A continuum treatment of growth in biological tissue: The coupling of mass transport and mechanics

Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited, the theory is reformulated, and consequences for balance laws and constitutive relations are deduced. The treatment incorporates multiple species. Sources and fluxes of mass, and terms for momentum and energy transfer between species are introduced to enhance the classical balance laws. The transported species include: (\romannumeral 1) a fluid phase, and (\romannumeral 2) the precursors and byproducts of the reactions that create and break down tissue. A notable feature is that the full extent of coupling between mass transport and mechanics emerges from the thermodynamics. Contributions to fluxes from the concentration gradient, chemical potential gradient, stress gradient, body force and inertia have not emerged in a unified fashion from previous formulations of the problem. The present work demonstrates these effects via a physically-consistent treatment. The presence of multiple, interacting species requires that the formulation be consistent with mixture theory. This requirement has far-reaching consequences. A preliminary numerical example is included to demonstrate some aspects of the coupled formulation.Comment: 29 pages, 11 figures, accepted for publication in Journal of the Mechanics and Physics of Solids. See journal for final versio

Biological remodelling: Stationary energy, configurational change, internal variables and dissipation

Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical setting. While some examples of remodelling are conveniently modelled as evolution of the reference configuration (Case I), others are more suited to an internal variable description (Case II). In this paper we explore the applicability of stationary energy states to remodelled systems. A variational treatment is introduced by assuming that stationary energy states are attained by changes in microstructure via one of the two mechanisms--Cases I and II. An example is presented to illustrate each case. The example illustrating Case II is further studied in the context of the thermodynamic dissipation inequality.Comment: 24 pages, 4 figures. Replaced version has corrections to typos in equations, and the corresponding correct plot of the solution--all in Section

AN INVESTIGATION OF CERTAIN THERMODYNAMIC AND TRANSPORT PROPERTIES OF WATER AND WATER VAPOR IN THE CRITICAL REGION

An accurate knowledge of thermodynamic and transport properties of water in the critical region is required in order to analyze future power cycles, nuclear reactor configurations, and other types of heat transfer apparatus. Preliminnry investigations showed that this was rot possible with presently existing tabulations. Experimentel data from volumetric viscosity and thermal conductivity studies were therefore selected and retabulated. Smoothings of these data are described and, for the first time, a tabulation at close intervals of pressure and temperature of the volumetric data is possible for steam in the critical region. A graphical presentation is given of volumetric data from 700 to 750 deg F. An important result of this study was that excellent agreement existed between the many P-V-T measurements for this substance even though some of the data was obtained many years ago. Differences occurring between the tabulated data of various steam tables were found to arise from the use of inexact equations of state or interpolation techniques rather than from faulty primary data. New P-V-T data were derived from measurements of other investigators, by a graphical technique and it is estimated that it yielded pressure values accurate to some five parts in ten thousand except in the subcooled liquid region (for specific volumes below 0.040 ftsup 3/lb), where the uncertainty may be some twenty parts in ten thousand. Study of the existing thermal conductivity and viscosity data suggests that the Russian work is the most consistent. However, it appears that the empirical equations proposed for interpolation do not adequately represent the data in the critical region. No attempt has been made to derive thermodynamic functions or to analyze the transport data. (auth

State Space and Transfer Function Modeling of Evanescent Waves in Two-Dimensional Acoustics

Abstract With intense current interest in active noise control, it is desirable to develop models of acoustic phenomena that are useful for state-space-based control methodologies. Consequently, this paper extends the one-dimensional modeling of acoustic transfer functions developed in earlier work to the case of two-dimensional acoustics. This extension must therefore account for the phenomenon of evanescent waves, which are non-propagating and thus affect only the near field. While evanescent waves are well understood within the context of wave models, their presence is less apparent in state space-based model modals. This paper thus presents a derivation of state space models for two-dimensional acoustics which are shown to predict the presence of evanescent waves

Applied & Computational MathematicsChallenges for the Design and Control of Dynamic Energy Systems

The Energy Independence and Security Act of 2007 (EISA) was passed with the goal 'to move the United States toward greater energy independence and security.' Energy security and independence cannot be achieved unless the United States addresses the issue of energy consumption in the building sector and significantly reduces energy consumption in buildings. Commercial and residential buildings account for approximately 40% of the U.S. energy consumption and emit 50% of CO{sub 2} emissions in the U.S. which is more than twice the total energy consumption of the entire U.S. automobile and light truck fleet. A 50%-80% improvement in building energy efficiency in both new construction and in retrofitting existing buildings could significantly reduce U.S. energy consumption and mitigate climate change. Reaching these aggressive building efficiency goals will not happen without significant Federal investments in areas of computational and mathematical sciences. Applied and computational mathematics are required to enable the development of algorithms and tools to design, control and optimize energy efficient buildings. The challenge has been issued by the U.S. Secretary of Energy, Dr. Steven Chu (emphasis added): 'We need to do more transformational research at DOE including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.' On July 8-9, 2010 a team of technical experts from industry, government and academia were assembled in Arlington, Virginia to identify the challenges associated with developing and deploying newcomputational methodologies and tools thatwill address building energy efficiency. These experts concluded that investments in fundamental applied and computational mathematics will be required to build enabling technology that can be used to realize the target of 80% reductions in energy consumption. In addition the finding was that there are tools and technologies that can be assembled and deployed in the short term - the next 3-5 years - that can be used to significantly reduce the cost and time effective delivery of moderate energy savings in the U.S. building stock. Simulation tools, which are a core strength of current DOE computational research programs, provide only a part of the answer by providing a basis for simulation enabled design. New investments will be required within a broad dynamics and control research agenda which must focus on dynamics, control, optimization and simulation of multi-scale energy systems during design and operation. U.S. investments in high performance and high productivity computing (HP2C) should be leveraged and coupled with advances in dynamics and control to impact both the existing building stock through retrofits and also new construction. The essential R&D areas requiring investment are: (1) Characterizing the Dynamics of Multi-scale Energy Systems; (2) Control and Optimization Methodologies of Multi-scale Energy Systems Under Uncertainty; and (3) Multiscale Modeling and Simulation Enabled Design and Operation. The concept of using design and control specific computational tools is a new idea for the building industry. The potential payoffs in terms of accelerated design cycle times, performance optimization and optimal supervisory control to obtain and maintain energy savings are huge. Recent advances in computational power, computer science, and mathematical algorithms offer the foundations to address the control problems presented by the complex dynamics of whole building systems. The key areas for focus and associated metrics with targets for establishing competitiveness in energy efficient building design and operation are: (1) Scalability - Current methodology and tools can provide design guidance for very low energy buildings in weeks to months; what is needed is hours to days. A 50X improvement is needed. (2) Installation and commissioning - Current methodology and tools can target a three month window for commissioning of building subsystems; what is needed is one week. A 10X improvement is needed. (3) Quality - Current design tools can achieve 30% accuracy; what is needed to make design decisions is 5% with quantification of uncertainty. A 5X improvement is needed. These challenges cannot be overcome by raw computational power alone and require the development of new algorithms. Here algorithms mean much more than simulating the building physics but need to be inclusive of a much better understanding of the building and the control systems associated with the building and to capture the entire set of dynamics. The algorithmsmust represent computationally new mathematical approaches to modeling, simulation, optimization and control of large multi-scale dynamic systems and bringing these elements to bear on industry in simulation enabled design approaches

Primary pericardial malignant mesothelioma and response to radiation therapy

We report a case of a primary pericardial malignant mesothelioma. A 59-year-old male presented with episodic chest pain and dyspnea on exertion. Cardiac magnetic resonance imaging revealed a large mass in the pericardium attached to the right ventricle. Partial resection of the mass was undertaken revealing malignant mesothelioma, byphasic type. The patient was treated with chemotherapy intermittently over a period of 3 years, but his disease continued to progress. The patient was then treated with definitive radiation therapy to 64 Gy to the primary tumor using a six field 3D conformal technique. The patient remains free of progressive disease 86 months from the time of diagnosis and 50 months from the completion of his radiotherapy

Did aid promote democracy in Africa?: the role of technical assistance in Africa’s transitions

Did foreign aid impede or catalyze democratization in Africa in the 1990s? We argue that after the Cold War, donors increased their use of technical assistance in aid packages, improving their monitoring capacity and thus reducing autocrats’ ability to use aid for patronage. To remain in power, autocrats responded by conceding political rights to their opponents—from legalizing opposition parties to staging elections. We test our theory with panel data for all sub-Saharan African countries. While other factors played pivotal roles in Africa’s political liberalization, we find technical assistance helps to explain the timing and extent of Africa’s democratization

In Vivo Outer Hair Cell Length Changes Expose the Active Process in the Cochlea

BACKGROUND: Mammalian hearing is refined by amplification of the sound-evoked vibration of the cochlear partition. This amplification is at least partly due to forces produced by protein motors residing in the cylindrical body of the outer hair cell. To transmit power to the cochlear partition, it is required that the outer hair cells dynamically change their length, in addition to generating force. These length changes, which have not previously been measured in vivo, must be correctly timed with the acoustic stimulus to produce amplification. METHODOLOGY/PRINCIPAL FINDINGS: Using in vivo optical coherence tomography, we demonstrate that outer hair cells in living guinea pigs have length changes with unexpected timing and magnitudes that depend on the stimulus level in the sensitive cochlea. CONCLUSIONS/SIGNIFICANCE: The level-dependent length change is a necessary condition for directly validating that power is expended by the active process presumed to underlie normal hearing