Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Dosimetric impact of geometric errors due to respiratory motion prediction on dynamic multileaf collimator-based four-dimensional radiation delivery

The synchronization of dynamic multileaf collimator (DMLC) response with respiratory motion is critical to ensure the accuracy of DMLC-based four dimensional (4D) radiation delivery. In practice, however, a finite time delay (response time) between the acquisition of tumor position and multileaf collimator response necessitates predictive models of respiratory tumor motion to synchronize radiation delivery. Predicting a complex process such as respiratory motion introduces geometric errors, which have been reported in several publications. However, the dosimetric effect of such errors on 4D radiation delivery has not yet been investigated. Thus, our aim in this work was to quantify the dosimetric effects of geometric error due to prediction under several different conditions. Conformal and intensity modulated radiation therapy (IMRT) plans for a lung patient were generated for anterior-posterior/posterior-anterior (AP/PA) beam arrangements at 6 and 18 MV energies to provide planned dose distributions. Respiratory motion data was obtained from 60 diaphragm-motion fluoroscopy recordings from five patients. A linear adaptive filter was employed to predict the tumor position. The geometric error of prediction was defined as the absolute difference between predicted and actual positions at each diaphragm position. Distributions of geometric error of prediction were obtained for all of the respiratory motion data. Planned dose distributions were then convolved with distributions for the geometric error of prediction to obtain convolved dose distributions. The dosimetric effect of such geometric errors was determined as a function of several variables: response time (0-0.6 s), beam energy (6/18 MV), treatment delivery (3D/4D), treatment type (conformal/IMRT), beam direction (AP/PA), and breathing training type (free breathing/audio instruction/visual feedback). Dose difference and distance-to-agreement analysis was employed to quantify results. Based on our data, the dosimetric impact of prediction (a) increased with response time, (b) was larger for 3D radiation therapy as compared with 4D radiation therapy, (c) was relatively insensitive to change in beam energy and beam direction, (d) was greater for IMRT distributions as compared with conformal distributions, (e) was smaller than the dosimetric impact of latency, and (f) was greatest for respiration motion with audio instructions, followed by visual feedback and free breathing. Geometric errors of prediction that occur during 4D radiation delivery introduce dosimetric errors that are dependent on several factors, such as response time, treatment-delivery type, and beam energy. Even for relatively small response times of 0.6 s into the future, dosimetric errors due to prediction could approach delivery errors when respiratory motion is not accounted for at all. To reduce the dosimetric impact, better predictive models and/or shorter response times are required.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

The long-term stability of self-esteem: Its time-dependent decay and nonzero asymptote

How stable are individual differences in self-esteem? We examined the time-dependent decay of rank-order stability of self-esteem and tested whether stability asymptotically approaches zero or a nonzero value across long test–retest intervals. Analyses were based on 6 assessments across a 29-year period of a sample of 3,180 individuals aged 14 to 102 years. The results indicated that, as test–retest intervals increased, stability exponentially decayed and asymptotically approached a nonzero value (estimated as .43). The exponential decay function explained a large proportion of variance in observed stability coefficients, provided a better fit than alternative functions, and held across gender and for all age groups from adolescence to old age. Moreover, structural equation modeling of the individual-level data suggested that a perfectly stable trait component underlies stability of self-esteem. The findings suggest that the stability of self-esteem is relatively large, even across very long periods, and that self-esteem is a trait-like characteristic.

Experimental Validation of Finite Element Analysis of Human Vertebral Collapse Under Large Compressive Strains

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towardsthe prediction of extended vertebral collapse may help in assessing fracture stability in future work.

Comparison of theoretical fixation stability of three devices employed in medial opening wedge high tibial osteotomy: a finite element analysis.

BACKGROUND Medial open wedge high tibial osteotomy is a well-established procedure for the treatment of unicompartmental osteoarthritis and symptomatic varus malalignment. We hypothesized that different fixation devices generate different fixation stability profiles for the various wedge sizes in a finite element (FE) analysis. METHODS Four types of fixation were compared: 1) first and 2) second generation Puddu plates, and 3) TomoFix plate with and 4) without bone graft. Cortical and cancellous bone was modelled and five different opening wedge sizes were studied for each model. Outcome measures included: 1) stresses in bone, 2) relative displacement of the proximal and distal tibial fragments, 3) stresses in the plates, 4) stresses on the upper and lower screw surfaces in the screw channels. RESULTS The highest load for all fixation types occurred in the plate axis. For the vast majority of the wedge sizes and fixation types the shear stress (von Mises stress) was dominating in the bone independent of fixation type. The relative displacements of the tibial fragments were low (in μm range). With an increasing wedge size this displacement tended to increase for both Puddu plates and the TomoFix plate with bone graft. For the TomoFix plate without bone graft a rather opposite trend was observed.For all fixation types the occurring stresses at the screw-bone contact areas pulled at the screws and exceeded the allowable threshold of 1.2 MPa for at least one screw surface. Of the six screw surfaces that were studied, the TomoFix plate with bone graft showed a stress excess of one out of twelve and without bone graft, five out of twelve. With the Puddu plates, an excess stress occurred in the majority of screw surfaces. CONCLUSIONS The different fixation devices generate different fixation stability profiles for different opening wedge sizes. Based on the computational simulations, none of the studied osteosynthesis fixation types warranted an intransigent full weight bearing per se. The highest fixation stability was observed for the TomoFix plates and the lowest for the first generation Puddu plate. These findings were revealed in theoretical models and need to be validated in controlled clinical settings.

Biomechanical validation of computer assisted planning of periacetabular osteotomy: A preliminary study based on finite element analysis

Periacetabular Osteotomy (PAO) is a joint preserving surgical intervention intended to increase femoral head coverage and thereby to improve stability in young patients with hip dysplasia. Previously, we developed a CT-based, computer-assisted program for PAO diagnosis and planning, which allows for quantifying the 3D acetabular morphology with parameters such as acetabular version, inclination, lateral center edge (LCE) angle and femoral head coverage ratio (CO). In order to verify the hypothesis that our morphology-based planning strategy can improve biomechanical characteristics of dysplastic hips, we developed a 3D finite element model based on patient-specific geometry to predict cartilage contact stress change before and after morphology-based planning. Our experimental results demonstrated that the morphology-based planning strategy could reduce cartilage contact pressures and at the same time increase contact areas. In conclusion, our computer-assisted system is an efficient tool for PAO planning.

Prediction of dental implant torque with a fast and automatic finite element analysis: a pilot study

Despite its importance, implant removal torque can be assessed at present only after implantation. This paper presents a new technique to help clinicians preoperatively evaluate implant stability.

On the terminal homologation of physiologically active peptides as a means of increasing stability in human serum--neurotensin, opiorphin, B27-KK10 epitope, NPY

The terminal homologation by CH(2) insertion into the peptides mentioned in the title is described. This involves replacement of the N-terminal amino acid residue by a β(2) - and of the C-terminal amino acid residue by a β(3) -homo-amino acid moiety (β(2) hXaa and β(3) hXaa, resp.; Fig. 1). In this way, the structure of the peptide chain from the N-terminal to the C-terminal stereogenic center is identical, and the modified peptide is protected against cleavage by exopeptidases (Figs. 2 and 3). Neurotensin (NT; 1) and its C-terminal fragment NT(8-13) are ligands of the G-protein-coupled receptors (GPCR) NT1, NT2, NT3, and NT analogs are promising tools to be used in cancer diagnostics and therapy. The affinities of homologated NT analogs, 2b-2e, for NT1 and NT2 receptors were determined by using cell homogenates and tumor tissues (Table 1); in the latter experiments, the affinities for the NT1 receptor are more or less the same as those of NT (0.5-1.3 vs. 0.6 nM). At the same time, one of the homologated NT analogs, 2c, survives in human plasma for 7 days at 37° (Fig. 6). An NMR analysis of NT(8-13) (Tables 2 and 4, and Fig. 8) reveals that this N-terminal NT fragment folds to a turn in CD(3) OH. - In the case of the human analgesic opiorphin (3a), a pentapeptide, and of the HIV-derived B27-KK10 (4a), a decapeptide, terminal homologation (→3b and 4b, resp.) led to a 7- and 70-fold half-life increase in plasma (Fig. 9). With N-terminally homologated NPY, 5c, we were not able to determine serum stability; the peptide consisting of 36 amino acid residues is subject to cleavage by endopetidases. Three of the homologated compounds, 2b, 2c, and 5c, were shown to be agonists (Fig. 7 and 11). A comparison of terminal homologation with other stability-increasing terminal modifications of peptides is performed (Fig. 5), and possible applications of the neurotensin analogs, described herein, are discussed.

Comparison of implant stability by means of resonance frequency analysis for flapless and conventionally inserted implants

Background: Resonance frequency analysis (RFA) is a noninvasive technique for the quantitative assessment of implant stability. Information on the implant stability quotient (ISQ) of transmucosally inserted implants is limited. Purpose: The aim of this investigation was to compare the ISQ of conventionally inserted implants by raising a muco-periostal flap with implants inserted using a flapless procedure. Materials and Methods: Forty elderly patients with complete edentulous maxilla were consecutively admitted for treatment with implant-supported prostheses. A computer tomography was obtained for the computer-assisted implant planning. One hundred ten implants were placed conventionally in 23 patients (flap-group) and 85 implants in 17 patients by means of the flapless method (flapless-group) using a stereolithographic template. RFA measurements were performed after implant placement (baseline) and after a healing time of 12 weeks (reentry). Results: All implants exhibited clinically and radiographically successful osseointegration. Bone level did not change significantly neither for genders nor type of surgical protocol. Mean ISQ values of the flapless-group were significantly higher at baseline (p < .001) and at reentry (p < .001) compared with the flap-group. The ISQ values were significantly lower at reentry compared with baseline for the flap-group (p = .028) but not for the flapless-group. This group showed a moderate, but insignificant increase. RFA measurements of males resulted in ISQ values that were thoroughly higher as compared with females at both time-points in both groups. Correlation between RFA and bone level was not found. Conclusions: The flapless procedure showed favorable conditions with regard to implant stability and crestal bone level. Some changes of the ISQ values that represent primary (mechanical) and secondary (bone remodeling) implant stability were observed in slight favor of the flapless method and male patients. In properly planned and well-selected cases, the minimal invasive transmucosal technique using a drill-guide is a safe procedure.

Phosphatase and tensin homolog regulates stability and activity of EphB1 receptor

Deregulation of receptor tyrosine kinases (RTKs) is linked to a broad range of cancers, stressing the necessity of studying their regulatory pathways. We and others demonstrated previously that c-Cbl is necessary for the lysosomal degradation of erythropoietin-producing hepatocellular B1 (EphB1) carcinoma and epidermal growth factor receptor (EGFR) RTKs. Moreover, the tumor suppressor phosphatase and tensin homolog (PTEN) was shown to modulate c-Cbl-dependent EGFR degradation. We therefore investigated the involvement of PTEN in EphB1 signaling and degradation. We used PTEN mutants, PTEN, and NHERF1 small interfering RNA in CHO-EphB1 and SW480 cells endogenously expressing EphB1 to delineate EphB1-PTEN interactions. PTEN was constitutively associated with c-Cbl, protecting it from degradation. EphB1 stimulation triggered ∼50% serine-threonine PTEN dephosphorylation and PTEN-Cbl complex disruption, a process requiring PTEN protein phosphatase activity. Both proteins independently translocated to EphB1, with PTEN in association with the scaffold protein NHERF1. Biologically, PTEN lipid phosphatase activity impairs EphB1-dependent cell adhesion and chemotaxis. This study demonstrates for the first time in mammalian cells that the Eph receptor and PTEN associate and influence their signaling. Moreover, it contributes to the emerging concept that PTEN regulates expression of RTKs through modulation of their degradation. Finally, it reveals a new role for PTEN protein phosphatase activity involved in this process.

The long-term mechanical integrity of non-reinforced PEEK-OPTIMA polymer for demanding spinal applications: experimental and finite-element analysis

Polyetheretherketone (PEEK) is a novel polymer with potential advantages for its use in demanding orthopaedic applications (e.g. intervertebral cages). However, the influence of a physiological environment on the mechanical stability of PEEK has not been reported. Furthermore, the suitability of the polymer for use in highly stressed spinal implants such as intervertebral cages has not been investigated. Therefore, a combined experimental and analytical study was performed to address these open questions. A quasi-static mechanical compression test was performed to compare the initial mechanical properties of PEEK-OPTIMA polymer in a dry, room-temperature and in an aqueous, 37 degrees C environment (n=10 per group). The creep behaviour of cylindrical PEEK polymer specimens (n=6) was measured in a simulated physiological environment at an applied stress level of 10 MPa for a loading duration of 2000 hours (12 weeks). To compare the biomechanical performance of different intervertebral cage types made from PEEK and titanium under complex loading conditions, a three-dimensional finite element model of a functional spinal unit was created. The elastic modulus of PEEK polymer specimens in a physiological environment was 1.8% lower than that of specimens tested at dry, room temperature conditions (P<0.001). The results from the creep test showed an average creep strain of less than 0.1% after 2000 hours of loading. The finite element analysis demonstrated high strain and stress concentrations at the bone/implant interface, emphasizing the importance of cage geometry for load distribution. The stress and strain maxima in the implants were well below the material strength limits of PEEK. In summary, the experimental results verified the mechanical stability of the PEEK-OPTIMA polymer in a simulated physiological environment, and over extended loading periods. Finite element analysis supported the use of PEEK-OPTIMA for load-bearing intervertebral implants.

Statistical finite element model for bone shape and biomechanical properties

We present a framework for statistical finite element analysis combining shape and material properties, and allowing performing statistical statements of biomechanical performance across a given population. In this paper, we focus on the design of orthopaedic implants that fit a maximum percentage of the target population, both in terms of geometry and biomechanical stability. CT scans of the bone under consideration are registered non-rigidly to obtain correspondences in position and intensity between them. A statistical model of shape and intensity (bone density) is computed by means of principal component analysis. Afterwards, finite element analysis (FEA) is performed to analyse the biomechanical performance of the bones. Realistic forces are applied on the bones and the resulting displacement and bone stress distribution are calculated. The mechanical behaviour of different PCA bone instances is compared.

Significance of primary stability for osseointegration of dental implants

AIM: To investigate the significance of the initial stability of dental implants for the establishment of osseointegration in an experimental capsule model for bone augmentation. MATERIAL AND METHODS: Sixteen male rats were used in the study. In each rat, muscle-periosteal flaps were elevated on the lateral aspect of the mandibular ramus on both sides, resulting in exposure of the bone surface. Small perforations were then produced in the ramus. A rigid, hemispherical Teflon capsule with a diameter of 6 mm and a height of 4 mm and with a hole in its middle portion, prepared to fit the circumference of an ITI HC titanium implant of 2.8 mm in diameter, was fixed to the ramus using 4 mini-screws. On one side of the jaw, the implant was placed through the hole in such a way that its apex did not make contact with the mandibular ramus (test). This placement of the implant did not ensure primary stability. On the other side of the jaw, a similar implant was placed through the hole of the capsule in such a way that contact was made between the implant and the surface of the ramus (control). This provided primary stability of the implant. After placement of the implants, the soft tissues were repositioned over the capsules and sutured. After 1, 3, 6 and 9 months, four animals were sacrificed and subjected to histometric analysis. RESULTS: The mean height of direct bone-to-implant contact of implants with primary stability was 38.8%, 52.9%, 64.6% and 81.3% of the implant length at 1, 3, 6 and 9 months, respectively. Of the bone adjacent to the implant surface, 28.1%, 28.9%, 52.6% and 69.6%, respectively, consisted of mineralized bone. At the test implants, no bone-to-implant contact was observed at any observation time or in any of these non-stabilized specimens. CONCLUSION: The findings of the present study indicate that primary implant stability is a prerequisite for successful osseointegration, and that implant instability results in fibrous encapsulation, thus confirming previously made clinical observations.