Karl Grosh: Research Projects

Cochlear mechanics

Understanding the mechanics of normal hearing is central to building prothesis and noninvasive diagnostic tools. Our overarching goal in this project is to build a virtual laboratory for simulating the response of the cochlea. Such a capability will enable the prediction of the effects of different types of damage, efferent stimulation and the effects of electrical stimulation on the cochlea. In this project, hybrid numerical techniques are used to model the acoustic repsonse of the fluid-loaded basilar membrane and attached structures (including the outer hair cell-Deiter cell-tectorial membrane system). Through this computational framework, models for the linear, nonlinear and active mechanics of the organ of corti have been developed, tested and compared with experimental data from in vivo test data performed close collaboration with Dr. Fred Nuttall from Oregon Health Sciences University, Dr. Dave Dolan and Kresge Hearing Research Institute. Typcially one graduate student and one post-doc. Alumni are Drs. Anand Parthasarathi, Sripriya Ramamoorthy, and Niranjan Deo. Post-docs have been Dr. Ed Givelberg and Dr. Xiaoai Jiang. Current graduate students on the project are Julien Meaud and Yizeng Li.

S. Ramamoorthy, N. V. Deo, and K. Grosh. A mechano-electro-acoustical model for the cochlea: Response to acoustic stimuli. J. Acoust. Soc. Amer., 121(5), pp. 2758-2773, (2007).

A. A. Spector, N. Deo, K. Grosh, J. Tilak Ratnanather, R. M. Raphael.  Electromechanical models of the outer hair cell composite membrane.  J. Membrane Biology, 209 (2-3), pp 135-152 (2006).

N. Deo and K. Grosh, A modified area motor model for outer hair cell mechanics. Biophys. J., 86(6), 2004. Nonlinear constitutive model for outer hair cell forward and reverse electromecahnical transduction based on a two-state Boltzman including a state dependent stiffness.

Anand A. Parthasarathi , Karl Grosh and Alfred L. Nuttall.  Three--dimensional numerical modeling for global cochlear dynamics. J. Acoust. Soc. Amer., 107(1), Jan. 2000, pp. 474-485 (2000). A systematic method for including three-dimensional effects into a cochlear model allowing for model enhancement inside a variational framework.

K. Halsey, K. Fegelman, K. Grosh, and D. F. Dolan.  Long term effects of acoustic trauma on the electrically evoked otoacoustic emission. J. Assoc. for Res. in Otolaryngology, 6(4), pp 324-340, (2005).

K. Grosh, J. Zheng, E. deBoer, A. L. Nuttall. High frequency electromotility of the cochlea.  J. Acoust. Soc. of Amer, 115, 2178-2184, (2004). We show that in vivo electrically evoked basilar membrane motion extends to 100 kHz. This motilty is reversibly reduced by salicylate.

Anand A. Parthasarathi, Karl Grosh, Alfred L. Nuttall, and Jiefu Zheng.  Influence of direct current stimulation on the in vivo basilar membrane velocity response. J. Acoust. Soc. Amer., 113, pp. 442-452, (2003). The effect of electrical stimulation on the basilar membrane response to acoustic stimulation is quantified experimentally and analyzed.

Alfred L. Nuttall, Tianying Ren, Egbert de Boer, Jiefu Zheng, Anand Parthasarathi, Karl Grosh, Menghe Guo,  and David Dolan.  In vivo micromechanical measurements of the organ of Corti in the basal cochlear turn.  Audiology and Neuro-otology  7 (1) pp. 21-26, (2002)

L. Nuttall, Grosh, K., Zheng, J., de Boer, E., Ren, T., Zhao, Y., Spontaneous basilar membrane  oscillation  and otoacoustic emission at 15 kHz in a guinea pig.  To appear J. Assoc. Res. Otolaryngology 2004. A guinea pig exhibited a 15 kHz spontaneous otoacoustic emission that I could hear (!) - analysis and discussion of relevance.

 

Cochlear Analog Electroacoustic Transducers

Here we try to co-opt the design of the cochlea for the purposes of designing better microphones and hydrophones. Currently we have two emphases (1) to build a micromachined cochlea with multi-channel output (2) optimize the output of a single-channel transducer consisting of a fluid coupled device. Robert D. White, Lei Cheng and Robert Littrell are graduate students working on the project.

 

R. D. White and K. Grosh, Microengineered hydrodynamical cochlear model.  Proc. of the National Acad. of Sci., 102 (5), pp 1296-1301 (2005).

 

See Rob White's wepage for a compilation of papers and presentations for micromachined electroacoustic transducers .  Funding for this project has come from ONR, NSF and The University of Michigan.  The National Science Foundation ran a nice piece on this work and it implications, click here to view.  Further, there were a few other webstories written regarding the PNAS paper  - please see the PhysicsWeb article and group picture and the MSNBC article as examples.

 

Growth of Biological Tissue

With Professors Ellen Arruda and Krishna Garikipati, we have developed a framework for studying the growth of biological tissue using computational and in vitro biological models. We are collaborating with clinicians to implant the in vitro constructs and develop controlled in vivo models of growth. The hallmark of our work is the careful control and study of the influence of mechanical loading and the chemical environment on growth. The tissue engineering work of graduate student Sarah Calve (in collaboration with us and Prof. Robert Dennis now at North Carolina State University) is central to the efforts along with the computational efforts of Harish Naraynan. Joe Olberding and Devin O'Connor are the current graduate students on the project.

 

J. E. Olberding, H. Narayanan, E. M. Arruda, K. Grosh, S. Calve.  Biological Remodelling: Stationary Energy, configuration change, internal variables and dissipation. J. Mechs. and Physics of Solids, 54 (7), pp 1493-1515, (2006).

K. Garikipati, Arruda, E. M., Grosh, K., Narayanan, H., Calve, S., A continuum treatment of growth in biological tissue: The coupling of mass transport and growth.   J. Mechs. Phys. of Solids, 52(7), pp 1595-1625, (2004).

S. Calve, R. G. Dennis, P. E. Kosnik II, K. Baar, K. Grosh, and E. M. Arruda.  Engineering of functional tendon.  Tissue Engineering  10 (5-6), pp 755-761 (2004).

Next listed is Jeff Bischoff's work on soft tissue constitutive modeling done with Ellen and me. The idea here was to develop micromechanically motivated constitutive laws for soft biological tissues with as few parameters as possible.

 

J. E. Bischoff, E. M. Arruda, K. Grosh.   A rheological network formulation for orthotropic viscoelasticity in soft tissue.  Biomechanics and Modeling in Mechanobiology,  3(1), pp. 56-65  (2004).

J. E. Bischoff, E. M. Arruda, and  K. Grosh. A microstructurally based orthotropic hyperelastic constitutive law. ASME J. Appl. Mech., 69 (5), pp. 570-579, (2002).

J. E. Bischoff, E. M. Arruda, and  K. Grosh. Finite element simulations of orthotropic hyperelasticity. Finite Element Analysis and Design, 38 (10), pp. 983-998, (2002)

J. E. Bischoff, E. M. Arruda, and  K. Grosh.  Orthotropic hyperelasticity in terms of an arbitrary molecular model.  ASME J. Appl. Mech., 69 (2), pp. 198-201, (2002).

J. E. Bischoff, E. M. Arruda, and  K. Grosh.  A new constitutive model for the compressibility of elastomers at finite deformations. J. Rubber Chem. and Tec, 74 (4), pp. 541-559, (2001).

J. E. Bischoff, E. M. Arruda, and  K. Grosh.  Nonlinear constitutive models for skin response.   J. Biomech. 33, pp. 645-652, (2000).

J. E. Bischoff, E. M. Arruda, and K. Grosh,  A rheological  network formulation for orthotropic viscoelasticity in soft tissue.  Biomechanics and Modeling in Mechanobiology,  to appear.

Completed Research Projects

These projects represent areas of interest and previous work that are not currently active.

Design of Ultrasonic Phased Arrays for Noninvasive Therapy

The objective of this project was to develop and apply state of the art finite element tools for modeling the response of an ultrasonic phased array of piezoelectric transducers in contact with the human body. Novel finite element techniques and parallel computer algorithms are used to speed computations. In particular, the predictive capability is applied to (i) the design of arrays for high intensity focused ultrasound (HIFU) for tissue ablation (ii) the evaluation of treatment strategies for HIFU for cardiac and cancer therapy. We interacted with array designers for experimental comparisons and with U of M Medical school personnel for applications and tissue modeling.

Pictured: Pressure field from simple four element piezoelectric array at 0.5 MHz; yellow areas show focus regions.

Results and papers

Two graduate students graduated with PhDs (Yuan Lin and John Dodson) with roughly 4 years of funding (from the Whitaker Foundation and ONR).

Yuan Lin and K. Grosh.  Iterative solution strategies for three-dimensional high frequency response of fluid-loaded piezoelectric transducers. Finite Element Analysis and Design 39 (10): 951-964, (2003). We show the effectiveness of various iterative solvers for the coupled piezoelectric elastic and fluid coupling problem. We find that SSOR with a QMR algorithm works well with good memory to iteration count trade-off. Saad's ILU techniques also work well, with higher memory requirements. Convergence is an issue as the problem size increases and with added losses (mostly acoustic in this case).

Yuan Lin and Karl Grosh.  Topology optimization of the kerf filling in ultrasonic phased arrays.  J. Acoust. Soc. Amer., 112 (5) pp 1968-1979, (2002). Here we show how topology optimization can be used to design the fillings between ultrasonic transducer elements. In order to verify the various optimization alogorithms we build the arrays (in the model) and show how large arrarys of transducer elements can be effectively modelled.

Yuan Lin and K. Grosh. Design of ultrasonic array elements for acoustic power considerations.   IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.  2002. 49 (1) pp. 20-28 (2002). Standard rules for transducer design do not hold for the optimal power output at a single frequency (i.e., 1/4 matching layer is not always optimal). Design procedures, numerical examples of optimized design are compared to experiments.

DYNAMICS OF FLUID-LOADED STRUCTURES

Wave-vector filtering algorithms

Development of Prony based parameter estimation techniques for extracting the complex wave-vector nature of the response of structures (beams, plates and shells, with and without fluid loading). This work started with Earl Williams while I was at NRL. Pete Halliday extended the idea by using maximum likelihood methods, which are more powerful, robust and flexible to the problem in his elegant paper. These techniques will be of use not only for spectral and parameter estimation, but also for intensity/powerflow analysis.

Karl Grosh and Earl G. Williams.  Complex wave--number decomposition of structural vibrations. Journal of the Acoustical Society of America, 93(2), pp.836-848, (1993). A simple and effective way to obtain the wavenumbers and corresponding amplitudes from measured data.

Pete Halliday and K. Grosh.  Maximum likelihood estimation of structural wave components from noisy data. J. Acoust. Soc. Amer. 111 (4), pp. 1709-1717 (2002). Our approach takes advantage of the Golub and Pereya method for nonlinear least squares of systems whose variables separate into linear dependence (amplitudes -- easy part) and nonlinear (wavenumbers -- harder). Also nice is Greg McDaniel's paper using nonlinear least squares for the whole problem. We also have unpublished (except in Pete's thesis) results for intensity analysis and constitutive parameter estimation (including complex modulus).

Modeling intersections and joints

Real structures involve the intersection of members at joints (e.g., welds or rivets). Methods are developed for consistently coupling elasto-dynamic theory (necessary to describe the complex geometry of the joint) with reduced theories (beams, plates or shells, which are adequate away from the inhomogeneity). Using these methods, one may study the effect of joint geometry and develop reduced order models for complex joints.

Pete Halliday and K. Grosh.  Dynamic response of complex structural intersections using hybrid methods.  ASME J. Applied Mech. 66(3), pp 653-659, (1999). We develop a variationally consistent method for coupling reduced models of structures (like beams) to elastodynamics finite element models. Our model results are compared to the nice techniques of Gopalakrishnan and Doyle (of course, we like our method better!).

Finite element method development

Mid and high frequency structural acoustics problems pose a significant challenge to existing computational algorithms and hardware. In this work, Galerkin generalized least squares (GGLS) methods are developed to reduce the real costs of computatation (memory and compute time). GGLS methods enable the inclusion of analytic information about the wave-nature of the structural system into the discrete, finite element setting. For coupled, two-dimensional problems, more than an order of magnitude improvement has been achieved in memory and computational time. This work was largely done at Stanford with Peter Pinsky.

Karl Grosh.  Residual based methods for fluid-loaded beams. Computer Methods in Applied Mechanics and Engineering, 190, pp. 2543-2554, (2001).

Karl Grosh and Peter M. Pinsky.  Galerkin generalized least squares finite element  methods for time harmonic structural acoustics. Computer Methods in Applied Mechanics and Engineering, 154 (3-4), pp. 299-318, (1998). How to improve the accuracy of finite element interpolations of fluid-loaded plates.

Isaac Harari, Karl Grosh, Thomas J. R. Hughes, Manish Malhotra, Peter M. Pinsky, Lonny L. Thompson.  Recent developments in finite element methods for structural acoustics.  Archives of Computational Methods in Engineering,  3 (2-3), pp.131-309, (1996).

Karl Grosh and Peter M. Pinsky.  Galerkin generalized least squares methods for Timoshenko beams. Computer Methods in Applied Mechanics and Engineering, 132, pp.1-16, (1996).

Karl Grosh and Peter M. Pinsky.  Complex wave--number  dispersion analysis of Galerkin and Galerkin least squares methods for fluid-loaded plates. Computer Methods in Applied Mechanics and Engineering, 113, pp. 67-98, (1994). How to do dispersion analysis for finite element approximations for coupled systems. Specific results for the accuracy of finite element interpolations of fluid loaded plates. The error estimates provided by dispersion analysis give real guidlelines for discretization of coupled problems.

Smart structures

Design of efficient horn speaker systems by via curvature changes to PVDF, piezo-active film. Model predictions using Abaqus and Comet acoustics are used to drive the design; comparisons to experimental measurements of prototypes. With Prof. Diann Brei (MEAM).

Kelly Bailo, Diann Brei and Karl Grosh. Investigation of piezoelectric polymeric active diaphragms for sound sources. ASME J. Vib. Acoust.,  125 (2): 145-154, (2003). A complete study (experiments, numerical simulations and analytic approximation) of the radiation of sound from a arch-shaped sound source. Optimized sizing for sound radiation developed. Our unpublished studies show that an elastica shape can improve upon the arch design for radiated sound -- we did not finish that study however.

NONLINEAR DYNAMICS, VIBRATIONS AND NOISE

Contact and rattle generated noise and vibration

Contact and rattle noise have become an important area for automotive applications. These noise sources are generated by the impact of two structural components. Vibration and noise levels are a function of two nonlinear processes: contact and multibody dynamics. Numerical and analytic models have been developed to predict the motion and acoustic response. With Dr. Zheng-Dong Ma (MEAM) and Karen Fegeleman's PhD research (about 3 years of industry funding).

Karen. J. L. Fegelman and K. Grosh.  Dynamics of a flexible beam contacting a linear spring: experiment and analysis. ASME J. Vib. Acoust. 124 (2), pp. 237-249 (2002). Carefully controlled experiments and analytic analysis of the dynamics of a impacting system that spends most of its time in contact, a hinged plate undergoing base motion. In addition to studying the dynamics, we relate subtle changes in the response (e.g., number of contacts per period) to dramatic changes in the spectral quality of the sound (both measured and perceived).

Gear noise

The linear and nonlinear equations of motion of interacting gear sets are developed. Linearized stability analysis and nonlinear direct computations are performed. With Prof. Jim Barber (MEAM), Sejoong Oh's PhD research.

Sejoong Oh, Karl Grosh and J. R. Barber.  Energy conserving equations for gear systems.   ASME J. Vib. Acous.  to appear, 2004. Here is either a new result in gear mechanics that challenges the conventional wisdon on the topic (we could not find any papers on this topic) -- during any change in the number of teeth in contact in a gear system and impulsive load is applied to the system even for perfect involute gears. We show the importance of this harmonic load on the frequency response of the system is great at low RPM (near idle of an engine, say, where the potential energy is coparable to the kinetic energy of the system) and not as important at higher RPM where kinetic energy dominates.

James R. Barber, Karl Grosh and Sejoong Oh,  Energy considerations in systems with varying stiffness.  ASME, J. Appl. Mech., 70 (4), pp. 465-469, (2003). Inspired by our analysis of the gear system's variable stiffness, we examine the energetics of an elastic body with a moving load.

Silencing and Noise Control in Ducts (mufflers and hydraulic silencers)

Sripriya Ramamoorthy, K. Grosh, and Tony Nawar.  Structural acoustic silencers-Design and experiment.  J. Acoust. Soc. Amer., 114 (5), pp. 2812-2824, (2003).

Sripriya Ramamoorthy, Karl Grosh, John M. Dodson.  A theoretical study of structural acoustic silencers for hydraulic systems.  J. Acoust. Soc. Amer., 111 (5),  pp. 2097-2108, (2002). These first two papers discuss modeling techniques for structural acoustic silencers. Experimental measurements are compared to theoretical predictions for air-conveying ducts. We find designs which meet and exceed, say expansion chamber devices of the same dimension. One key advantage is the slow wavespeed of the coupled fluid-structure system which enables reactive silence of low frequency sound with much smaller devices -- this is a key advantage of the approach.

John M. Dodson, David R. Dowling and Karl Grosh. Design and effectiveness of in-line tuning cables for quieting hydraulic power units. J. of Noise Control Engineering 46 (1), pp. 15-22, (1998).