A2T and A2V Aß peptides exhibit different aggregation kinetics, primary nucleation, morphology, structure, and LTP inhibition.

The histopathological hallmark of Alzheimer's disease (AD) is the aggregation and accumulation of the amyloid beta peptide (Aß) into misfolded oligomers and fibrils. Here we examine the biophysical properties of a protective Aß variant against AD, A2T, and a causative mutation, A2T, along with the wild type (WT) peptide. The main finding here is that the A2V native monomer is more stable than both A2T and WT, and this manifests itself in different biophysical behaviors: the kinetics of aggregation, the initial monomer conversion to an aggregation prone state (primary nucleation), the abundances of oligomers, and extended conformations. Aggregation reaction modeling of the conversion kinetics from native monomers to fibrils predicts the enhanced stability of the A2V monomer, while ion mobility spectrometry-mass spectrometry measures this directly confirming earlier predictions. Additionally, unique morphologies of the A2T aggregates are observed using atomic force microscopy, providing a basis for the reduction in long term potentiation inhibition of hippocampal cells for A2T compared with A2V and the wild type (WT) peptide. The stability difference of the A2V monomer and the difference in aggregate morphology for A2T (both compared with WT) are offered as alternate explanations for their pathological effects.

Cosolute effects on amyloid aggregation in a nondiffusion limited regime: intrinsic osmolyte properties and the volume exclusion principle.

The effects of cosolutes on amyloid aggregation kinetics in vivo are critical and not fully understood. To explore the effects of cosolute additives, the in vitro behavior of destabilizing and stabilizing osmolytes with polymer cosolutes on the aggregation of a model amyloid, human insulin, is probed using experiments coupled with an amyloid aggregation reaction model. The destabilizing osmolyte, guanidine hydrochloride (GuHCl), induces biphasic behavior on the amyloid aggregation rate exhibited by an enhancement of the aggregation kinetics at low concentrations of GuHCl (<0.6 M) and a reduction in kinetics at higher GuHCl concentrations. Stabilizing osmolytes, glycerol, sorbitol and trimethylamine N-oxide, slow the rate of aggregation by reducing the rate of monomer unfolding. Polymer cosolutes, polyvinylpyrrolidone 3.5 kDa and 40 kDa, delay amyloid aggregation mainly through a decrease in the nucleation reaction. These results are in good agreement with the volume exclusion principle for polymer crowding and supports the need to include conformational rearrangement of monomers prior to nucleation. Using fluorescence correlation spectroscopy, we demonstrate that amyloid aggregation is nondiffusion limited, except during fibril accumulation in the presence of high concentrations of long chain polymers. Lastly, the neutral surface area of osmolytes correlates well with the time to initiate fibril formation, tlag, which implicates an intrinsic osmolyte property underlying preferential interactions.

ACT5 Electrical Impedance Tomography System.

OBJECTIVE: This article introduces the Adaptive Current Tomograph 5 (ACT5) Electrical Impedance Tomography (EIT) system. ACT5 is a 32 electrode applied-current multiple-source EIT system that can display real-time images of conductivity and susceptivity at 27 frames per second. The adaptive current sources in ACT5 can apply fully programmable current patterns with frequencies varying from 5 kHz to 500 kHz. The system also displays real-time ECG readings during the EIT imaging process. METHODS: The hardware and software design and specifications are presented, including the current source design, FPGA hardware, safety features, calibration, and shunt impedance measurement. RESULTS: Images of conductivity and susceptivity are presented from ACT5 data collected on tank phantoms and a human subject illustrating the system's ability to provide real-time images of pulsatile perfusion and ECG traces. SIGNIFICANCE: The portability, high signal-to-noise ratio, and flexibility of applied currents over a wide range of frequencies enable this instrument to be used to obtain useful human subject data with relative clinical ease.

A mathematical model of cell cycle effects in gastric cancer chemotherapy.

A mathematical model is presented to investigate the relationship between drug order and treatment response in gastric cancer chemotherapy involving a taxane (either paclitaxel or docetaxel) coupled with flavopiridol. To model treatment effects, we simulate treatment by bolus injection and employ a pulsing condition to indicate cell kill as well as instantaneous changes to the cell's transition rates. Cell population growth is described using an ordinary differential equation model whereby we examine the treatment effects upon cells in various stages of the cell cycle. Ultimately, the results generated support prior clinical investigations which indicate that for an enhanced synergistic effect, flavopiridol must be administered following taxane therapy.

A mathematical model for the effects of HER2 over-expression on cell cycle progression in breast cancer.

In this paper, we present a mathematical model predicting the fraction of proliferating cells in G1, S, and G2/M phases of the cell cycle as a function of EGFR and HER2. We show that it is possible to find parameters for the mathematical model so that its predictions agree with the experimental observations that HER2 over-expression results in: (1) a shorter G1-phase and early S-phase entry; (2) and that with a 1-to-1 ration between EGFR and HER2, the growth advantage in HER2 over-expressing cells is indeed associated with the increase of the HER2 expression level.

A mathematical model of breast cancer treatment with CMF and doxorubicin.

A mathematical model is presented to investigate the ordering phenomenon observed in the comparison of alternating to sequential regimens of CMF (cyclophosphamide, methotrexate, 5-fluorouracil) and doxorubicin used in breast cancer chemo-therapy. The ordinary differential equation model incorporates cell cycle specificity and resistance to study why doses of the same drugs given in different orders result in different clinical outcomes. The model employs a pulsing condition to simulate treatment and induced resistance, and we investigate treatment outcome by simulating a patient population by varying parameters using uniform distributions. The results of these simulations correspond to those observed in prior clinical studies and suggest that drug resistance might be a key mechanism in the sequential regimen's superiority.

A two-layered forward model of tissue for electrical impedance tomography.

Electrical impedance tomography is being explored as a technique to detect breast cancer, exploiting the differences in admittivity between normal tissue and tumors. In this paper, the geometry is modeled as an infinite half space under a hand-held probe. A forward solution and a reconstruction algorithm for this geometry were developed previously by Mueller et al (1999 IEEE Trans. Biomed. Eng. 46 1379). In this paper, we present a different approach which uses the decomposition of the forward solution into its Fourier components to obtain the forward solution and the reconstructions. The two approaches are compared in terms of the forward solutions and the reconstructions of experimental tank data. We also introduce a two-layered model to incorporate the presence of the skin that surrounds the body area being imaged. We demonstrate an improvement in the reconstruction of a target in a layered medium using this layered model with finite difference simulated data. We then extend the application of our layered model to human subject data and estimate the skin and the tissue admittivities for data collected on the human abdomen using an ultrasound-like hand-held EIT probe. Lastly, we show that for this set of human subject data, the layered model yields an improvement in predicting the measured voltages of around 81% for the lowest temporal frequency (3 kHz) and around 61% for the highest temporal frequency (1 MHz) applied when compared to the homogeneous model.

A mathematical model for the effects of HER2 overexpression on cell proliferation in breast cancer.

We present a mathematical model to study the effects of HER2 over-expression on cell proliferation in breast cancer. The model illustrates the proliferative behavior of cells as a function of HER2 and EGFR receptors numbers, and the growth factor EGF. This mathematical model comprises kinetic equations describing the cell surface binding of EGF growth factor to EGFR and HER2 receptors, coupled to a model for the dependence of cell proliferation rate on growth factor receptors binding. The simulation results from this model predict: (1) a growth advantage associated with excess HER2 receptors; (2) that HER2-over-expression is an insufficient parameter to predict the proliferation response of cancer cells to epidermal growth factors; and (3) the EGFR receptor expression level in HER2-over-expressing cells plays a key role in mediating the proliferation response to receptor-ligand signaling. This mathematical model also elucidates the interaction and roles of other model parameters in determining cell proliferation rate of HER2-over-expressing cells.

An analytical layered forward model for breasts in electrical impedance tomography.

Electrical impedance tomography (EIT) can be used to determine the admittivity distribution within the breast from measurements made on its surface. It has been reported that the electrical impedance spectrum of normal breast tissue is significantly different from that of malignant tissue, making EIT a candidate technology for breast cancer detection. The inhomogeneous structure of breasts, with thin low-admittivity skin layers covering the relatively high-admittivity tissue inside, makes the breast imaging problem difficult. In addition, studies show that the electrical properties of skin vary considerably over frequency. This paper proposes a layered forward model which incorporates the presence of skin. Our layered model has three layers, thin low-admittivity top and bottom layers representing skin and a thicker high-admittivity middle layer representing breast tissue. We solve for the forward solution of the layered geometry and compare its behavior with the previously used homogeneous model. Next we develop an iterative method to estimate the skin and breast tissue admittivities from the measured data, and study the robustness and accuracy of the method for various simulated and experimental data. We then look at the reconstruction of a target embedded in a layered body when the homogeneous forward solution is replaced by the layered forward solution. Lastly, we demonstrate the improvement that the layered forward model produces over the homogeneous model when working with clinical data.

An Algorithm for Applying Multiple Currents Using Voltage Sources in Electrical Impedance Tomography.

A method to produce a desired current pattern in a multiple-source EIT system using voltage sources is presented. Application of current patterns to a body is known to be superior to the application of voltage patterns in terms of high spatial frequency noise suppression, resulting in high accuracy in conductivity and permittivity images. Since current sources are difficult and expensive to build, the use of voltage sources to apply the current pattern is desirable. An iterative algorithm presented in this paper generates the necessary voltage pattern that will produce the desired current pattern. The convergence of the algorithm is shown under the condition that the estimation error of the linear mapping matrix from voltage to current is small. Simulation results are presented to illustrate the convergence of the output current.

3-D electrical impedance tomography for piecewise constant domains with known internal boundaries.

Electrical impedance tomography (EIT) is a badly posed inverse problem, but can be stabilized if one assumes that the conductivity is piecewise constant, with a relatively small number of distinct regions, and that the region boundaries are known, for example from prior anatomical imaging. With this assumption, we introduce a three-dimensional (3-D) boundary element method (BEM) model for the forward EIT map from injected currents to measured voltages, and 3-D inverse solutions for both BEM and the finite element method (FEM) which explicitly take into account the parameterization implied by the known boundary locations. We develop expressions for the Jacobians for both methods, since they are nonlinear, to more rapidly solve the inverse problem. We show simulation results in a torso geometry with the heart and lungs as inhomogeneities. In a simulation study, we could reconstruct the conductive values of some internal organs of a human torso with more than 92% accuracy even with inaccurate internal boundary locations, a randomized rather than constant conductivity profile (with the standard deviation of the Gaussian-distributed conductivities set to 20% of their mean values), signal to measurement noise of 50 dB, and with different meshes used for the forward and inverse problems. BEM and FEM perform similarly, leading to the conclusion that the choice between them should be based on secondary considerations such as computational efficiency or the need to model conductivity anisotropies.

A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry.

The conductivity and permittivity of breast tumors are known to differ significantly from those of normal breast tissues, and electrical impedance tomography (EIT) is being studied as a modality for breast cancer imaging to exploit these differences. At present, X-ray mammography is the primary standard imaging modality used for breast cancer screening in clinical practice, so it is desirable to study EIT in the geometry of mammography. This paper presents a forward model of a simplified mammography geometry and a reconstruction algorithm for breast tumor imaging using EIT techniques. The mammography geometry is modeled as a rectangular box with electrode arrays on the top and bottom planes. A forward model for the electrical impedance imaging problem is derived for a homogeneous conductivity distribution and is validated by experiment using a phantom tank. A reconstruction algorithm for breast tumor imaging based on a linearization approach and the proposed forward model is presented. It is found that the proposed reconstruction algorithm performs well in the phantom experiment, and that the locations of a 5-mm-cube metal target and a 6-mm-cube agar target could be recovered at a target depth of 15 mm using a 32 electrode system.

A method for analyzing electrical impedance spectroscopy data from breast cancer patients.

Research on freshly-excised malignant breast tissues and surrounding normal tissues in an in vitro impedance cell has shown that breast tumors have different conductivity and permittivity from normal or non-malignant tissues. This contrast may provide a basis for breast cancer detection using electrical impedance imaging. This paper describes a procedure for collecting electrical impedance spectroscopy data simultaneously and in register with tomosynthesis data from patients. We describe the methods used to analyze the data in order to determine if the electrodes are making contact with the breast of the patient. Canonical voltage patterns are applied and used to synthesize the data that would have resulted from constant voltage patterns applied to each of two parallel mammography plates. A type of Cole-Cole plot is generated and displayed from each of the currents measured on each of the electrodes for each of the frequencies (5, 10, 30, 100 and 300 kHz) of applied voltages. We illustrate the potential usefulness of these displays in distinguishing breast cancer from benign lesions with the Cole-Cole plots for two patients--one having cancer and one having a benign lesion--by comparing these graphs with electrical impedance spectra previously found by Jossinet and Schmitt in tissue samples taken from a variety of patients.

The complete electrode model for EIT in a mammography geometry.

We have developed an EIT system for simultaneous use in a mammography examination, allowing for highly accurate co-registration between the two modalities. In this pre-clinical study, we investigate the importance of properly modeling the interface between the electrodes and the medium being imaged. We have implemented the complete electrode model for a parallel-plane mammography geometry, in which currents are injected into the medium through two planar sets of electrodes above and below the medium. We make use of the ACT4 device to conduct saline-tank experiments showing the improvement of the complete model over an ave-gap model, which ignores both the conductivity of the electrodes and the surface impedance. The experimental results show an improvement in both forward modeling accuracy and in the quality of the resulting reconstructed images using the complete electrode model, as compared to the ave-gap model.

Efficient Simultaneous Reconstruction of Time-Varying Images and Electrode Contact Impedances in Electrical Impedance Tomography.

OBJECTIVE: In electrical impedance tomography (EIT), we apply patterns of currents on a set of electrodes at the external boundary of an object, measure the resulting potentials at the electrodes, and, given the aggregate dataset, reconstruct the complex conductivity and permittivity within the object. It is possible to maximize sensitivity to internal conductivity changes by simultaneously applying currents and measuring potentials on all electrodes but this approach also maximizes sensitivity to changes in impedance at the interface. METHODS: We have, therefore, developed algorithms to assess contact impedance changes at the interface as well as to efficiently and simultaneously reconstruct internal conductivity/permittivity changes within the body. We use simple linear algebraic manipulations, the generalized singular value decomposition, and a dual-mesh finite-element-based framework to reconstruct images in real time. We are also able to efficiently compute the linearized reconstruction for a wide range of regularization parameters and to compute both the generalized cross-validation parameter as well as the L-curve, objective approaches to determining the optimal regularization parameter, in a similarly efficient manner. RESULTS: Results are shown using data from a normal subject and from a clinical intensive care unit patient, both acquired with the GE GENESIS prototype EIT system, demonstrating significantly reduced boundary artifacts due to electrode drift and motion artifact.

Electrode boundary conditions and experimental validation for BEM-based EIT forward and inverse solutions.

In this paper, we present theoretical developments and experimental results for the problem of estimating the conductivity map inside a volume using electrical impedance tomography (EIT) when the boundary locations of any internal inhomogeneities are known. We describe boundary element method (BEM) implementations of advanced electrode models for the forward problem of EIT. We then use them in the inverse problem with known internal boundaries and derive the associated Jacobians. We report on the results of two EIT phantom studies, one using a homogeneous cubical tank, and one using a cylindrical tank with agar conductivity inhomogeneities. We test both the accuracy of our BEM forward model, including the electrode models, as well as our inverse solution, against the measured data. Results show good agreement between measured values and both forward-computed tank voltages and inverse-computed conductivities; for instance, in a phantom experiment, we reconstructed the conductivities of three agar objects inside a cylindrical tank with an error less than 2% of their true value.

Dynamic electrical impedance imaging of a chest phantom using the Kalman filter.

A dynamic complex impedance imaging technique is developed with the aid of the linearized Kalman filter (LKF) for real-time reconstruction of the human chest. The forward problem is solved by an analytical method based on the separation of variables and Fourier series. The inverse problem is treated as a state estimation problem. The nonlinear measurement equation is linearized about the best homogeneous impedivity value as an initial guess, and the impedivity distribution is estimated with the aid of the Kalman estimator. The Kalman gain matrix is pre-computed and stored off-line to minimize the on-line computational time. Simulation and phantom experiment are reported to illustrate the reconstruction performances in the sense of spatio-temporal resolution in a simplified geometry of the human chest.

Early Treatment Critical: Bexarotene Reduces Amyloid-Beta Burden In Silico.

Amyloid-beta peptides have long been implicated in the pathology of Alzheimer's disease. Bexarotene, a drug approved by the U.S. Food and Drug Administration for treating a class of non-Hodgkin's lymphoma, has been reported to facilitate the removal of amyloid-beta. We have developed a mathematical model to explore the efficacy of bexarotene treatment in reducing amyloid-beta load, and simulate amyloid-beta production throughout the lifespan of diseased mice. Both aspects of the model are based on and consistent with previous experimental results. Beyond what is known empirically, our model shows that low dosages of bexarotene are unable to reverse symptoms in diseased mice, but dosages at and above an age-dependent critical concentration can recover healthy brain cells. Further, early treatment was shown to have significantly improved efficacy versus treatment in older mice. Relevance with respect to bexarotene-based amyloid-beta-clearance mechanism and direct treatment for Alzheimer's disease is emphasized.

Correction: Early Treatment Critical: Bexarotene Reduces Amyloid-Beta Burden In Silico.

[This corrects the article DOI: 10.1371/journal.pone.0153150.].

Comparison of impedance measurements near the skin of newborns and adults.

Electrical impedance tomography (EIT) is a non-invasive imaging technology that has been extensively studied for monitoring lung function of neonatal and adult subjects, especially in neonatal intensive care unit (NICU) and intensive care unit (ICU) environments. The sources of the total impedance in these applications include internal organs, near-boundary tissues, electrode-skin impedance, electrodes and conducting wires. This total impedance must be considered for system design and setting voltage gain since it will contribute to the measured voltage. To adapt a single instrument for use on infants and adults, we studied the difference between the impedance near the skin in both classes of patients. We used a simultaneous multi-source EIT (SMS-EIT) system to make impedance measurements. Characteristic resistance was calculated for two different current patterns: one that is more sensitive to boundary region impedance and another that is more sensitive to interior changes. We present ratios of these resistances to assess the relative contribution of near-skin effects to the overall impedance. Twenty adult ICU subjects (10 male, 10 female, age: 49.05 ± 16.32 years (mean ± standard deviation)) and 45 neonates (23 male, 22 female, gestational age: 37.67 ± 2.11 weeks, postnatal age, 2.56 ± 2.67 d) were studied at Columbia University Medical Center. Impedance measurements at 10 kHz were collected for approximately one hour from each subject. The characteristic resistance ratio for each subject was computed and analyzed. The result shows the impedance at or near the skin of newborns is significantly higher than in adult subjects.