We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third ...side as diameter. In particular, we find a nice relation involving the radii of the inner and outer Apollonius circles of the three circles in the triad.
We study properties of certain circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the arc of a circle erected ...internally on the third side.
Let P be a point inside a convex quadrilateral ABCD. The lines from P to the vertices of the quadrilateral divide the quadrilateral into four triangles. If we locate a triangle center in each of ...these triangles, the four triangle centers form another quadrilateral called a central quadrilateral. For each of various shaped quadrilaterals, and each of 1000 different triangle centers, we compare the reference quadrilateral to the central quadrilateral. Using a computer, we determine how the two quadrilaterals are related. For example, we test to see if the two quadrilaterals are congruent, similar, have the same area, or have the same perimeter. We also look for such relationships when P is a special point associated with the reference quadrilateral, such as being the diagonal point, Steiner point, or Poncelet point.
The diagonals of a quadrilateral form four component triangles (in two ways). For each of various shaped quadrilaterals, we examine 1000 triangle centers located in these four component triangles. ...Using a computer, we determine when the four centers form a special quadrilateral, such as a rhombus or a cyclic quadrilateral. A typical result is the following. The diagonals of an equidiagonal quadrilateral divide the quadrilateral into four nonoverlapping triangles. Then the Nagel points of these four triangles form an orthodiagonal quadrilateral.
The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of ...the triangle. We use a computer to discover and catalog properties of the Gergonne point.
Introduction
Deep brain stimulation of the subthalamic nucleus (STN-DBS) can exert relevant effects on the voice of patients with Parkinson's disease (PD). In this study, we used artificial ...intelligence to objectively analyze the voices of PD patients with STN-DBS.
Materials and methods
In a cross-sectional study, we enrolled 108 controls and 101 patients with PD. The cohort of PD was divided into two groups: the first group included 50 patients with STN-DBS, and the second group included 51 patients receiving the best medical treatment. The voices were clinically evaluated using the Unified Parkinson's Disease Rating Scale part-III subitem for voice (UPDRS-III-v). We recorded and then analyzed voices using specific machine-learning algorithms. The likelihood ratio (LR) was also calculated as an objective measure for clinical-instrumental correlations.
Results
Clinically, voice impairment was greater in STN-DBS patients than in those who received oral treatment. Using machine learning, we objectively and accurately distinguished between the voices of STN-DBS patients and those under oral treatments. We also found significant clinical-instrumental correlations since the greater the LRs, the higher the UPDRS-III-v scores.
Discussion
STN-DBS deteriorates speech in patients with PD, as objectively demonstrated by machine-learning voice analysis.
Directional deep brain stimulation (DBS) leads allow a fine-tuning control of the stimulation field, however, this new technology could increase the DBS programming time because of the higher number ...of the possible combinations used in directional DBS than in standard nondirectional electrodes. Neuroimaging leads localization techniques and local field potentials (LFPs) recorded from DBS electrodes implanted in basal ganglia are among the most studied biomarkers for DBS programing.
This study aimed to evaluate whether intraoperative LFPs beta power and neuroimaging reconstructions correlate with contact selection in clinical programming of DBS in patients with Parkinson disease (PD).
In this retrospective study, routine intraoperative LFPs recorded from all contacts in the subthalamic nucleus (STN) of 14 patients with PD were analyzed to calculate the beta band power for each contact. Neuroimaging reconstruction obtained through Brainlab Elements Planning software detected contacts localized within the STN. Clinical DBS programming contact scheme data were collected after one year from the implant. Statistical analysis evaluated the diagnostic performance of LFPs beta band power and neuroimaging data for identification of the contacts selected with clinical programming. We evaluated whether the most effective contacts identified based on the clinical response after one year from implant were also those with the highest level of beta activity and localized within the STN in neuroimaging reconstruction.
LFPs beta power showed a sensitivity of 67%, a negative predictive value (NPV) of 84%, a diagnostic odds ratio (DOR) of 2.7 in predicting the most effective contacts as evaluated through the clinical response. Neuroimaging reconstructions showed a sensitivity of 62%, a NPV of 77%, a DOR of 1.20 for contact effectivity prediction. The combined use of the two methods showed a sensitivity of 87%, a NPV of 87%, a DOR of 2.7 for predicting the clinically more effective contacts.
The combined use of LFPs beta power and neuroimaging localization and segmentations predict which are the most effective contacts as selected on the basis of clinical programming after one year from implant of DBS. The use of predictors in contact selection could guide clinical programming and reduce time needed for it.
Liver damage worsens the prognosis of coronavirus 19 disease (COVID-19). However, the best strategy to stratify mortality risk according to liver damage has not been established. The aim of this ...study is to test the predictive value of the validated Fibrosis-4 (FIB-4) Index and compared it to liver transaminases and to the AST-to-Platelet ratio index (APRI). Multicenter cohort study including 992 consecutive COVID-19 patients admitted to the Emergency Department. FIB-4 > 3.25 and APRI > 0.7 were used to define liver damage. Multivariable Cox regression and ROC curve analysis for mortality were performed. Secondary endpoints were (1) need for high-flow oxygen and (2) mechanical ventilation. 240 (24.2%) patients had a FIB-4 > 3.25. FIB-4 > 3.25 associated with an increased mortality (
n
= 119, log-rank test
p
< 0.001 and adjusted hazard ratio (HR) 1.72 (95% confidence interval 95%CI 1.14–2.59,
p
= 0.010). ROC analysis for mortality showed that FIB-4 (AUC 0.734, 95% CI 0.705–0.761) had a higher predictive value than AST (
p
= 0.0018) and ALT (
p
< 0.0001). FIB-4 > 3.25 was also superior to APRI > 0.7 (AUC 0.58, 95% CI 0.553–0.615,
p
= 0.0008). Using an optimized cut-off > 2.76 (AUC 0.689, 95% CI 0.659–0.718,
p
< 0.0001), FIB-4 was superior to FIB-4 > 3.25 (
p
= 0.0302), APRI > 0.7 (
p
< 0.0001), AST > 51 (
p
= 0.0119) and ALT > 42 (
p
< 0.0001). FIB-4 was also associated with high-flow oxygen use (
n
= 255, HR 1.69, 95% CI 1.25–2.28,
p
= 0.001) and mechanical ventilation (
n
= 39, HR 2.07, 95% CI 1.03–4.19,
p
= 0.043). FIB-4 score predicts mortality better than liver transaminases and APRI score. FIB-4 score may be an easy tool to identify COVID-19 patients at worse prognosis in the emergency department.
