Exact Curve Research Articles

A Prospective Study of Hepatic Vein Waveform, Damping Index, and Splenoportal Index in Liver Cirrhosis: Correlation with Child-Pugh Score

Background:Chronic liver disease evaluation is commonly conducted using the Child-Pugh and Model for End-Stage Liver Disease (MELD) scoring systems. While the hepatic venous pressure gradient (HVPG) is the gold standard for measuring portal hypertension in cirrhotic patients, non-invasive alternatives such as Doppler ultrasonography offer a cost-effective, rapid, and less invasive option for assessment. Objective: This study aimed to investigate the correlation between hepatic vein waveform patterns, damping index, splenoportal index, and the Child-Pugh score in patients with liver cirrhosis to evaluate the efficacy of Doppler ultrasound as a non-invasive diagnostic tool. Methods: A prospective cross-sectional study was conducted at the Radiology Department of a public teaching hospital in Rawalpindi, Pakistan, from December 2023 to June 2024. A total of 52 patients with liver cirrhosis were included after excluding those with incomplete data or confounding conditions. Doppler ultrasound was used to assess hepatic vein waveform patterns, damping index, and splenoportal index. The Child-Pugh score was calculated based on clinical and laboratory parameters. Statistical analysis was performed using SPSS version 25, with a p-value of <0.05 considered significant. The chi-square test, Fisher’s exact test, ANOVA, and ROC curve analyses were utilized for data evaluation. Results: The final cohort consisted of 52 patients, with 39 males (75%) and 13 females (25%). The mean age was 55.3 years. The damping index showed a significant increase from Child-Pugh Class A (0.45 ± 0.10) to Class C (0.75 ± 0.15) (p=0.003). The splenoportal index also demonstrated a significant rise from Class A (1.4 ± 0.3) to Class C (2.0 ± 0.5) (p=0.015). The sensitivity and specificity of the damping index (> 0.6) in predicting higher Child-Pugh scores (B + C) were 52.6% and 85.7%, respectively, with a positive predictive value of 90.9%. Conclusion: The study found strong correlations between the severity of liver cirrhosis, as assessed by the Child-Pugh score, and Doppler ultrasound parameters such as hepatic vein waveforms and the damping index. Doppler ultrasound, therefore, presents itself as a precise, non-invasive alternative for evaluating the severity of liver disease, potentially replacing more invasive procedures.

Arctic curves of the T-system with slanted initial data

We study the T-system of type A∞ , also known as the octahedron recurrence/equation, viewed as a 2+1 -dimensional discrete evolution equation. Generalizing earlier work on arctic curves for the Aztec Diamond obtained from solutions of the octahedron recurrence with ‘flat’ initial data, we consider initial data along parallel ‘slanted’ planes perpendicular to an arbitrary admissible direction (r,s,t)∈Z+3 . The corresponding solutions of the T-system are interpreted as partition functions of dimer models on some suitable ‘pinecone’ graphs introduced by Bousquet–Mélou, Propp, and West in 2009. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system. This direct approach bypasses the standard general theory of dimers using the Kasteleyn matrix approach and uses instead the theory of Analytic Combinatorics in Several Variables, by focusing on a linear system obeyed by the dimer density generating function.

The hip fracture assessment tool: A scoring system to assess high risk geriatric hip fracture patients for post-operative critical care monitoring

IntroductionIntensive care unit risk stratification models have been utilized in elective joint arthroplasty; however, hip fracture patients are fundamentally different in their clinical course. Having a critical care risk calculator utilizing pre-operative risk factors can improve resourcing for hip fracture patients in the peri‑operative period. MethodsA cohort of geriatric hip fracture patients at a single institution were reviewed over a three-year period. Non-operative patients, peri‑implant fractures, additional procedures performed under the same anesthesia period, and patients admitted to the intensive care unit (ICU) prior to surgery were excluded. Pre-operative laboratory values, Revised Cardiac Risk Index (RCRI), and American Society of Anesthesiologists (ASA) scores were calculated. Pre-operative ambulatory status was determined. The primary outcome measure was ICU admission in the post-operative period. Outcomes were assessed with Fisher's exact test, Kruskal-Wallis test, logistic regression, and ROC curve. Results315 patient charts were analyzed with 262 patients meeting inclusion criteria. Age ≥ 80 years, ASA ≥ 4, pre-operative hemoglobin < 10 g/dL, and a history of CVA/TIA were found to be significant factors and utilized within a “training” data set to create a 4-point scoring system after reverse stepwise elimination. The 4-point scoring system was then assessed within a separate “validation” data set to yield an ROC area under the curve (AUC) of 0.747. Score ≥ 3 was associated with 96.8 % specificity and 14.2 % sensitivity for predicting post-op ICU admission. Score ≥ 3 was associated with a 50 % positive predictive value and 83 % negative predictive value. ConclusionA hip fracture risk stratification scoring system utilizing pre-operative patient specific values to stratify geriatric hip patients to the ICU post-operatively can improve the pre-operative decision-making of surgical and critical care teams. This has important implications for triaging vital hospital resources. Level of evidenceIII (retrospective study)

Enhancing precision in proton therapy: Utilizing machine learning for predicting Bragg curve peak location in cancer treatment

In proton beam therapy, the Bragg peak is the point where protons lose energy the fastest. This point is crucial for dose control, preserving healthy tissues, minimizing lateral scattering, and the success of treatment planning. However, accurately predicting the location of the Bragg peak is challenging due to the complex interactions of protons with tissues. This study proposes a machine learning (ML) approach to predict the exact location of the Bragg peak from phantom tissue proton beam therapy experiments. A dataset comprising the eight most commonly used biomaterials, which mimic human tissue in proton therapy procedures, has been curated for this study. Various ML models are benchmarked to find the most successful approach. ML model parameters are further optimized using a metaheuristic approach to achieve the highest prediction capability. In addition, feature contributions of each feature in the dataset are analyzed using an explainable artificial intelligence (XAI) technique. According to experimental results, Random Forest (RF) model that is optimized with Genetic Algorithm (GA) achieved 0.742 Correlation Coefficient (CC) value, 0.069 Mean Absolute Error (MAE) and 0.145 Root Mean Square Error (RMSE) outperforming other ML models. The proposed approach can track and predict the movement of the proton beam in real-time during treatment, enhancing treatment safety and contributing to the more effective management of the treatment process. This study is the first to predict exact Bragg curve peak locations from proton beam therapy experiments using ML approaches. The optimized ML model can provide higher precision in identifying the needed beam dosage for targeted tumor and improving treatment outcomes.

On the steady-state interfacial waves with two-dimensional type-A double exact resonance

Steady-state interfacial waves under two-dimensional (2D) type-A exact triad resonance and other related resonances are researched in a two-layer liquid model with a free surface in contact with air. Five groups (groups 1–5) of convergent series solutions are achieved via the homotopy analysis method. It is found that the phenomenon of double exact resonance could exist in periodic interfacial waves if physical parameters correspond to the intersection of two exact resonance curves. The double exact resonance considered here contains a 2D type-A triad resonance and an other resonance. Under the 2D type-A exact triad resonance, the other resonant triad could obviously enlarge or reduce the wave amplitudes and energy proportions of primary and resonant components. Nevertheless, other resonant quartet, quintet, sextet, and septet all produce no influence on interfacial waves when the 2D type-A exact triad resonance occurs. The above-mentioned results indicate that in the neighborhood of the double exact triad resonance, small perturbations of wave vector of a primary component can cause huge changes on wave profiles of free surface and interface, wave amplitude spectrum, and energy distribution of internal waves in real ocean. In addition, the closer the interfacial waves are to the double exact triad resonance, the more possible energy combinations exist in the wave system, and the greater the number of steady-state interfacial wave solutions. All of this should deepen our understanding of nonlinear resonance interactions in short-crested internal waves.

Steady-state interfacial gravity waves with one-dimensional class-IV triad resonance

Steady-state interfacial waves under a one-dimensional (1-D) class-IV exact triad resonance are investigated in a two-layer fluid with a free surface upper boundary. Four groups (G1–G4) of convergent series solutions are obtained by the homotopy analysis method. Though the harmonic resonance conditions are contained in the class-IV resonance criteria, the influences of 1:2 harmonic resonances on the energy spectrum could be neglected. Unlike former steady-state resonant interfacial wave spectrum where all the components joining the resonance are significant, the energy of one primary component can be ignored for two groups (G2 and G4) of wave solutions obtained in this paper. It is found that a little energy induced from the external environment might greatly change the energy spectrum for G1. However, the energy introduced from the outside cannot vary the wave energy distribution for G2. The reason for the extremely high crests on the instantaneous profiles of free surfaces of G2 and G4 is that the peaks of the class-IV exactly resonant and some trivial components momentarily overlap at some special horizontal positions. The class-IV exact triad resonance curve could be divided into four pieces containing the existence ranges of G3 and G4 and two regions with no solution found. One of the regions without convergent solutions results from an infinite number of singularities or small divisors caused by infinite exact or near resonances. Our results indicate that steady-state interfacial waves with class-IV triad resonance interactions among one surface and two internal wave modes could exist.

Composition Dependent Instabilities in Mixtures with Many Components.

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study phase ordering instabilities in a paradigmatic model that represents the complexity of-e.g., biological-mixtures via random second virial coefficients. Using tools from free probability theory we obtain the exact spinodal curve and the nature of instabilities for a mixture with an arbitrary composition, thus lifting an important restriction in previous work. We show that, by controlling the concentration of only a few components, one can systematically change the nature of the spinodal instability and achieve demixing for realistic scenarios by a strong composition imbalance amplification. This results from a nontrivial interplay of interaction complexity and entropic effects due to the nonuniform composition. Our approach can be extended to include additional systematic interactions, leading to a competition between different forms of demixing as density is varied.

An exploration of circumbinary systems using gravitational microlensing

Gravitational microlensing is one of the methods to detect exoplanets–planets outside our solar system. Here, we focus on the theoretical modeling of systems with three lensing objects and in particular circumbinary systems. Circumbinary systems include two stars and at least one planet and are estimated to represent a sizeable portion of all exoplanets. Extending a method developed for binary lenses to the three lens case, we explore the parameter space of circumbinary systems, producing exact magnification maps and light curves.

Improved identification of stiffness coefficients of non intrusive nonlinear geometric reduced order models of structures

Significant, successful efforts have been devoted in recent years to the non intrusive construction from finite element software of reduced order models of the nonlinear geometric response of structures. A key assumption in these models is that the elastic restoring forces can be represented as cubic polynomials of their generalized coordinates. However, there has been only very limited discussion of whether this representation is appropriate, how deviations from this polynomial form affect the identification of its coefficients and ultimately the prediction of the structural response, and how current identification strategies can be improved.These questions are the focus of the present investigation which considers first a simple structural model that exhibits the potential for snap-through and thus represents an interesting validation case with strongly nonlinear geometric behavior. It is shown that the force–displacement relationship which can be derived in closed form is not exactly a cubic polynomial but can be very closely modeled by one. However, the match between exact curve and polynomial fit is very sensitive to small changes in the linear, quadratic, and cubic stiffness coefficients and thus the prediction of the response may range from excellent to significantly in error depending on how the identification of the coefficients is performed. In particular, it is found that a cubic approximation obtained by Taylor series around the undeformed configuration is not very accurate post snap-through.Based on these findings, two strategies are proposed to improve the identification of the stiffness coefficients of these reduced order models. The first one is a tuning procedure in which a limited number of key coefficients of the model are adjusted to fit additional static response data. The second approach performs the identification of the stiffness coefficients at a series of different levels, as opposed to one as currently performed, and seeks the most appropriate value of each coefficient based on a “small change” criterion.The applicability of these two novel strategies is demonstrated on several challenging structural models: a clamped–clamped curved beam undergoing snap-through as well as a curved panel and a hat stiffened one. It is found that the reduced order models identified via the tuning or multi-level strategies not only lead to more accurate predictions of the structural response as compared to the original finite element model but also are more computationally stable than their counterparts identified with the current single-level strategy.

Potential energy curves, partition functions and line intensities of HF and HCl molecules under the improved Hulburt‐Hirschfelder quantum mechanical anharmonic oscillator model

AbstractAn improved Hulburt‐Hirschfelder (IHH) quantum mechanical anharmonic oscillator model which describes the exact analytical potential energy curves (PECs) of diatomic molecules is presented. The IHH analytical potential function that involves a variable parameter, four empirically determined low‐order molecular vibrational and rotational spectral constants and the dissociation energy was applied to the ground electronic states of HF and HCl, yielding a good agreement between the Rydberg‐Klein‐Rees (RKR) potential energy points and the calculations. Correspondingly, with the determined IHH PECs, the partition functions at temperatures 300–6000 Kelvin (K) and rovibrational line intensities are evaluated, and coincide well with those quoted in the HITRAN2020 database compilation. The methodology could be valuable for the detection of molecules in interstellar clouds using infrared spectroscopy, as well as thermochemical reactions.

New interaction formula for plastic resistance of channel sections under combinations of bending moments My,Ed, Mz,Ed and bimoment BEd

The interaction formulae for the plastic resistance of channel sections under combination of 4 internal forces: the bending moment about strong axis My,Ed, the bending moment about weak axis Mz,Ed, the bimoment BEd and the axial force NEd were created and analyzed. The exact interaction curves obtained by the linear programming for 4 internal forces have enabled to create and to verify the proposed approximate interaction formula for 3 internal forces.The approximate interaction formula for the design plastic resistance of channel sections under combination of 3 internal forces: the bending moment about strong axis My,Ed, the bending moment about weak axis Mz,Ed and the bimoment BEd was analyzed and verified. The explicit interaction formula that takes into account these 3 internal forces is missing in Eurocodes. A large parametrical study was performed for the rolled channel profiles within the size range UPE 80 UPE 400. The differences between the results of the approximate interaction formula and the exact interaction curves were analyzed and summarized.Till today nobody presented results of the parametrical study of the channel sections under the combination of 4 internal forces.

Dynamic Oligopoly and Price Stickiness

How does market concentration affect the potency of monetary policy? To address this question we embed a dynamic oligopolistic game into a general-equilibrium macroeconomic model. We provide a sufficient-statistic formula for the response to monetary shocks involving demand elasticities, concentration and markups. We discipline our model with evidence on pass-through and find that higher concentration amplifies nonneutrality and stickiness. We isolate strategic effects from oligopoly by comparing our model to one with naive firms. We derive an exact Phillips curve featuring novel higher-order terms, but show that a standard New Keynesian one recalibrated with higher stickiness provides an excellent approximation. (JEL D43, E12, E21, E31, E43, E51, E52)

Effect of lamina fiber orientation interfaced with semi-flexible adhesive layer on strength and failure mode of composite single-lap joints

Various geometric and material parameters such as adhesive thickness, adhesive overlap, adherend thickness, and composite layup may affect the strength of the joint under quasi-static loading and failure mode of bonded composite-to-composite single-lap joints (SLJs) and are investigated by previous studies. The study herein broadens these findings by looking into the effect of lamina fiber angle adjacent to the adhesive layer on the damage initiation and evolution in detail. In this regard, a composite-to-composite adhesively bonded SLJ with adherends made of E-glass/epoxy composites and [04//θ/03] (where//shows the adhesive location) layups are manufactured and tested under quasi-static tensile loading. The adhesive type is semi-flexible Araldite 2015. Experimental results show that by increasing the fiber angle from 0° to 90°, the shear stress in the adhesive layer is decreased while the peel stress is increased. In examining typical fracture interfaces for each layup configuration, a full description of failure mode assessment is obtained. In particular, the SLJ is modeled in Abaqus using cohesive elements with bilinear traction-separation law. Numerical results indicate that the bilinear cohesive law cannot model the exact load-displacement curve due to semi-flexible behavior of the epoxy adhesive, but it can predict maximum strength precisely. The failure of composite joints is significantly influenced by shear stress.

An exact and explicit PV panel curve computation assisted by two 2-port networks

The single-diode-model (SDM) is more often used for the photovoltaic module current–voltage (I–V) curve computation. However, the SDM being implicit, demands iterative methods and makes the computation tedious. Optionally, the Lambert-W function-based curve computation provides an explicit and accurate solution. The function evaluations and the associated problems are really mathematical challenges. This paper proposes a novel curve computation method derived from the SDM decomposition. The voltage across the diode in the SDM equivalent circuit acts as an independent variable and makes the curve computation explicit. Also, the I–V curve can be obtained using the dual approach, i.e. I-approach and V-approach. The method is employed for the silicon cell and modules’ curves computations in uniform operating conditions and partial shading conditions. The novel method outperforms in comparison with the Newton-Raphson and the Lambert-W based curve computation in terms of an explicit, exact, and fast solution. Similar to the SDM, the method is successfully adopted for the double-diode-model photovoltaics.

Unlisted

Unlisted

CT findings predicting lung resection in children with complicated community-acquired pneumonia.

To investigate computed tomography (CT) features which predict lung resection in children with complicated community-acquired pneumonia. A retrospective study of CT findings of patients with complicated pneumonia treated between January 2010 and December 2019. Fisher's exact test and ROC curves were used for statistical analysis. The study cohort consisted of 84 patients who underwent chest CT for complicated pneumonia. Lung resection was performed in 36 patients, 3 patients were treated by lung decortication, 45 patients were cured conservatively. Seven CT features were found statistically significant among the patients who underwent lung resection. 80.5% of patients from the resection group had two or more of these features on the initial CT scan, 64% had three or more. According to ROC analysis, simultaneous occurrence of multiple cavities equal to or greater than 3cm and lung abscess predicted a pulmonary resection. The combination of CT features which clearly predict lung resection are the simultaneous occurrence of multiple cavities ≥ 3cm and lung abscess. The most common triple combination of CT signs in the resected group of patients were multiple cavities ≥ 3cm, consolidation of lung tissue and pleural effusion < 3cm.

Optimal Scaling Approaches for Perfusion MRI with Distorted Arterial Input Function (AIF) in Patients with Ischemic Stroke.

Background: Diagnosis and timely treatment of ischemic stroke depends on the fast and accurate quantification of perfusion parameters. Arterial input function (AIF) describes contrast agent concentration over time as it enters the brain through the brain feeding artery. AIF is the central quantity required to estimate perfusion parameters. Inaccurate and distorted AIF, due to partial volume effects (PVE), would lead to inaccurate quantification of perfusion parameters. Methods: Fifteen patients suffering from stroke underwent perfusion MRI imaging at the Tri-Service General Hospital, Taipei. Various degrees of the PVE were induced on the AIF and subsequently corrected using rescaling methods. Results: Rescaled AIFs match the exact reference AIF curve either at peak height or at tail. Inaccurate estimation of CBF values estimated from non-rescaled AIFs increase with increasing PVE. Rescaling of the AIF using all three approaches resulted in reduced deviation of CBF values from the reference CBF values. In most cases, CBF map generated by rescaled AIF approaches show increased CBF and Tmax values on the slices in the left and right hemispheres. Conclusion: Rescaling AIF by VOF approach seems to be a robust and adaptable approach for correction of the PVE-affected multivoxel AIF. Utilizing an AIF scaling approach leads to more reasonable absolute perfusion parameter values, represented by the increased mean CBF/Tmax values and CBF/Tmax images.

Semi-Analytical Finite Element Method for calculating dispersion curves of a CFRP plate

Composite Materials are widely used thanks to their mechanical characteristics. Non destructive evaluation requires knowing the exact dispersion curves to determine the propagative waves and to resolve the phase velocity of symmetrical and antisymmetrical modes. The aim of this paper is to plot the dispersion curves of a Carbon Fibre Reinforced Polymer plate using Semi Analytical Finite Element Method algorithm. This method combines the analytical expression of the displacement and the finite element method procedure. The resultant advantage is both simplicity and rapidity. The obtained results showed that the method accuracy depends on the elements number of meshing. To ensure good precision and fast computation of the method, the elements number and the order of the interpolation functions must be optimized.

CO2 Automated Angiography in Endovascular Aortic Repair Preserves Renal Function to a Greater Extent Compared with Iodinated Contrast Medium. Analysis of Technical and Anatomical Details

Contrast induced nephropathy occurs in up to 7.5% of cases in endovascular aortic repair (EVAR). Carbon dioxide (CO2) has been proposed as an alternative agent to iodinated contrast medium (ICM); however, specific protocols are not universally adopted, and the visualization of the renal arteries may be suboptimal in some cases. The aim of this study was to analyze our CO2-EVAR experience with automatic injections, in order to identify the anatomical characteristics associated with the best visualization of all the aortic vessels, with particular attention to the lowest renal artery (LoRA). From 2016 to 2019, all EVAR performed with either CO2 or ICM were analyzed and compared. CO2-EVAR was performed using an automated injector (600 mm Hg pressure; 100 cc volume); a small amount of ICM was injected in case of difficulty in LoRA visualization or doubts at the completion angiogram. Clinical and CT-Scan preoperative characteristics were considered. The study endpoints were technical success, amount of ICM and radiation dose, postoperative renal function and possible CO2-related adverse events. Statistical analysis was by Fisher's exact, t-Student, Mann-Whitney tests and ROC curve. In the considered period, 321 EVAR procedures, 72 (22.4%) with CO2 and 249 (77.6%) with ICM, were performed. The 2 groups were similar for clinical characteristics and preoperative renal function. ICM was injected in a significantly lower amount in the CO2-EVAR group (52.8 ± 6.1 vs. 88.1 ±9.2 cc, P < 0.001), which received a significantly higher mean radiation dose (Total DAP: 500,550.8 ± 377,394.6 mGy/cm2 CO2-EVAR vs. 332,301.8 ±230,139.3 mGy/cm2 ICM-EVAR, P=0.001). Postoperative eGFR decreased significantly less in the CO2-EVAR (2.3 ± 1.1 mL/min) compared with the ICM-EVAR group (10.6 ±5.3 mL/min), P < 0.001. LoRA was correctly visualized in 50/72 (69.4%) cases of CO2-EVAR, which had a significantly longer proximal neck (Median [IQR]: 30 [14] vs. 18 [15] mm, P=0.001). At ROC curve, a proximal neck length >24.5 mm was predictive of LoRA visualization (72.1% sensitivity, 73.8% specificity). Three CO2-EVAR cases had intraoperative transient hypotension with no consequences. Sixteen/72 (22.2%) CO2-EVAR procedures were performed using 0 cc of ICM. CO2-EVAR by automated injections is safe and requires a lower amount of ICM if compared with ICM-EVAR, with a consequent significant benefit on postoperative renal function. If specific anatomical situations are present, ICM may be completely unnecessary. The radiation dose is however significantly higher, therefore procedural protocols need further refinements.

Comparison of peripheral blood smear examination with automated haematology analyzer for diagnosing different types of anemia.

Objective: This study aims to determine diagnostic accuracy of peripheral blood smear and automated haematology analyzer and to determine frequency of different types of anemia diagnosed by peripheral blood smear and automated hematology analyzer. Study Design: Cross Sectional study. Setting: Department of Pathology, Rawal Institute of Health Sciences, Islamabad. Period: November 2015 to April 2016. Material &amp; Methods: Sample size of 149 suspected anemia patients was calculated using WHO calculator with 95% confidence interval. Research approval was taken from hospital ethical board. Patients were approached through non probability consecutive sampling method. Both peripheral blood smear examination and automated haematology analysis of each sample was performed. Diagnostic accuracy and frequency of anemia types was measured. Data analysis was done with the help of SPSS version 25. Chi-square and fissure exact test and ROC curve analysis was applied and significant (p&lt;0.05) results were reported. Results: Total 149 patients were included in study. There were 42(28.2%) male and 107(71.8%) female. Mean age of patients was 35.1±2.1SD. Peripheral blood smear and automated haematology analyzer showed sensitivity (68% vs 92%), specificity (59% vs 88%), PPV (72% vs 92%), NPV (55% vs 88%) and diagnostic accuracy (64% vs 91) respectively. Most common type of anemia diagnosed with peripheral blood smear was microcytic hypochromic anemia with raised RDW 36.7% followed by normocytic normochromic anemia with raised RDW 13.3% and macrocytic anemia (p=0.001) while in automated haematology analyzer microc ytic hypochromic anemia with raised RDW54.4% followed by normochromic normocytic anemoia with normal RDW 11.1% (p=0.000). Conclusion: Automated haematyology analyzer had high diagnostic accuracy for diagnosis of anemia. Microcytic hypochromic anemia and normocytic normochromic are most common anemias diagnosed by peripheral blood smear and automated hematology analyzer and peripheral blood smear cannot be completely replaced by automated haemolytic analyzer. However, if both methods are used simultaneously, more accurate results can be obtained.