Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short-and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer

Background: Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon’s entropy in the histological diagnosis of prostate cancer. Methods: Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon’s entropy (SE) and number of cell nuclei (NCN) in these areas were compared. Results: FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p < 0.05) at a magnification of 40x; T vs. N (p < 0.01) at 100x and H vs. N (p < 0.01) at 400x. SE analysis revealed the following significant differences groups: T vs. H and T vs. N (p < 0.05) at 100x; and T vs. H and T vs. N (p < 0.001) at 400x. NCN analysis demonstrated the following significant differences between groups: T vs. H and T vs. N (p < 0.05) at 40x; T vs. H and T vs. N (p < 0.0001) at 100x; and T vs. H and T vs. N (p < 0.01) at 400x. Conclusions: The quantification of the FD and SE, together with the number of cell nuclei, has potential clinical applications in the histological diagnosis of prostate cancer.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.

Foetal heart rate recording: analysis and comparison of different methodologies

Monitoring foetal health is a very important task in clinical practice to appropriately plan pregnancy management and delivery. In the third trimester of pregnancy, ultrasound cardiotocography is the most employed diagnostic technique: foetal heart rate and uterine contractions signals are simultaneously recorded and analysed in order to ascertain foetal health. Because ultrasound cardiotocography interpretation still lacks of complete reliability, new parameters and methods of interpretation, or alternative methodologies, are necessary to further support physicians’ decisions. To this aim, in this thesis, foetal phonocardiography and electrocardiography are considered as different techniques. Further, variability of foetal heart rate is thoroughly studied. Frequency components and their modifications can be analysed by applying a time-frequency approach, for a distinct understanding of the spectral components and their change over time related to foetal reactions to internal and external stimuli (such as uterine contractions). Such modifications of the power spectrum can be a sign of autonomic nervous system reactions and therefore represent additional, objective information about foetal reactivity and health. However, some limits of ultrasonic cardiotocography still remain, such as in long-term foetal surveillance, which is often recommendable mainly in risky pregnancies. In these cases, the fully non-invasive acoustic recording, foetal phonocardiography, through maternal abdomen, represents a valuable alternative to the ultrasonic cardiotocography. Unfortunately, the so recorded foetal heart sound signal is heavily loaded by noise, thus the determination of the foetal heart rate raises serious signal processing issues. A new algorithm for foetal heart rate estimation from foetal phonocardiographic recordings is presented in this thesis. Different filtering and enhancement techniques, to enhance the first foetal heart sounds, were applied, so that different signal processing techniques were implemented, evaluated and compared, by identifying the strategy characterized on average by the best results. In particular, phonocardiographic signals were recorded simultaneously to ultrasonic cardiotocographic signals in order to compare the two foetal heart rate series (the one estimated by the developed algorithm and the other provided by cardiotocographic device). The algorithm performances were tested on phonocardiographic signals recorded on pregnant women, showing reliable foetal heart rate signals, very close to the ultrasound cardiotocographic recordings, considered as reference. The algorithm was also tested by using a foetal phonocardiographic recording simulator developed and presented in this research thesis. The target was to provide a software for simulating recordings relative to different foetal conditions and recordings situations and to use it as a test tool for comparing and assessing different foetal heart rate extraction algorithms. Since there are few studies about foetal heart sounds time characteristics and frequency content and the available literature is poor and not rigorous in this area, a data collection pilot study was also conducted with the purpose of specifically characterising both foetal and maternal heart sounds. Finally, in this thesis, the use of foetal phonocardiographic and electrocardiographic methodology and their combination, are presented in order to detect foetal heart rate and other functioning anomalies. The developed methodologies, suitable for longer-term assessment, were able to detect heart beat events correctly, such as first and second heart sounds and QRS waves. The detection of such events provides reliable measures of foetal heart rate, potentially information about measurement of the systolic time intervals and foetus circulatory impedance.

Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Approximate entropy (ApEn) of blood pressure (BP) can be easily measured based on software analysing 24-h ambulatory BP monitoring (ABPM), but the clinical value of this measure is unknown. In a prospective study we investigated whether ApEn of BP predicts, in addition to average and variability of BP, the risk of hypertensive crisis. In 57 patients with known hypertension we measured ApEn, average and variability of systolic and diastolic BP based on 24-h ABPM. Eight of these fifty-seven patients developed hypertensive crisis during follow-up (mean follow-up duration 726 days). In bivariate regression analysis, ApEn of systolic BP (P<0.01), average of systolic BP (P=0.02) and average of diastolic BP (P=0.03) were significant predictors of hypertensive crisis. The incidence rate ratio of hypertensive crisis was 14.0 (95% confidence interval (CI) 1.8, 631.5; P<0.01) for high ApEn of systolic BP as compared to low values. In multivariable regression analysis, ApEn of systolic (P=0.01) and average of diastolic BP (P<0.01) were independent predictors of hypertensive crisis. A combination of these two measures had a positive predictive value of 75%, and a negative predictive value of 91%, respectively. ApEn, combined with other measures of 24-h ABPM, is a potentially powerful predictor of hypertensive crisis. If confirmed in independent samples, these findings have major clinical implications since measures predicting the risk of hypertensive crisis define patients requiring intensive follow-up and intensified therapy.

Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

T1(Gd) gives comparable information as Delta T1 relaxation rate in dGEMRIC evaluation of cartilage repair tissue

OBJECTIVES: To evaluate the relationship between T1 after intravenous contrast administration (T1Gd) and Delta relaxation rate (DeltaR1) = (1/T1(Gd) - 1/T1o) in the delayed Gadolinium-Enhanced MRI of cartilage (dGEMRIC) evaluation of cartilage repair tissue. MATERIALS AND METHODS: Thirty single MR examinations from 30 patients after matrix-associated autologous chondrocyte transplantations of the knee joint with different postoperative intervals were examined using an 8-channel knee-coil at 3T. T1 mapping using a 3D GRE sequence with a 35/10 degrees flip angle excitation pulse combination was performed before and after contrast administration (dGEMRIC technique). T1 postcontrast (T1(Gd)) and the DeltaR1 (relative index of pre- and postcontrast R1 value) were calculated for repair tissue and the weight-bearing normal appearing control cartilage. For evaluation of the different postoperative intervals, MR exams were subdivided into 3 groups (up to 12 months, 12-24 months, more than 24 months). For statistical analysis Spearman correlation coefficients were calculated. RESULTS: The mean value for T1 postcontrast was 427 +/- 159 ms, for DeltaR1 1.85 +/- 1.0; in reference cartilage 636 +/- 181 ms for T1 postcontrast and 0.83 +/- 0.5 for DeltaR1.The correlation coefficients were highly significant between T1 (Gd) and DeltaR1 for repair tissue (0.969) as well as normal reference cartilage (0.928) in total, and for the reparative cartilage in the early, middle postoperative, and late postoperative interval after surgery (R values: -0.986, -0.970, and -0.978, respectively). Using either T1(Gd) or DeltaR1, the 2 metrics resulted in similar conclusions regarding the time course of change of repair tissue and control tissue, namely that highly significant (P > 0.01) differences between cartilage repair tissue and reference cartilage were found for all follow-up groups. Additionally, for both metrics highly significant differences (P < 0.01) between early follow up and the 2 later postoperative groups for cartilage repair tissue were found. No statistical differences were found between the 2 later follow-up groups of reparative cartilage either for T1 (Gd) or DeltaR1. CONCLUSION: The high correlation between T1 (Gd) and DeltaR1 and the comparable conclusions reached utilizing metric implies that T1 mapping before intravenous administration of MR contrast agent is not necessary for the evaluation of repair tissue. This will help to reduce costs, inconvenience for the patients, simplifies the examination procedure, and makes dGEMRIC more attractive for follow-up of patients after cartilage repair surgeries.

Seasonal variation of VO 2 max and the VO2-work rate relationship in elite Alpine skiers

PURPOSE: Alpine ski performance relates closely to both anaerobic and aerobic capacities. During their competitive season, skiers greatly reduce endurance and weight training, and on-snow training becomes predominant. To typify this shift, we compared exhaustive ramp cycling and squat (SJ) and countermovement jumping (CMJ) performance in elite males before and after their competitive season. RESULTS: In postseason compared with preseason: 1) maximal oxygen uptake (VO 2 max) normalized to bodyweight was higher (55.2 +/- 5.2 vs 52.7 +/- 3.6 mL x kg(-1) x min(-1), P < 0.01), but corresponding work rate (W) was unchanged; 2) at ventilatory thresholds (VT), absolute and relative work rates were similar but heart rates were lower; 3) VO2/W slope was greater (9.59 +/- 0.6 vs 9.19 +/- 0.4 mL O2 x min(-1) x W(-1), P = 0.02), with similar flattening (P < 0.01) above V T1 at both time points; and 4) jump height was greater in SJ (47.4 +/- 4.4 vs 44.7 +/- 4.3 cm, P < 0.01) and CMJ (52.7 +/- 4.6 vs 50.4 +/- 5.0 cm, P < 0.01). DISCUSSION: We believe that aerobic capacity and leg power were constrained in preseason and that improvements primarily reflected an in-season recovery from a fatigued state, which was caused by incongruous preseason training. Residual adaptations to high-altitude exposure in preseason could have also affected the results. Nonetheless, modern alpine skiing seemingly provides an ample cardiovascular training stimulus for skiers to maintain their aerobic capacities during the racing season. CONCLUSIONS: We conclude that aerobic fitness and leg explosiveness can be maintained in-season but may be compromised by heavy or excessive preseason training. In addition, ramp test V O2/W slope analysis could be useful for monitoring both positive and negative responses to training.

Relative Value of White Corn When Fed to Finishing Cattle and Its Effects on Color of Carcass Fat

White corn was compared with yellow corn in a 180-day finishing trial with 600 lb. Angus steers fed 90% concentrate diets. Steers fed yellow corn consumed 3.3% less feed and were 3.8% more efficient in feed utilization. Rate of gain and carcass characteristics were similar for steers fed white or yellow corn. The color of subcutaneous fat over the ribs was significantly whiter from carcasses of steers fed white corn compared with those fed yellow corn. The results of this study indicate that white corn may be used instead of barley to produce whiter fat in beef carcasses.

Relative Energy Balance, CKD, and Risk of Cardiovascular and All-Cause Mortality.

BACKGROUND Mortality risk for people with chronic kidney disease is substantially greater than that for the general population, increasing to a 7-fold greater risk for those on dialysis therapy. Higher body mass index, generally due to higher energy intake, appears protective for people on dialysis therapy, but the relationship between energy intake and survival in those with reduced kidney function is unknown. STUDY DESIGN Prospective cohort study with a median follow-up of 14.5 (IQR, 11.2-15.2) years. SETTING & PARTICIPANTS Blue Mountains Area, west of Sydney, Australia. Participants in the general community enrolled in the Blue Mountains Eye Study (n=2,664) who underwent a detailed interview, food frequency questionnaire, and physical examination including body weight, height, blood pressure, and laboratory tests. PREDICTORS Relative energy intake, food components (carbohydrates, total sugars, fat, protein, and water), and estimated glomerular filtration rate (eGFR). Relative energy intake was dichotomized at 100%, and eGFR, at 60mL/min/1.73m(2). OUTCOMES All-cause and cardiovascular mortality. MEASUREMENTS All-cause and cardiovascular mortality using unadjusted and adjusted Cox proportional regression models. RESULTS 949 people died during follow-up, 318 of cardiovascular events. In people with eGFR<60mL/min/1.73m(2) (n=852), there was an increased risk of all-cause mortality (HR, 1.48; P=0.03), but no increased risk of cardiovascular mortality (HR, 1.59; P=0.1) among those with higher relative energy intake compared with those with lower relative energy intake. Increasing intake of carbohydrates (HR per 100g/d, 1.50; P=0.04) and total sugars (HR per 100g/d, 1.62; P=0.03) was associated significantly with increased risk of cardiovascular mortality. LIMITATIONS Under-reporting of energy intake, baseline laboratory and food intake values only, white population. CONCLUSIONS Increasing relative energy intake was associated with increased all-cause mortality in patients with eGFR<60mL/min/1.73m(2). This effect may be mediated by increasing total sugars intake on subsequent cardiovascular events.

Does Sex Speed Up Evolutionary Rate and Increase Biodiversity?

Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity.

Heart rate is a prognostic risk factor for myocardial infarction: a post hoc analysis in the PERFORM (Prevention of cerebrovascular and cardiovascular Events of ischemic origin with teRutroban in patients with a history oF ischemic strOke or tRansient ischeMic attack) study population

BACKGROUND Elevated resting heart rate is known to be detrimental to morbidity and mortality in cardiovascular disease, though its effect in patients with ischemic stroke is unclear. We analyzed the effect of baseline resting heart rate on myocardial infarction (MI) in patients with a recent noncardioembolic cerebral ischemic event participating in PERFORM. METHODS We compared fatal or nonfatal MI using adjusted Cox proportional hazards models for PERFORM patients with baseline heart rate <70 bpm (n=8178) or ≥70 bpm (n=10,802). In addition, heart rate was analyzed as a continuous variable. Other cerebrovascular and cardiovascular outcomes were also explored. RESULTS Heart rate ≥70 bpm was associated with increased relative risk for fatal or nonfatal MI (HR 1.32, 95% CI 1.03-1.69, P=0.029). For every 5-bpm increase in heart rate, there was an increase in relative risk for fatal and nonfatal MI (11.3%, P=0.0002). Heart rate ≥70 bpm was also associated with increased relative risk for a composite of fatal or nonfatal ischemic stroke, fatal or nonfatal MI, or other vascular death (excluding hemorrhagic death) (P<0001); vascular death (P<0001); all-cause mortality (P<0001); and fatal or nonfatal stroke (P=0.04). For every 5-bpm increase in heart rate, there were increases in relative risk for fatal or nonfatal ischemic stroke, fatal or nonfatal MI, or other vascular death (4.7%, P<0.0001), vascular death (11.0%, P<0.0001), all-cause mortality (8.0%, P<0.0001), and fatal and nonfatal stroke (2.4%, P=0.057). CONCLUSION Elevated heart rate ≥70 bpm places patients with a noncardioembolic cerebral ischemic event at increased risk for MI.

Determinants of Acidobacteria activity inferred from the relative abundances of 16S rRNA transcripts in German grassland and forest soils

16S rRNA genes and transcripts of Acidobacteria were investigated in 57 grassland and forest soils of three different geographic regions. Acidobacteria contributed 9-31% of bacterial 16S rRNA genes whereas the relative abundances of the respective transcripts were 4-16%. The specific cellular 16S rRNA content (determined as molar ratio of rRNA:rRNA genes) ranged between 3 and 80, indicating a low in situ growth rate. Correlations with flagellate numbers, vascular plant diversity and soil respiration suggest that biotic interactions are important determinants of Acidobacteria 16S rRNA transcript abundances in soils. While the phylogenetic composition of Acidobacteria differed significantly between grassland and forest soils, high throughput denaturing gradient gel electrophoresis and terminal restriction fragment length polymorphism fingerprinting detected 16S rRNA transcripts of most phylotypes in situ. Partial least squares regression suggested that chemical soil conditions such as pH, total nitrogen, C:N ratio, ammonia concentrations and total phosphorus affect the composition of this active fraction of Acidobacteria. Transcript abundance for individual Acidobacteria phylotypes was found to correlate with particular physicochemical (pH, temperature, nitrogen or phosphorus) and, most notably, biological parameters (respiration rates, abundances of ciliates or amoebae, vascular plant diversity), providing culture-independent evidence for a distinct niche specialization of different Acidobacteria even from the same subdivision.

Infection rate of emergency bolt-kit vs. non-emergency conventional implanted silver bearing external ventricular drainage catheters.

BACKGROUND Bolt-kit systems are increasingly used as an alternative to conventional external cerebrospinal fluid (CSF) drainage systems. Since 2009 we regularly utilize bolt-kit external ventricular drainage (EVD) systems with silver-bearing catheters inserted manually with a hand drill and skull screws for emergency ventriculostomy. For non-emergency situations, we use conventional ventriculostomy with subcutaneous tunneled silver-bearing catheters, performed in the operating room with a pneumatic drill. This retrospective analysis compared the two techniques in terms of infection rates. METHODS 152 patients (aged 17-85 years, mean=55.4 years) were included in the final analysis; 95 received bolt-kit silver-bearing catheters and 57 received conventionally implanted silver-bearing catheters. The primary endpoint combined infection parameters: occurrence of positive CSF culture, colonization of catheter tips, or elevated CSF white blood cell counts (>4/μl). Secondary outcome parameters were presence of microorganisms in CSF or on catheter tips. Incidence of increased CSF cell counts and number of patients with catheter malposition were also compared. RESULTS The primary outcome, defined as analysis of combined infection parameters (occurrence of either positive CSF culture, colonization of the catheter tips or raised CSF white blood cell counts >4/μl)was not significantly different between the groups (58.9% bolt-kit group vs. 63.2% conventionally implanted group, p=0.61, chi-square-test). The bolt-kit group was non-inferior and not superior to the conventional group (relative risk reduction of 6.7%; 90% confidence interval: -19.9% to 25.6%). Secondary outcomes showed no statistically significant difference in the incidence of microorganisms in CSF (2.1% bolt-kit vs. 5.3% conventionally implanted; p=0.30; chi-square-test). CONCLUSIONS This analysis indicates that silver-bearing EVD catheters implanted with a bolt-kit system outside the operating room do not significantly elevate the risk of CSF infection as compared to conventional implant methods.