequency of histologic lesions found in documented cases of Meniere disease. Conclusions This model analysis of a human membranous labyrinth indicates that substantial disparities in stress exist among the several vestibular chambers due to macrostructural membrane configuration. Low stress levels in the canals are the result of thick highly curved membranes, and the high levels computed for the saccule reflect its thin and relatively flat membranes. These findings suggest that chamber configuration may be a factor controlling the progression of endolymphatic hydrops in Meniere disease.(AU)

Membrane Stress in the Human Labyrinth and Meniere Disease: A Model Analysis.

Introduction The nature and extent of membrane damage encountered in Meniere disease remains unexplained. Pressure-induced membrane stress may underlie the characteristic hydropic distention. Analysis of stress in the several vestibular chambers may offer insight into the nature and progression of Meniere disease. Objective Membrane stress levels will be assessed by constructing a specific model of the human membranous labyrinth through the application of human dimensions to an existing generic model of the mammalian labyrinth. Methods Nominal dimensions for a model of the human membranous labyrinth were obtained from fixed human tissue. Stress proclivities were calculated and normalized based on shell theory applied to the various geometric figures comprising the model. Results Normalized peak stress levels were projected to be highest in the saccule (38.8), followed by the utricle (5.4), then ampulla (2.4), and lowest in the canal system (1.0). These results reflect macrostructural variations in membrane shape, size, and thickness among the several chambers of the labyrinth. These decreasing stress proclivities parallel the decreasing frequency of histologic lesions found in documented cases of Meniere disease. Conclusions This model analysis of a human membranous labyrinth indicates that substantial disparities in stress exist among the several vestibular chambers due to macrostructural membrane configuration. Low stress levels in the canals are the result of thick highly curved membranes, and the high levels computed for the saccule reflect its thin and relatively flat membranes. These findings suggest that chamber configuration may be a factor controlling the progression of endolymphatic hydrops in Meniere disease.

A model design for the labyrinthine membranes in mammals.

OBJECTIVES/HYPOTHESIS: A model of the labyrinthine membranes in mammals may be useful in the study of conditions that involve membrane stress and deformation such as Meniere's disease and diving injuries. STUDY DESIGN: Conceptual design of a model of the labyrinthine membranes in mammals. METHODS: The model is constructed by emulating each of the several chambers of the membranous labyrinth and their connections with mathematically defined geometric shapes. RESULTS: The model design uses a torus to emulate each semicircular canal, prolate spheroids for each ampulla, cylinders for the crus commune and utricle, an oblate spheroid for the saccule, hyperboloids of revolution for junctional zones, and a spiral torus for the cochlea membranes. CONCLUSIONS: A complete model of the labyrinthine membranes has been designed that can serve as a platform for stress analysis when numerical dimensions are available for any particular species including man. LEVEL OF EVIDENCE: NA.

Membrane stress proclivities in the Mammalian labyrinth.

Introduction The membranes of the inferior division of the labyrinth in some mammals appear more vulnerable to hydropic distention than those of the superior division. This finding in guinea pigs, cats, and humans has been attributed to the evidently thinner membranes with implied higher stress levels. Objective The objective of this study is to identify other configurational features, if any, that may contribute to membrane stress proclivity and therefore might act to augment or ameliorate stress in the several chambers of the membranous labyrinth. Methods Stress proclivity can be investigated using shell theory to analyze a geometric model of the labyrinthine membranes in mammals. Such an approach can provide the necessary mathematical descriptions of stress in each chamber of the labyrinth. Results Stress proclivity depends on three physical features: membrane thickness, radial size, and chamber shape. Lower stress proclivities are projected for smaller chambers with thick, highly synclastic membranes. Higher stress levels are projected for larger chambers with thin, flat, or anticlastic membranes. Conclusions In the mammalian labyrinth, pars superior chambers exhibit permutations of membrane thickness, size, and favorable shapes that reduce stress proclivity. In contrast, the pars inferior chambers are characterized by thin membranes with flat contours and adverse shapes that make them especially vulnerable to hydropic distention.

Membrane Stress Proclivities in the Mammalian Labyrinth

Introduction: The membranes of the inferior division of the labyrinth in some mammals appear more vulnerable to hydropic distention than those of the superior division. This finding in guinea pigs, cats, and humans has been attributed to the evidently thinner membranes with implied higher stress levels. Objective: The objective of this study is to identify other configurational features, if any, that may contribute to membrane stress proclivity and therefore might act to augment or ameliorate stress in the several chambers of the membranous labyrinth. Methods: Stress proclivity can be investigated using shell theory to analyze a geometric model of the labyrinthine membranes in mammals. Such an approach can provide the necessary mathematical descriptions of stress in each chamber of the labyrinth. Results Stress proclivity depends on three physical features: membrane thickness, radial size, and chamber shape. Lower stress proclivities are projected for smaller chambers with thick, highly synclastic membranes. Higher stress levels are projected for larger chambers with thin, flat, or anticlastic membranes. Conclusions: In the mammalian labyrinth, pars superior chambers exhibit permutations of membrane thickness, size, and favorable shapes that reduce stress proclivity. In contrast, the pars inferior chambers are characterized by thin membranes with flat contours and adverse shapes that make them especially vulnerable to hydropic distention...

A toolbox of geometric elements for labyrinth model design and analysis.

OBJECTIVES/HYPOTHESIS: To develop a toolbox of defined geometric shapes that can aid in the emulation of the architecture of the labyrinthine membranes. STUDY DESIGN: Analytical review of geometric shapes that are candidates for inclusion in the toolbox. METHODS: The mammalian labyrinth appears to have an overall tubular configuration. The bulges, bends and constrictions manifest by these chambers and conduits may be construed to be variations on an underlying core cylindrical structure. Four geometries that embrace the cylindrical shape are identified, namely the cylinder itself, the ellipsoid, the hyperboloid, and the torus. These can be exploited as model design tools and used to approximate the individual components of the labyrinth. RESULTS: A toolbox of geometric elements is identified for use in modeling the mammalian labyrinth. The toolbox includes cylindrical, ellipsoidal, hyperboloidal, and toroidal elements, their figures and mathematical definitions, as well as derivative characteristics that relate to contour and curvature. CONCLUSIONS: This analysis suggests that there is a heuristic value in considering the underlying structure of the mammalian labyrinth to be cylindrical. Four principal geometric shapes that are based on the cylinder have been identified for use in a toolbox of design elements. This toolbox can be used to model any mammalian labyrinth.

A model analysis of tensile stress in the toadfish vestibular membranes.

Background. A theoretical model analysis of stress in the vestibular membranes has identified a geometrical stress factor incorporating shape, size, and thickness that can be used to assess peak stress in the various chambers. Methods. Using published measurements of the toadfish vestibular membranes made during surgery, the geometrical stress factor can be evaluated for each chamber based on the model. Results. The mean geometrical stress factor is calculated to be the lowest in the semicircular canal (4.4), intermediate in the ampulla (6.0), and the highest in the utricle (17.4). Conclusions. The model predicts that substantial hoop stress disparities exist in the toadfish vestibular labyrinth. Stress is least in the semicircular canal, which therefore appears to be the structure with greatest stability. The utricle is found to be the most stress prone structure in the vestibular labyrinth and therefore appears to be the chamber most vulnerable to distention and potential modification.

A model analysis of static stress in the vestibular membranes.

BACKGROUND: The scheme of the core vestibular membranes, consisting of serially connected utricle, ampulla and semicircular canal, first appeared hundreds of millions of years ago in primitive fish and has remained largely unchanged during the subsequent course of evolution. The labyrinths of higher organisms build on this core structure, with the addition of the phylogenetically newer membrane structures, namely, saccule, lagena and cochlea. An analysis of static stress in these core vestibular membranes may contribute to a better understanding of the role of stress in the evolution of derivative membrane structures over the long term as well as the short-term membrane distortions seen in Meniere's disease. METHODS: A model of these core vestibular membranes is proposed in order to analyze the distribution of stress in the walls of the component chambers. The model uses basic geometrical elements of hollow cylinders and spheres to emulate the actual structures. These model elements lend themselves to a mathematical analysis of static stress in their membranes. RESULTS: Hoop stress, akin to the stress in hoops used to reinforce barrel walls, is found to be the predominant stress in the model membranes. The level of hoop stress depends not only on pressure but as well on a geometric stress factor that incorporates membrane shape, thickness and curvature. This result implies that hoop stress may be unevenly distributed in the membranes of the several vestibular chambers due to variations in these dimensional parameters. These results provide a theoretical framework for appraising hoop stress levels in any vestibular labyrinth whose dimensions are known. CONCLUSION: Static hoop stress disparities are likely to exist in the vestibular membranes given their complex physical configurations. Such stress disparities may contribute to the development of membrane pathologies as seen in Meniere's Disease. They may also factor in the evolutionary development of other derivative membrane structures such as the saccule, the lagena, and the cochlea found in higher animals.

Gentamicin tympanoclysis: effects on the labyrinthine sensory cells.

OBJECTIVES: The objective of the study was to determine whether a selective vestibular hair cell toxicity with sparing of the cochlear hair cells could be achieved by infusing different concentrations of gentamicin into the middle ears of adult cats. STUDY DESIGN: Prospective experimental animal study treating only the left ear of each cat, the right ear serving as individual control. METHODS: Gentamicin solution at concentrations of either 30 or 3 mg/mL was infused daily into the left middle ear of adult cats until overt ataxia occurred. After 1 month or 6 months, each cat was killed and its temporal bones prepared for optical microscopy. RESULTS: Animals treated with 30 mg/mL gentamicin until ataxic required a median of five daily doses. These animals had clear-cut cochlear basal turn hair cell losses accompanying toxic lesions in the utricle and cristae. In contrast, animals treated with 3 mg/mL gentamicin until ataxic required an average of 19 daily doses. These animals had lesions restricted to the utricle and cristae with sparing of the cochlea hair cells. Animals that failed to develop ataxia manifested neither lesions of the cochlear nor vestibular hair cells. CONCLUSION: Gentamicin tympanoclysis in the cat animal model, using a dilute solution and continued once daily until clinical ataxia occurs, is capable of producing selective vestibular hair cell toxicity while sparing cochlea hair cells.