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Background Given the young age of patients with CNS WHO grade 2 and 3 oligodendrogliomas and the relevant risk of neurocognitive, functional, and quality-of-life impairment with the current aggressive standard of care treatment, chemoradiation with PCV, of the tumour located in the brain optimizing care is the major challenge. Methods NOA-18 aims at improving qualified overall survival (qOS) for adult patients with CNS WHO grade 2 and 3 oligodendrogliomas by randomizing between standard chemoradiation with up to six six-weekly cycles with PCV and six six-weekly cycles with lomustine and temozolomide (CETEG) ( n  = 182 patients per group accrued over 4 years) thereby delaying radiotherapy and adding the chemoradiotherapy concept at progression after initial radiation-free chemotherapy, allowing for effective salvage treatment and delaying potentially deleterious side effects. QOS represents a new concept and is defined as OS without functional and/or cognitive and/or quality of life deterioration regardless of whether tumour progression or toxicity is the main cause. The primary objective is to show superiority of an initial CETEG treatment followed by partial brain radiotherapy (RT) plus PCV (RT-PCV) at progression over partial brain radiotherapy (RT) followed by procarbazine, lomustine, and vincristine (PCV) chemotherapy (RT-PCV) and best investigators choice (BIC) at progression for sustained qOS. An event concerning a sustained qOS is then defined as a functional and/or cognitive and/or quality of life deterioration after completion of primary therapy on two consecutive study visits with an interval of 3 months, tolerating a deviation of at most 1 month. Assessments are done with a 3-monthly MRI, assessment of the NANO scale, HRQoL, and KPS, and annual cognitive testing. Secondary objectives are evaluation and comparison of the two groups regarding secondary endpoints (short-term qOS, PFS, OS, complete and partial response rate). The trial is planned to be conducted at a minimum of 18 NOA study sites in Germany. Discussion qOS represents a new concept. The present NOA trial aims at showing the superiority of CETEG plus RT-PCV over RT-PCV plus BIC as determined at the level of OS without sustained functional deterioration for all patients with oligodendroglioma diagnosed according to the most recent WHO classification. Trial registration Clinicaltrials.gov NCT05331521 . EudraCT 2018–005027-16.

We present a new method for electronic structure calculations based on novel algorithms for nonlinear approximations. We maintain a functional form for the spatial orbitals as a linear combination of products of decaying exponentials and spherical harmonics centred at the nuclear cusps. Although such representations bare some resemblance to the classical Slater-type orbitals, the complex-valued exponents in the representations are dynamically optimized via recently developed algorithms, yielding highly accurate solutions with guaranteed error bounds. These new algorithms make dynamic optimization an effective way to combine the efficiency of Slater-type orbitals with the adaptivity of modern multi-resolution methods. We develop numerical calculus suitable for electronic structure calculations. For any spatial orbital in this functional form, we represent its product with the Coulomb potential, its convolution with the Poisson kernel, etc., in the same functional form with optimized parameters. Algorithms for this purpose scale linearly in the number of nuclei. We compute electronic structure by casting the relevant equations in an integral form and solving for the spatial orbitals via iteration. As an example, for several diatomic molecules we solve the Hartree-Fock equations with speeds competitive to those of multi-resolution methods and achieve high accuracy using a small number of parameters.

Post-traumatic osteoarthritis (PTOA) is a debilitating disease that is a result of a breakdown of knee joint tissues following traumatic impact. The interplay of how these tissues influence each other has received little attention because of complex interactions. This study was designed to correlate the degeneration of the menisci, cartilage and subchondral bone following an acute traumatic event that resulted in anterior cruciate ligament (ACL) and medial meniscus tears. We used a well-defined impact injury animal model that ruptures the ACL and tears the menisci. Subsequently, the knee joints underwent ACL reconstruction and morphological analyses were performed on the menisci, cartilage and subchondral bone at 1-, 3- and 6-months following injury. The results showed that the morphological scores of the medial and lateral menisci worsened with time, as did the tibial plateau and femoral condyle articular cartilage scores. The medial meniscus was significantly correlated to the medial tibial subchondral bone at 1 month ( p = 0.01), and to the medial tibial cartilage at 3 months ( p = 0.04). There was only one significant correlation in the lateral hemijoint, i.e., the lateral tibial cartilage to the lateral tibial subchondral bone at 6 months ( p = 0.05). These data may suggest that, following trauma, the observed medial meniscal damage should be treated acutely by means other than a full or partial meniscectomy, since that procedure may have been the primary cause of degenerative changes in the underlying cartilage and subchondral bone. In addition to potentially treating meniscal damage differently, improvements could be made in optimizing treatment of acute knee trauma.

The need to compute small con-eigenvalues and the associated con-eigenvectors of positive-definite Cauchy matrices naturally arises when constructing rational approximations with a (near) optimally small $L^{\\infty}$ error. Specifically, given a rational function with $n$ poles in the unit disk, a rational approximation with $m\\ll n$ poles in the unit disk may be obtained from the $m$th con-eigenvector of an $n\\times n$ Cauchy matrix, where the associated con-eigenvalue $\\lambda_{m}>0$ gives the approximation error in the $L^{\\infty}$ norm. Unfortunately, standard algorithms do not accurately compute small con-eigenvalues (and the associated con-eigenvectors) and, in particular, yield few or no correct digits for con-eigenvalues smaller than the machine roundoff. We develop a fast and accurate algorithm for computing con-eigenvalues and con-eigenvectors of positive-definite Cauchy matrices, yielding even the tiniest con-eigenvalues with high relative accuracy. The algorithm computes the $m$th con-eigenvalue in $\\mathcal{O}\\left(m^{2}n\\right)$ operations and, since the con-eigenvalues of positive-definite Cauchy matrices decay exponentially fast, we obtain (near) optimal rational approximations in $\\mathcal{O}(n\\left(\\log\\delta^{-1}\\right)^{2})$ operations, where $\\delta$ is the approximation error in the $L^{\\infty}$ norm. We provide error bounds demonstrating high relative accuracy of the computed con-eigenvalues and the high accuracy of the unit con-eigenvectors. We also provide examples of using the algorithm to compute (near) optimal rational approximations of functions with singularities and sharp transitions, where approximation errors close to machine roundoff are obtained. Finally, we present numerical tests on random (complex-valued) Cauchy matrices to show that the algorithm computes all the con-eigenvalues and con-eigenvectors with nearly full precision. [PUBLICATION ABSTRACT]

A non-local formulation, depending on a free spectral parameter, is presented governing two ideal fluids separated by a free interface and bounded above either by a free surface or by a rigid lid. This formulation is shown to be related to the Dirichlet–Neumann operators associated with the two-fluid equations. As an application, long wave equations are obtained; these include generalizations of the Benney–Luke and intermediate long wave equations, as well as their higher order perturbations. Computational studies reveal that both equations possess lump-type solutions, which indicate the possible existence of fully localized solitary waves in interfacial fluids with sufficient surface tension.

Fluid flow has been shown to be a potent physical stimulus in the regulation of bone cell metabolism. In addition to membrane shear stress, loading-induced fluid flow will enhance chemotransport due to convection or mass transport thereby affecting the biochemical environment surrounding the cell. This study investigated the role of oscillating fluid flow induced shear stress and chemotransport in cellular mechanotransduction mechanisms in bone. Intracellular calcium mobilization and prostaglandin E 2 (PGE 2) production were studied with varying levels of shear stress and chemotransport. In this study MC3T3-E1 cells responded to oscillating fluid flow with both an increase in intracellular calcium concentration ([Ca 2+] i) and an increase in PGE 2 production. These fluid flow induced responses were modulated by chemotransport. The percentage of cells responding with an [Ca 2+] i oscillation increased with increasing flow rate, as did the production of PGE 2. In addition, depriving the cells of nutrients during fluid flow resulted in an inhibition of both [Ca 2+] i mobilization and PGE 2 production. These data suggest that depriving the cells of a yet to be determined biochemical factor in media affects the responsiveness of bone cells even at a constant peak shear stress. Chemotransport alone will not elicit a response, but it appears that sufficient nutrient supply or waste removal is needed for the response to oscillating fluid flow induced shear stress.

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech2 solution of the Korteweg-de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev-Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes' extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney-Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

Motivated by our interest in examining meniscal mechanotransduction processes, we report on the validation of a new tissue engineering bioreactor. This paper describes the design and performance capabilities of a tissue engineering bioreactor for cyclic compression of meniscal explants. We showed that the system maintains a tissue culture environment equivalent to that provided by conventional incubators and that its strain output was uniform and reproducible. The system incorporates a linear actuator and load cell aligned together in a frame that is contained within an incubator and allows for large loads and small displacements. A plunger with six Teflon-filled Delrin compression rods is attached to the actuator compressing up to six tissue explants simultaneously and with even pressure. The bioreactor system was used to study proteoglycan (PG) breakdown in porcine meniscal explants following various input loading tests (0-20% strain, 0-0.1 MPa). The greatest PG breakdown was measured following 20% compressive strain. These strain and stress levels have been shown to correspond to partial meniscectomy. Thus, these data suggest that removing 30-60% of meniscal tissue will result in the breakdown of meniscal tissue proteoglycans.

It has been suggested that the success of a meniscal replacement is dependent on several factors, one of which is the secure fixation and firm attachment of the replacement to the tibial plateau [Chen, M.I., Branch, T.P., et al., 1996. Is it important to secure the horns during lateral meniscal transplantation? A cadaveric study. Arthroscopy 12(2), 174–181; Alhalki, M.M., et al., 1999. How three methods for fixing a medial meniscal autograft affect tibial contact mechanics. American Journal of Sports Medicine 27(3), 320–328; Haut Donahue, T.L., et al., 2003. How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint. Journal of Biomechanics 36(1), 19–34]. The complex loading environment in the knee lends itself to different loading environments for each meniscal attachment. We hypothesize that the creep and stress relaxation characteristics of the horn attachments will be different for the anterior versus posterior, and medial versus lateral attachments. To test this hypothesis, the stress relaxation and creep characteristics of the meniscal horn attachments were determined. The stress relaxation properties of load/stress at the end of the test, and the load/stress relaxation rate demonstrated no significant statistical differences between the attachments. Unlike the stress relaxation properties, the creep properties demonstrated some significant differences amongst the attachments. The normalized displacement at the end of the test, normalized creep rate and strain creep rate for the lateral anterior attachment were significantly different than those of the medial posterior attachment ( p < 0.0 5 ). The two anterior attachments had significantly different strains at the end of the test, as well as significantly different creep strain rates ( p < 0.0 5 ). The two attachments of the medial meniscus revealed no significant differences between any of the creep properties measured ( p > 0.0 5 ). The time dependent properties obtained in this experiment provide insight into the behavior of meniscal horn attachments under various loading situations. The results indicate that a suitable meniscal replacement may require different properties for the lateral and medial horns.

To evaluate and improve on the procedures used by a tissue bank in selecting donor menisci for transplantation, this study was designed to fulfill four objectives: (a) define and quantify a set of independent parameters for describing the geometry of the medial and lateral menisci, (b) determine how well the sizing protocol of the tissue bank (i.e., two transverse roentgenographic measurements obtained from the injured knee or six transverse magnetic resonance imaging measurements obtained from the contralateral knee) predicts the four standard transverse parameters of the menisci, (c) determine if including one additional transverse roentgenographic measurement for each compartment improves the ability of roentgenograms to predict transverse meniscal parameters, and (d) determine if five magnetic resonance imaging measurements at three different meniscal cross sections of the contralateral knee predict the 15 standard cross‐sectional parameters of the meniscus in the injured knee. A laser‐based, noncontacting three‐dimensional coordinate digitizing system was used to determine surface coordinates from which menisci were reconstructed in a computer. For each reconstructed meniscus, four parameters in the transverse plane and five cross‐sectional parameters in each of three regions (i.e., anterior, middle, and posterior) were defined, yielding a set of 19 standard parameters to describe the geometry. Through a correlation analysis, these standard parameters were shown to be largely unrelated to one another, thus confirming that the parameters form an independent set describing the three‐dimensional geometry of the menisci. The two roentgenographic measurements were poor predictors of transverse standard meniscal parameters, predicting only one of four standard parameters for the medial meniscus and none of four standard parameters for the lateral meniscus with coefficients of determination greater than on equal to 0.5. Including one additional roentgenographic measurement to the tissue bank protocol increased the number of standard transverse parameters predicted to three of four for the medial meniscus and two of four for the lateral meniscus. Magnetic resonance imaging was better than roentgenography for predicting the three‐dimensional meniscal geometry. The transverse measurements from magnetic resonance imaging predicted three of four standard transverse parameters for the medial meniscus and all four for the lateral meniscus. With the addition of the cross‐sectional measurements by magnetic resonance imaging, seven of 15 standard cross‐sectional parameters were predicted for both the medial and lateral menisci. Assuming that a successful clinical outcome depends on how well an allograft matches the size and shape of the original meniscus, magnetic resonance imaging rather than roentgenography should be used for allograft size‐matching by tissue banks.