Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

A novel target-field method for finite-length magnetic resonance shim coils: I. Zonal shims

This paper presents a new approach for the design of genuinely finite-length shim and gradient coils, intended for use in magnetic resonance imaging equipment. A cylindrical target region is located asymmetrically, at an arbitrary position within a coil of finite length. A desired target field is specified on the surface of that region, and a method is given that enables winding patterns on the surface of the coil to be designed, to produce the desired field at the inner target region. The method uses a minimization technique combined with regularization, to find the current density on the surface of the coil. The method is illustrated for linear, quadratic and cubic magnetic target fields located asymmetrically within a finite-length coil.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Finite, three-dimensional adsorbed phase growth in activated carbon mesopores

The role of PACs (primary adsorption centers) in the mesopore (i.e., transport) region of activated carbons during adsorption of polar species, such as water, is unclear. A classical model of three-dimensional adsorption on finite PACs is presented. The model is a preliminary, theoretical investigation into adsorption on mesopore PACs and is intended to give some insight into the energetic and physical processes at work. Work processes are developed to obtain isotherms and three-dimensional sorbate growth on PACs of varying size and energetic characteristics. The work processes allow two forms of adsorbed phase growth: densification at constant boundary and boundary growth at constant density. Relatively strong sorbate-sorbent interactions and strong surface tension favor adsorbed phase densification over boundary growth. Conversely, relatively weak sorbate-sorbent interactions and weak surface tension favor boundary growth over densification. If sorbate-sorbate interactions are strong compared to sorbate-sorbent interactions, condensation with hysteresis occurs. This can also give rise to delayed boundary growth, where all initial adsorption occurs in the monolayer only. The results indicate that adsorbed phase growth on PACs may be quite complex.

Cadherin-directed actin assembly: E-cadherin physically associates with the Arp2/3 complex to direct actin assembly in nascent adhesive contacts

Cadherin cell adhesion molecules are major determinants of tissue patterning which function in cooperation with the actin cytoskeleton [1-4]. In the context of stable adhesion [1], cadherin/catenin complexes are often envisaged to passively scaffold onto cortical actin filaments. However, cadherins also form dynamic adhesive contacts during wound healing and morphogenesis [2]. Here actin polymerization has been proposed to drive cell surfaces together [5], although F-actin reorganization also occurs as cell contacts mature [6]. The interaction between cadherins and actin is therefore likely to depend on the functional state of adhesion. We sought to analyze the relationship between cadherin homophilic binding and cytoskeletal activity during early cadherin adhesive contacts. Dissecting the specific effect of cadherin ligation alone on actin regulation is difficult in native cell-cell contacts, due to the range of juxtacrine signals that can arise when two cell surfaces adhere [7]. We therefore activated homophilic ligation using a specific functional recombinant protein. We report the first evidence that E-cadherin associates with the Arp2/3 complex actin nucleator and demonstrate that cadherin binding can exert an active, instructive influence on cells to mark sites for actin assembly at the cell surface.

E-cadherin homophilic ligation directly signals through Rac and phosphatidylinositol 3-kinase to regulate adhesive contacts

Classical cadherins mediate cell recognition and cohesion in many tissues of the body. It is increasingly apparent that dynamic cadherin contacts play key roles during morphogenesis and that a range of cell signals are activated as cells form contacts with one another. It has been difficult, however, to determine whether these signals represent direct downstream consequences of cadherin ligation or are juxtacrine signals that are activated when cadherin adhesion brings cell surfaces together but are not direct downstream targets of cadherin signaling. In this study, we used a functional cadherin ligand (hE/Fc) to directly test whether E-cadherin ligation regulates phosphatidylinositol 3-kinase (PI 3-kinase) and Rac signaling. We report that homophilic cadherin ligation recruits Rae to nascent adhesive contacts and specifically stimulates Rae signaling. Adhesion to hE/Fc also recruits PI 3-kinase to the cadherin complex, leading to the production of phosphatidylinositol 3,4,5-trisphosphate in nascent cadherin contacts. Rae activation involved an early phase, which was PI 3-kinase-independent, and a later amplification phase, which was inhibited by wortmannin. PI 3-kinase and Rae activity were necessary for productive adhesive contacts to form following initial homophilic ligation. We conclude that E-cadherin is a cellular receptor that is activated upon homophilic ligation to signal through PI 3-kinase and Rae. We propose that a key function of these cadherin-activated signals is to control adhesive contacts, probably via regulation of the actin cytoskeleton, which ultimately serves to mediate adhesive cell-cell recognition.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Electropalatographic assessment of tongue-to-palate contacts exhibited in dysarthria following traumatic brain injury: Spatial characteristics

Consonant imprecision has been reported to be a common feature of the dysarthric speech disturbances exhibited by individuals who have sustained a traumatic brain injury (TBI). Inaccurate tongue placements against the hard palate during consonant articulation may be one factor underlying the imprecision. To investigate this hypothesis, electropalatography (EPG) was used to assess the spatial characteristics of the tongue-to-palate contacts exhibited by three males (aged 23-29 years) with dysarthria following severe TBI. Five nonneurologically impaired adults served as control subjects. Twelve single-syllable words of CV or CVC construction (where initial C = /t, d, S, z, k, g/, V=/i, a/) were read aloud three times by each subject while wearing an EPG palate. Spatial characteristics were analyzed in terms of the location, pattern, and amount of tongue-to-palate contact at the frame of maximum contact during production of each consonant. The results revealed that for the majority of consonants, the patterns and locations of contacts exhibited by the TBI subjects were consistent with the contacts generated by the group of control subjects. One notable exception was one subject's production of the alveolar fricatives in which complete closure across the palate was demonstrated, rather than the characteristic groove configuration. Major discrepancies were also noted in relation to the amount of tongue-to-palate contact exhibited, with two TBI subjects consistently demonstrating increased contacts compared to the control subjects. The implications of these findings for the development of treatment programs for dysarthric speech disorders subsequent to TBI are highlighted.