Modeling the Effects of Multiple Myeloma on Kidney Function

Multiple myeloma (MM), a plasma cell cancer, is associated with many health challenges, including damage to the kidney by tubulointerstitial fibrosis. We develop a mathematical model which captures the qualitative behavior of the cell and protein populations involved. Specifically, we model the interaction between cells in the proximal tubule of the kidney, free light chains, renal fibroblasts, and myeloma cells. We analyze the model for steady-state solutions to find a mathematically and biologically relevant stable steady-state solution. This foundational model provides a representation of dynamics between key populations in tubulointerstitial fibrosis that demonstrates how these populations interact to affect patient prognosis in patients with MM and renal impairment.Comment: Included version of model without tumor with steady-state analysis, corrected equations for free light chains and renal fibroblasts in model with tumor to reflect steady-state analysis, updated abstract, updated and added reference

The Role of Osteocytes in Targeted Bone Remodeling: A Mathematical Model

Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin. Moreover, there is also increasing interest in sclerostin, an osteocyte-secreted bone formation inhibitor, and its role in regulating local response to changes in the bone microenvironment. Here we develop a cell population model of bone remodeling that includes the role of osteocytes, sclerostin, and allows for the possibility of RANKL expression by osteocyte cell populations. This model extends and complements many of the existing mathematical models for bone remodeling but can be used to explore aspects of the process of bone remodeling that were previously beyond the scope of prior modeling work. Through numerical simulations we demonstrate that our model can be used to theoretically explore many of the most recent experimental results for bone remodeling, and can be utilized to assess the effects of novel bone-targeting agents on the bone remodeling process

Phase diagram of the one dimensional anisotropic Kondo-necklace model

The one dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction (J) between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value, J_c. Moreover, our results show that the onset of anisotropy in the XY term of the itinerant interactions develops the antiferromagnetic order for J<J_c. This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic XY interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.Comment: 9 pages and 9 eps figure

Chronic critical leg ischaemia must include leg ulcers

Objectives:In a previous series on conservative treatment in patients with leg ulcers and severe arterial occlusive disease (systolic digital blood pressure (SDBP) < 30 mmHg) a 70% risk of leg amputation and a negligeable potential for ulcerhealing was found. This series assess the efficacy of arterial reconstruction in such patients.Design:Retrospective study of consecutive patients in a department of vascular surgery and of dermatology in cooperation with the wound healing center.Material and Methods:Thirty-nine patients with 42 ulcerated legs underwent arterial revascularisation. 88% of the procedures were distal to the inguinal ligament.Main results:One patient died postoperatively (3%). Seven (18%) had wound complications, but none had graft infections. After 1 year the cumulative secondary patency was 90%, ulcer healing 70% and the limb salvage 90%. Thus only four legs (10%) had been amputated.Conclusions:Arterial revascularisation for leg ulcers is indicated when conservative treatment fails. Legs with ulceration and SDBP < 30 mmHg should be included in the concept of chronic critical ischaemia

Polaron self-trapping in a honeycomb net

Small polaron behavior in a two dimensional honeycomb net is studied by applying the strong coupling perturbative method to the Holstein molecular crystal model. We find that small optical polarons can be mobile also if the electrons are strongly coupled to the lattice. Before the polarons localize and become very heavy, there is infact a window of {\it e-ph} couplings in which the polarons are small and have masses of order $\simeq 5 - 50$ times the bare band mass according to the value of the adiabaticity parameter. The 2D honeycomb net favors the mobility of small optical polarons in comparison with the square lattice.Comment: 6 pages, 3 figures, to appear in J.Phys.:Condensed Matter {PACS: 63.10.+a, 63.20.Dj, 71.38.+i

Fos Expression in Neurons of the Rat Vestibulo-Autonomic Pathway Activated by Sinusoidal Galvanic Vestibular Stimulation

The vestibular system sends projections to brainstem autonomic nuclei that modulate heart rate and blood pressure in response to changes in head and body position with regard to gravity. Consistent with this, binaural sinusoidally modulated galvanic vestibular stimulation (sGVS) in humans causes vasoconstriction in the legs, while low frequency (0.02–0.04 Hz) sGVS causes a rapid drop in heart rate and blood pressure in anesthetized rats. We have hypothesized that these responses occur through activation of vestibulo-sympathetic pathways. In the present study, c-Fos protein expression was examined in neurons of the vestibular nuclei and rostral ventrolateral medullary region (RVLM) that were activated by low frequency sGVS. We found c-Fos-labeled neurons in the spinal, medial, and superior vestibular nuclei (SpVN, MVN, and SVN, respectively) and the parasolitary nucleus. The highest density of c-Fos-positive vestibular nuclear neurons was observed in MVN, where immunolabeled cells were present throughout the rostro-caudal extent of the nucleus. c-Fos expression was concentrated in the parvocellular region and largely absent from magnocellular MVN. c-Fos-labeled cells were scattered throughout caudal SpVN, and the immunostained neurons in SVN were restricted to a discrete wedge-shaped area immediately lateral to the IVth ventricle. Immunofluorescence localization of c-Fos and glutamate revealed that approximately one third of the c-Fos-labeled vestibular neurons showed intense glutamate-like immunofluorescence, far in excess of the stain reflecting the metabolic pool of cytoplasmic glutamate. In the RVLM, which receives a direct projection from the vestibular nuclei and sends efferents to preganglionic sympathetic neurons in the spinal cord, we observed an approximately threefold increase in c-Fos labeling in the sGVS-activated rats. We conclude that localization of c-Fos protein following sGVS is a reliable marker for sGVS-activated neurons of the vestibulo-sympathetic pathway

Hall resistance in the hopping regime, a "Hall Insulator"?

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.Comment: Late

Polarons and Solitons in Jahn-Teller Systems

Using a semiclassical continuum model of an electron in a deformable molecular crystal, some properties of multicomponent generalizations of the polaron--``vector polarons''-- are elucidated. Analytical solutions for the case of two electronic bands coupled to two vibrational modes are given in detail. Within the model considered, the vector polaron can be classified by its wavefunction into several types and can have features that include: (1) a spatial variation in the electronic and vibrational character, and (2) low-energy internal degrees of freedom. For the case of electronic and vibrational degeneracy, local Jahn-Teller interactions can also lead to a novel spatiotemporal soliton, a long-lived excited state of the many-electron system stabilized by the conservation law resulting from degeneracy.Comment: 10 pages, 0 figures. International Symposium on Jahn-Teller Effects, ICTP, Trieste, Ital