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PubMed2006

Ultrasound absorption and entropy production in biological tissue: a novel approach to anticancer therapy.

UNLABELLED: The entropy production of tumorous cells is higher than that of normal cells, and entropy flow is therefore directed from tumorous toward healthy cells. This results in information concerning the cancer propagating into the surrounding normal tissue. However, ultrasound absorption results in additional entropy production in tissues. The entropy mechanism possibly provides a basis for a novel approach to anticancer therapy through the use of ultrasound irradiation. METHODS: Through the calculation of ultrasound-induced entropy production and comparison of the theoretical results with the experimental data on ultrasound absorption in biological tissues, we have demonstrated that ultrasound absorption will increase the entropy in normal tissue more efficiently than in tumorous tissue due to the more acidic nature of the latter. Consequently, the direction of entropy flow between these two kinds of cells may be reversed on exposure to ultrasound. CONCLUSION: The higher entropy accumulation of normal cells during ultrasound irradiation may possibly lead to a change in the original direction of entropy flow and avoid the propagation of information on the cancer into the normal tissues. We suggest that low-intensity, low-frequency ultrasound irradiation may be an efficient tool for the therapy of solid tumors.

Journal Article↗

PubMed1981

Entropy as an index of the informational state of neurons.

Techniques were developed for using the classical information theory descriptor, entropy, to quantify the "uncertainty" present in neuronal spike trains. Entropy was calculated on the basis of a method that describes the relative relationships of serially ordered interspike intervals by encoding the intervals as a series of symbols, each of which depicts the relative duration of two adjacent spike intervals. Each symbol, or set of symbols has a specific fractional entropy value, derived from its probability of occurrence; moreover, fractional entropy can describe the relative amount of "information" that is associated with the relative location of a given symbol in a string of symbols. Using spike trains from 12 single neurons in the cerebellar cortex of rats, we determined: (1) the mean and S.D. of information content of each symbol in each specific position in a group of symbols (2-4 symbols/group, based on 3-5 adjacent intervals), (2) the 4-symbol groups which had the least and the most average fractional entropy, (3) that the 4-symbol groups with both low and high fractional entropy had significant positive correlations with the probability of occurrence of those groups after a drug treatment (ethanol), and (4) that the degree of drug-induced change in the incidence of both low- and high-fractional entropy groups did not correlate with predrug entropy. Thus, the entropy of clusters of 3-5 adjacent spike intervals, when computed in this particular way, seems to be a useful measure or index of the informational state of neurons.

Action Potentials↗

PubMed2000

Side-chain conformational entropy in protein unfolded states.

The largest force disfavoring the folding of a protein is the loss of conformational entropy. A large contribution to this entropy loss is due to the side-chains, which are restricted, although not immobilized, in the folded protein. In order to accurately estimate the loss of side-chain conformational entropy that occurs upon folding it is necessary to have accurate estimates of the amount of entropy possessed by side-chains in the ensemble of unfolded states. A new scale of side-chain conformational entropies is presented here. This scale was derived from Monte Carlo computer simulations of small peptide models. It is demonstrated that the entropies are independent of host peptide length. This new scale has the advantage over previous scales of being more precise with low standard errors. Better estimates are obtained for long (e.g., Arg and Lys) and rare (e.g., Trp and Met) side-chains. Excellent agreement with previous side-chain entropy scales is achieved, indicating that further advancements in accuracy are likely to be small at best. Strikingly, longer side-chains are found to possess a smaller fraction of the theoretical maximum entropy available than short side-chains. This indicates that rotations about torsions after chi(2) are significantly affected by side-chain interactions with the polypeptide backbone. This finding invalidates previous assumptions about side-chain-backbone interactions. Proteins 2000;40:443-450.

Amino Acids↗

PubMed1998

15N backbone dynamics of the S-peptide from ribonuclease A in its free and S-protein bound forms: toward a site-specific analysis of entropy changes upon folding.

Backbone 15N relaxation parameters (R1, R2, 1H-15N NOE) have been measured for a 22-residue recombinant variant of the S-peptide in its free and S-protein bound forms. NMR relaxation data were analyzed using the "model-free" approach (Lipari & Szabo, 1982). Order parameters obtained from "model-free" simulations were used to calculate 1H-15N bond vector entropies using a recently described method (Yang & Kay, 1996), in which the form of the probability density function for bond vector fluctuations is derived from a diffusion-in-a-cone motional model. The average change in 1H-15N bond vector entropies for residues T3-S15, which become ordered upon binding of the S-peptide to the S-protein, is -12.6+/-1.4 J/mol.residue.K. 15N relaxation data suggest a gradient of decreasing entropy values moving from the termini toward the center of the free peptide. The difference between the entropies of the terminal and central residues is about -12 J/mol residue K, a value comparable to that of the average entropy change per residue upon complex formation. Similar entropy gradients are evident in NMR relaxation studies of other denatured proteins. Taken together, these observations suggest denatured proteins may contain entropic contributions from non-local interactions. Consequently, calculations that model the entropy of a residue in a denatured protein as that of a residue in a di- or tri-peptide, might over-estimate the magnitude of entropy changes upon folding.

Entropy↗

PubMed2006

Side-chain entropy effects on protein secondary structure formation.

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.

Amino Acid Sequence↗

PubMed2006

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences.

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.

Amino Acid Sequence↗

PubMed2006

HIV-1 GP120 V3 conformational and informational entropies.

In an attempt to analyze structure, function and evolution of HIV-1 GP120 V3, interactions among the Hartree-Fock energy, the conformational entropy and the Shannon entropy were determined for the 1NJ0 set of antibody-bound V3 loop conformers. The Hartree-Fock energy of each conformer was determined at the MINI level with GAMESS. The conformational entropy was determined per conformer and per residue from the mass-weighted covariance matrices. The Shannon entropy per residue was determined from sequence-substitution frequencies. Correlations were determined by linear regression analysis. There was a negative correlation between the Hartree-Fock energy and the conformational entropy (R=-0.4840, p=0.0078, df =28) that enhanced the negative Helmholtz-free-energy change for the binding of the GP120 ligand to target CD4. The Shannon entropy of V3 was a function of the conformational entropy variance (R=0.7225, p=0.00157, df=15) and of the V3 Hartree-Fock energy. Biological implications of this work are that (1) conformational entropy interacts with V3 Hartree-Fock energy to enhance GP120 binding to CD4 cell receptors and that (2) the Hartree-Fock energy of V3 interacts with the evolutionary system to participate in the regulation of V3 diversity.

Entropy↗

PubMed2004

Correlation of Narcotrend Index, entropy measures, and spectral parameters with calculated propofol effect-site concentrations during induction of propofol-remifentanil anaesthesia.

OBJECTIVE: The aim of this study was to compare the EEG parameter Narcotrend Index with the spectral and entropy-based EEG parameters median frequency, 95% spectral edge frequency, burst-compensated 95% spectral edge frequency, spectral entropy, amplitude entropy, and approximate entropy with regard to their ability to describe cerebral anaesthetic drug effects during induction of propofol-remifentanil anaesthesia. METHODS: Three induction schemes were studied with 10 patients each receiving 2 mg propofol/kg/60s (group 1), 4 mg/kg/120s (group 2), and 4 mg/kg/240s (group 3). The EEG was recorded with the EEG monitor Narcotrend. To analyse the relation between drug effect and EEG parameters, Spearman rank correlation of the different EEG parameters with the calculated propofol effect-site concentration was computed. RESULTS: In all groups Narcotrend Index showed the highest correlation with the propofol effect-site concentration and the lowest variability of individual correlation values. Furthermore, only the Narcotrend Index showed a monophasic behaviour over the entire time period analysed. In the group of entropy parameters approximate entropy yielded the best results. Among the spectral parameters the burst-compensated 95% spectral edge frequency had the highest correlation with the propofol effect-site concentration. It was markedly higher than for the standard spectral edge frequency. The correlations of median frequency and amplitude entropy with propofol effect-site concentration were the lowest. CONCLUSIONS. Changes in the propofol effect-site concentration during induction of anaesthesia were best described by the multivariate Narcotrend Index compared to conventional spectral EEG parameters and different entropy measures.

Adolescent↗

PubMed2006

Entropy.

The concept of entropy, originally derived from thermodynamics, has been successfully applied to EEG analysis. Various entropy algorithms have been used in clinical studies, but until now a commercially available monitor exists only for spectral entropy. By calculating two distinct values for the EEG dominated part of the spectrum (state entropy, SE) and the total spectrum (response entropy, RE), the M-Entropy module claims to provide useful information regarding the cortical state of the patient as well as an indirect measure of adequacy of analgesia. Generally, entropy has been studied for quantification of anaesthetic drug effect for various GABA-ergic i.v. induction agents and volatile anaesthetics like propofol and sevoflurane and overall was found comparable to the current clinical gold standard bispectral index (BIS). Entropy guidance may not be used during ketamine or nitrous oxide administration, since there is no reliable correlation to the patient's state of consciousness. The usefulness of RE as a surrogate for increased EMG activity due to painful stimulation has not been proven so far.

Analgesia↗

PubMed2002

The backbone conformational entropy of protein folding: experimental measures from atomic force microscopy.

The energy dissipated during the atomic force microscopy-based mechanical unfolding and extension of proteins is typically an order of magnitude greater than their folding free energy. The vast majority of the "excess" energy dissipated is thought to arise due to backbone conformational entropy losses as the solvated, random-coil unfolded state is stretched into an extended, low-entropy conformation. We have investigated this hypothesis in light of recent measurements of the energy dissipated during the mechanical unfolding of "polyproteins" comprised of multiple, homogeneous domains. Given the assumption that backbone conformational entropy losses account for the vast majority of the energy dissipated (an assumption supported by numerous lines of experimental evidence), we estimate that approximately 19(+/-2)J/(mol K residue) of entropy is lost during the extension of three mechanically stable beta-sheet polyproteins. If, as suggested by measured peak-to-peak extension distances, pulling proceeds to near completion, this estimate corresponds to the absolute backbone conformational entropy of the unfolded state. As such, it is exceedingly close to previous theoretical and semi-empirical estimates that place this value at approximately 20J/(mol K residue). The estimated backbone conformational entropy lost during the extension of two helical polyproteins, which, in contrast to the mechanically stable beta-sheet polyproteins, rupture at very low applied forces, is three- to sixfold less. Either previous estimates of the backbone conformational entropy are significantly in error, or the reduced mechanical strength of the helical proteins leads to the rupture of a subsequent domain before full extension (and thus complete entropy loss) is achieved.

Entropy↗

PubMed2004

Cortical entropy changes with general anaesthesia: theory and experiment.

Commonly used general anaesthetics cause a decrease in the spectral entropy of the electroencephalogram as the patient transits from the conscious to the unconscious state. Although the spectral entropy is a configurational entropy, it is plausible that the spectral entropy may be acting as a reliable indicator of real changes in cortical neuronal interactions. Using a mean field theory, the activity of the cerebral cortex may be modelled as fluctuations in mean soma potential around equilibrium states. In the adiabatic limit, the stochastic differential equations take the form of an Ornstein-Uhlenbeck process. It can be shown that spectral entropy is a logarithmic measure of the rate of synaptic interaction. This model predicts that the spectral entropy should decrease abruptly from values approximately 1.0 to values of approximately 0.7 as the patient becomes unconscious during induction of general anaesthesia, and then not decrease significantly on further deepening of anaesthesia. These predictions were compared with experimental results in which electrocorticograms and brain concentrations of propofol were recorded in seven sheep during induction of anaesthesia with intravenous propofol. The observed changes in spectral entropy agreed with the theoretical predictions. We conclude that spectral entropy may be a sensitive monitor of the consciousness-unconsciousness transition, rather than a progressive indicator of anaesthetic drug effect.

Anesthesia, General↗

PubMed2004

Entropy of EEG during anaesthetic induction: a comparative study with propofol or nitrous oxide as sole agent.

BACKGROUND: The search continues for an anaesthetic monitor that can define the level of anaesthesia in an individual patient irrespective of anaesthetic agent(s) used. Studies of available monitors based on bispectral analysis or evoked auditory potentials show the complexity of the problem. We assessed a new monitor, based on the entropy of the EEG, during induction of anaesthesia with either propofol or nitrous oxide. METHODS: In an open, randomized study (two groups; n=10) of day surgical patients, we induced loss of response with incremental boluses of propofol. The other group was given propofol 30 mg and then increasing concentrations of nitrous oxide until loss of response. We measured entropy with the M-Entropy Module S/5 (Datex-Ohmeda) using forehead electrodes and recorded response entropy (RE; including frontal electromyogram) and state entropy (SE; only the cortical EEG). Values are median (range). RESULTS: Baseline values were RE 98 (96-100), SE 89 (87-91) and RE 98 (96-99), SE 89 (87-91) for the propofol and nitrous oxide patients, respectively. During propofol induction, both entropy indices decreased with increasing sedation, with RE 40 (23-76) and SE 34 (17-70) at loss of response. Neither RE nor SE decreased during nitrous oxide inhalation, and at loss of response using nitrous oxide, RE and SE were unchanged at 98 (96-100) and 88 (85-91) respectively. CONCLUSIONS: The entropy monitor of anaesthetic depth shows a successive decrease with propofol but loss of consciousness with nitrous oxide is not associated with change in entropy indices.

Adult↗

PubMed2000

Approximate entropy as an electroencephalographic measure of anesthetic drug effect during desflurane anesthesia.

BACKGROUND: The authors hypothesized that the electroencephalogram (EEG) during higher anesthetic concentrations would show more "order" and less "randomness" than at lower anesthetic concentrations. "Approximate entropy" is a new statistical parameter derived from the Kolmogorov-Sinai entropy formula which quantifies the amount of regularity in data. The approximate entropy quantifies the predictability of subsequent amplitude values of the EEG based on the knowledge of the previous amplitude values. The authors investigated the dose-response relation of the EEG approximate entropy during desflurane anesthesia in comparison with spectral edge frequency 95, median frequency, and bispectral index. METHODS: Twelve female patients were studied during gynecologic laparotomies. Between opening and closure of the peritoneum, end-tidal desflurane concentrations were varied between 0.5 and 1.6 minimum alveolar concentration (MAC). The EEG approximate entropy, median EEG frequency, spectral edge frequency 95, and bispectral index were determined and the performance of each to predict the desflurane effect compartment concentration, obtained by simultaneous pharmacokinetic-pharmacodynamic modeling, was compared. RESULTS: Electroencephalogram approximate entropy decreased continuously over the observed concentration range of desflurane. The performance of the approximate entropy (prediction probability PK = 0.86 +/- 0.06) as an indicator for desflurane concentrations is similar to spectral edge frequency 95 (PK = 0.86 +/- 0.06) and bispectral index (PK = 0.82 +/- 0.06) and is statistically significantly better than median frequency (PK = 0.78 +/- 0.06). CONCLUSIONS: The amount of regularity in the EEG increases with increasing desflurane concentrations. The approximate entropy could be a useful EEG measure of anesthetic drug effect.

Adult↗

PubMed2001

Shannon entropy applied to the measurement of the electroencephalographic effects of desflurane.

BACKGROUND: The Shannon entropy is a standard measure for the order state of sequences. It quantifies the degree of skew of the distribution of values. Increasing hypnotic drug concentrations increase electroencephalographic amplitude. The probability density function of the amplitude values broadens and flattens, thereby changing from a skew distribution towards equal distribution. We investigated the dose-response relation of the Shannon entropy of the electroencephalographic amplitude values during desflurane monoanesthesia in comparison with previously used electroencephalographic parameters. METHODS: Electroencephalographic records previously obtained in 12 female patients during gynecologic laparotomies were reanalyzed. Between opening and closure of the peritoneum, desflurane vapor settings were varied between 0.5 and 1.6 minimum alveolar concentration. Electroencephalographic Shannon entropy, approximate entropy, median electroencephalographic frequency, SEF 95, total power, log total power, and Bispectral Index were determined, and their correlations with the desflurane effect compartment concentration, obtained by simultaneous pharmacokinetic-pharmacodynamic modeling, were compared. RESULTS: The electroencephalographic Shannon entropy increased continuously over the observed concentration range of desflurane. The correlation of the Shannon entropy (R2 = 0.84+/-0.08, mean +/- SD) with the desflurane effect compartment concentrations is similar to approximate entropy (R2 = 0.85+/-0.12), SEF 95 (R2 = 0.85+/-0.10), and Bispectral Index (R2 = 0.82+/-0.13) and is more statistically significant than median frequency (R2 = 0.72+/-0.17), total power (R2 = 0.67+/-0.18), and log total power (R2 = 0.80+/-0.09). CONCLUSIONS: The Shannon entropy seems to be a useful electroencephalographic measure of anesthetic drug effect.

Adult↗

PubMed2006

Spectral entropy as a measure of hypnosis in children.

BACKGROUND: The Datex-Ohmeda S/5 Entropy Module (Datex-Ohmeda Division, Instrumentarium Corp., Helsinki, Finland), using time-frequency balanced Spectral Entropy, is a novel tool for monitoring the hypnotic state during anesthesia. The Entropy Module produces two values, State Entropy (SE) and Response Entropy (RE), and in adults, it has been shown to measure reliably the hypnotic effects of various drugs. In children, Spectral Entropy has been only preliminary studied. The authors' aim was to study Spectral Entropy as a marker of hypnotic state during general anesthesia in infants and children. METHODS: Twenty infants (aged 1 month-1 yr) and 40 children (aged 1-15 yr) were anesthetized for surgery using standardized sevoflurane-nitrous oxide-based anesthesia. The relationships between SE, RE, or Bispectral Index (BIS) and (1) a modified Observer's Assessment of Alertness/Sedation Scale, (2) non-steady state end-tidal concentration of sevoflurane, (3) steady state end-tidal concentration of sevoflurane, and (4) hemodynamic values were calculated using prediction probability, nonlinear regression, and correlation coefficients, as appropriate. The performances of SE, RE, and BIS were compared. RESULTS: The prediction probability values (+/- SEM) of SE, RE, and BIS versus the modified Observer's Assessment of Alertness/Sedation Scale in the induction phase were 0.83 +/- 0.06, 0.88 +/- 0.06, and 0.87 +/- 0.08 for children and 0.76 +/- 0.08,0.79 +/- 0.08, and 0.73 +/- 0.10 for infants; values in the emergence phase were 0.68 +/- 0.05, 0.74 +/- 0.04, and 0.64 +/- 0.05 for children and 0.64 +/- 0.07, 0.69 +/- 0.06, and 0.72 +/- 0.06 for infants, respectively. SE, RE, and BIS values were inversely proportionally related to the end-tidal concentration of sevoflurane for children, but for infants, the correlation was much less clear. No significant correlations were found between SE, RE, or BIS values and the hemodynamic values. CONCLUSIONS: Spectral Entropy may be a useful tool for measuring the level of hypnosis in anesthetized children and seems to perform as well as BIS. In infants, the clinical usefulness of both these electroencephalogram-derived methods must be evaluated in further controlled studies.

Adolescent↗

PubMed2002

The pigeon's discrimination of visual entropy: a logarithmic function.

We taught 8 pigeons to discriminate 16-icon arrays that differed in their visual variability or "entropy" to see whether the relationship between entropy and discriminative behavior is linear (in which equivalent differences in entropy should produce equivalent changes in behavior) or logarithmic (in which higher entropy values should be less discriminable from one another than lower entropy values). Pigeons received a go/no-go task in which the lower entropy arrays were reinforced for one group and the higher entropy arrays were reinforced for a second group. The superior discrimination of the second group was predicted by a theoretical analysis in which excitatory and inhibitory stimulus generalization gradients fall along a logarithmic, but not a linear scale. Reanalysis of previously published data also yielded results consistent with a logarithmic relationship between entropy and discriminative behavior.

Animals↗

PubMed1997

Backbone entropy of loops as a measure of their flexibility: application to a ras protein simulated by molecular dynamics.

The flexibility of surface loops plays an important role in protein-protein and protein-peptide recognition; it is commonly studied by Molecular Dynamics or Monte Carlo stimulations. We propose to measure the relative backbone flexibility of loops by the difference in their backbone conformational entropies, which are calculated here with the local states (LS) method of Meirovitch. Thus, one can compare the entropies of loops of the same protein or, under certain simulation conditions, of different proteins. These loops should be equal in size but can differ in their sequence of amino acids residues. This methodology is applied successfully to three segments of 10 residues of a Ras protein simulated by the stochastic boundary molecular dynamics procedure. For the first time estimates of backbone entropy differences are obtained, and their correlation with B factors is pointed out; for example, the segments which consist of residues 60-65 and 112-117 have average B factors of 67 and 18 A2, respectively, and entropy difference T delta S = 5.4 +/- 0.1 kcal/mol at T = 300 K. In a large number of recent publications the entropy due to the fast motions (on the ps-ns time scale) of N-H and C-H vectors has been obtained from their order parameter, measured in nuclear magnetic resonance spin relaxation experiments. This enables one to estimate differences in the entropy of protein segments due to folding-unfolding transitions, for example. However, the vectors are assumed to be independent, and the effect of the neglected correlations is unknown; our method is expected to become an important tool for assessing this approximation. The present calculations, obtained with the LS method, suggest that the errors involved in experimental entropy differences might not be large; however, this should be verified in each case. Potential applications of entropy calculations to rational drug design are discussed.

Entropy↗

PubMed1998

Fractal dimension and approximate entropy of heart period and heart rate: awake versus sleep differences and methodological issues.

1. Investigations that assess cardiac autonomic function include non-linear techniques such as fractal dimension and approximate entropy in addition to the common time and frequency domain measures of both heart period and heart rate. This article evaluates the differences in using heart rate versus heart period to estimate fractal dimensions and approximate entropies of these time series.2. Twenty-four-hour ECG was recorded in 23 normal subjects using Holter records. Time series of heart rate and heart period were analysed using fractal dimensions, approximate entropies and spectral analysis for the quantification of absolute and relative heart period variability in bands of ultra low (<0.0033 Hz), very low (0. 0033-0.04 Hz), low (0.04-0.15 Hz) and high (0.15-0.5 Hz) frequency.3. Linear detrending of the time series did not significantly change the fractal dimension or approximate entropy values. We found significant differences in the analyses using heart rate versus heart period between waking up and sleep conditions for fractal dimensions, approximate entropies and absolute spectral powers, especially for the power in the band of 0.0033-0.5 Hz. Log transformation of the data revealed identical fractal dimension values for both heart rate and heart period. Mean heart period correlated significantly better with fractal dimensions and approximate entropies of heart period than did corresponding heart rate measures.4. Studies using heart period measures should take the effect of mean heart period into account even for the analyses of fractal dimension and approximate entropy. As the sleep-awake differences in fractal dimensions and approximate entropies are different between heart rate and heart period, the results should be interpreted accordingly.

Adult↗