Unique algorithm for the evaluation of embryo photon emission and viability.

Living cells have spontaneous ultraweak photon emission derived from metabolic reactions associated with physiological conditions. The ORCA-Quest CMOS camera (Hamamatsu Photonics, Japan) is a highly sensitive and essential tool for photon detection; its use with a microscope incubator (Olympus) enables the detection of photons emitted by embryos with the exclusion of harmful visible light. With the application of the second law of thermodynamics, the low-entropy energy absorbed and used by embryos can be distinguished from the higher-entropy energy released and detectable in their environment. To evaluate higher-entropy energy data from embryos, we developed a unique algorithm for the calculation of the entropy-weighted spectral fractal dimension, which demonstrates the self-similar structure of the energy (photons) released by embryos. Analyses based on this structure enabled the distinction of living and degenerated mouse embryos, and of frozen and fresh embryos and the background. This novel detection of ultra-weak photon emission from mouse embryos can provide the basis for the development of a photon emission embryo control system. The ultraweak photon emission fingerprints of embryos may be used for the selection of viable specimens in an ideal dark environment.

Characterization of antiseizure medications effects on the EEG neurodynamic by fractal dimension.

Objectives: An important challenge in epilepsy is to define biomarkers of response to treatment. Many electroencephalography (EEG) methods and indices have been developed mainly using linear methods, e.g., spectral power and individual alpha frequency peak (IAF). However, brain activity is complex and non-linear, hence there is a need to explore EEG neurodynamics using nonlinear approaches. Here, we use the Fractal Dimension (FD), a measure of whole brain signal complexity, to measure the response to anti-seizure therapy in patients with Focal Epilepsy (FE) and compare it with linear methods. Materials: Twenty-five drug-responder (DR) patients with focal epilepsy were studied before (t1, named DR-t1) and after (t2, named DR-t2) the introduction of the anti-seizure medications (ASMs). DR-t1 and DR-t2 EEG results were compared against 40 age-matched healthy controls (HC). Methods: EEG data were investigated from two different angles: frequency domain-spectral properties in δ, θ, α, ß, and γ bands and the IAF peak, and time-domain-FD as a signature of the nonlinear complexity of the EEG signals. Those features were compared among the three groups. Results: The δ power differed between DR patients pre and post-ASM and HC (DR-t1 vs. HC, p < 0.01 and DR-t2 vs. HC, p < 0.01). The θ power differed between DR-t1 and DR-t2 (p = 0.015) and between DR-t1 and HC (p = 0.01). The α power, similar to the δ, differed between DR patients pre and post-ASM and HC (DR-t1 vs. HC, p < 0.01 and DR-t2 vs. HC, p < 0.01). The IAF value was lower for DR-t1 than DR-t2 (p = 0.048) and HC (p = 0.042). The FD value was lower in DR-t1 than in DR-t2 (p = 0.015) and HC (p = 0.011). Finally, Bayes Factor analysis showed that FD was 195 times more likely to separate DR-t1 from DR-t2 than IAF and 231 times than θ. Discussion: FD measured in baseline EEG signals is a non-linear brain measure of complexity more sensitive than EEG power or IAF in detecting a response to ASMs. This likely reflects the non-oscillatory nature of neural activity, which FD better describes. Conclusion: Our work suggests that FD is a promising measure to monitor the response to ASMs in FE.

Scaling features in high-concentrations PM2.5 evolution: the Ignored factor affecting scarlet fever incidence.

As an acute respiratory disease, scarlet fever has great harm to public health. Some evidence indicates that the time distribution pattern of heavy PM2.5 pollution occurrence may have an impact on health risks. This study aims to reveal the relation between scaling features in high-concentrations PM2.5 (HC-PM2.5) evolution and scarlet fever incidence (SFI). Based on the data of Hong Kong from 2012 to 2019, fractal box-counting dimension (D) is introduced to capture the scaling features of HC-PM2.5. It has been found that index D can quantify the time distribution of HC-PM2.5, and lower D values indicate more cluster distribution of HC-PM2.5. Moreover, scale-invariance in HC-PM2.5 at different time scales has been discovered, which indicates that HC-PM2.5 occurrence is not random but follows a typical power-law distribution. Next, the exposure-response relationship between SFI and scale-invariance in HC-PM2.5 is explored by Distributed lag non-linear model, in conjunction with meteorological factors. It has been discovered that scale-invariance in HC-PM2.5 has a nonlinear effect on SFI. Low and moderate D values of HC-PM2.5 are identified as risk factors for SFI at small time-scale. Moreover, relative risk shows a decreasing trend with the increase of exposure time. These results suggest that exposure to short-term clustered HC-PM2.5 makes individual more prone to SFI than exposure to long-term uniform HC-PM2.5. This means that individuals in slightly-polluted regions may face a greater risk of SFI, once the PM2.5 concentration keeps rising. In the future, it is expected that the relative risk of scarlet fever for a specific region can be estimated based on the quantitative analysis of scaling features in high-concentrations PM2.5 evolution.

Banana fruit bruise detection using fractal dimension based image processing.

The study used the fractal dimension (FD), browning incidence, and grayscale values using machine vision to describe the bruise magnitude and quality of mechanically damaged 'Fard' bananas bruised from 20, 40, 60 cm drop heights by 66, 98, and 110 g ball weights conditioned at different storage temperatures (5, 13, 22 °C) after 48 h. Conventional analyses like bruise area (BA), bruise volume (BV), and bruise susceptibility (BS) were also conducted. A correlation was performed to determine the relationship between image processing and conventional assessment of bruise damage in bananas. Weight, firmness, color, sugar content, and acidity were investigated. The results demonstrated that bananas bruised from the highest force and stored at 5 and 22 °C reported the lowest FD with values of 1.7162 and 1.7403, respectively. Increasing the level of damage reduced the fractal dimension and grayscale values and increased browning incidence and bruise susceptibility values after 48 h of storage. The total color change values showed a strong Pearson's correlation coefficient (r≥-0.81) with image analysis fractal dimension and grayscale values. The findings also indicated that higher bruising and temperature can induce weight loss, firmness reduction, lightness, and yellowness increment, and sugar and acidity changes. Overall, the fractal image analysis conducted in this study was highly effective in describing the bruising magnitude of bananas under different conditions.

Development, Application and Utility of a Machine Learning Approach for Melanoma and Non-Melanoma Lesion Classification Using Counting Box Fractal Dimension.

The diagnosis and identification of melanoma are not always accurate, even for experienced dermatologists. Histopathology continues to be the gold standard, assessing specific parameters such as the Breslow index. However, it remains invasive and may lack effectiveness. Therefore, leveraging mathematical modeling and informatics has been a pursuit of diagnostic methods favoring early detection. Fractality, a mathematical parameter quantifying complexity and irregularity, has proven useful in melanoma diagnosis. Nonetheless, no studies have implemented this metric to feed artificial intelligence algorithms for the automatic classification of dermatological lesions, including melanoma. Hence, this study aimed to determine the combined utility of fractal dimension and unsupervised low-computational-requirements machine learning models in classifying melanoma and non-melanoma lesions. We analyzed 39,270 dermatological lesions obtained from the International Skin Imaging Collaboration. Box-counting fractal dimensions were calculated for these lesions. Fractal values were used to implement classification methods by unsupervised machine learning based on principal component analysis and iterated K-means (100 iterations). A clear separation was observed, using only fractal dimension values, between benign or malignant lesions (sensibility 72.4% and specificity 50.1%) and melanoma or non-melanoma lesions (sensibility 72.8% and specificity 50%) and subsequently, the classification quality based on the machine learning model was ≈80% for both benign and malignant or melanoma and non-melanoma lesions. However, the grouping of metastatic melanoma versus non-metastatic melanoma was less effective, probably due to the small sample size included in MM lesions. Nevertheless, we could suggest a decision algorithm based on fractal dimension for dermatological lesion discrimination. On the other hand, it was also determined that the fractal dimension is sufficient to generate unsupervised artificial intelligence models that allow for a more efficient classification of dermatological lesions.

Effect of Thermal Activation on the Structure and Electrochemical Properties of Carbon Material Obtained from Walnut Shells.

A simple activation method has been used to obtain porous carbon material from walnut shells. The effect of the activation duration at 400 °C in an atmosphere with limited air access on the structural, morphological, and electrochemical properties of the porous carbon material obtained from walnut shells has been studied. Moreover, the structure and morphology of the original and activated carbon samples have been characterized by SAXS, low-temperature adsorption porosimetry, SEM, and Raman spectroscopy. Therefore, the results indicate that increasing the duration of activation at a constant temperature results in a reduction in the thickness values of interplanar spacing (d002) in a range of 0.38-0.36 nm and lateral dimensions of the graphite crystallite from 3.79 to 2.52 nm. It has been demonstrated that thermal activation allows for an approximate doubling of the specific SBET surface area of the original carbon material and contributes to the development of its mesoporous structure, with a relative mesopore content of approximately 75-78% and an average pore diameter of about 5 nm. The fractal dimension of the obtained carbon materials was calculated using the Frenkel-Halsey-Hill method; it shows that its values for thermally activated samples (2.52, 2.69) are significantly higher than for the original sample (2.17). Thus, the porous carbon materials obtained were used to fabricate electrodes for electrochemical capacitors. Electrochemical investigations of these cells in a 6 M KOH aqueous electrolyte were conducted by cyclic voltammetry, galvanostatic charge/discharge, and impedance spectroscopy. Consequently, it was established that the carbon material activated at 400 °C for 2 h exhibits a specific capacity of approximately 110-130 F/g at a discharge current density ranging from 4 to 100 mA/g.

Research on the dynamic tensile characteristics and surface crack evolution of coal under impact loading.

The tensile properties of coal under dynamic loading are important mechanical characteristics of coal and are highly important for controlling coal rock stability under impact loading conditions, selecting blasting engineering parameters, and studying the mechanism of rockburst disasters. To investigate the dynamic tensile failure process of coal subjected to impact loading, this study used high-speed photography and digital image correlation technology to capture the dynamic tensile failure of coal under impact loading. The dynamic tensile evolution was quantitatively analyzed from the beginning of coal sample being loaded to failure. The captured images of the coal were processed, and the fractal dimension was used to quantitatively describe the evolution of the coal surface cracks under impact loading. The following conclusions were drawn from the experimental results: (1) An empirical formula was established to describe the dynamic tensile strength characteristics of coal under different loading rates. (2) Under impact loading, the maximum strain of a Brazilian disc coal sample first appeared at the contact end between the sample and the incident rod. (3) Under impact loading, a Brazilian disc coal sample cracked from the center of the sample outward, and the crack subsequently extended toward both ends. The fractal dimension of the crack exhibited a power function relationship with time, and the variation range of the fractal dimension of the crack was 1.05-1.39.

Experimental study on fractal dimension of energy dissipation and crack growth in saturated tuff at different strain rates.

In order to investigate the effects of strain rate and water saturation on the energy dissipation and crack growth of tuff, uniaxial compression tests were carried out on dry and water saturated tuff with different strain rates using an electro-hydraulic servo press and a 50 mm diameter split Hopkinson pressure rod (SHPB) device. High-speed camera and Image J image analysis software were used to obtain the crack growth process of the specimen under impact load, and fractal dimension was introduced to quantitatively study the crack growth degree. The results show that more than 90% of the energy is stored in the specimen as elastic energy when it reaches the peak stress under static load. The average total energy of water-saturated specimens is 67.55% of that of dry specimens. The average energy dissipation density of water-saturated specimens under 0.3 MPa, 0.4 MPa and 0.5 MPa air pressure is 0.79, 0.91 and 0.92 times of that of dry specimens, respectively. Water-saturated specimens will deteriorate and thus reduce their energy storage and energy absorption effects. The reflected energy, transmitted energy, absorbed energy and incident energy are linear, logarithmic and linear functions, respectively, and the energy absorptivity and specific energy absorptivity of water-saturated specimens are lower than those of dry specimens. Due to the existence of "stefan" effect, the increase of energy dissipation density of water-saturated specimen at high strain rate is greater than that of dry specimen. The mean fractal dimension of water-saturated specimens under 0.3 MPa, 0.4 MPa and 0.5 MPa is 1.09, 1.05 and 1.16 times that of dry specimens. At the same strain rate, the number and width of cracks in water-saturated specimens are larger than that in dry specimens. Water-saturated behavior reduces the energy absorption capacity of tuff, increases the fractal dimension of crack growth, and significantly reduces the resistance of water-saturated rock to external loads.

Accurate identification of individuals with subjective cognitive decline using 3D regional fractal dimensions on structural magnetic resonance imaging.

BACKGROUND AND OBJECTIVE: Accurate identification of individuals with subjective cognitive decline (SCD) is crucial for early intervention and prevention of neurodegenerative diseases. Fractal dimensionality (FD) has emerged as a robust and replicable measure, surpassing traditional geometric metrics, in characterizing the intricate fractal geometrical properties of brain structure. Nevertheless, the effectiveness of FD in identifying individuals with SCD remains largely unclear. A 3D regional FD method can be suggested to characterize and quantify the spatial complexity of the precise gray matter, providing insights into cognitive aging and aiding in the automated identification of individuals with SCD. METHODS: This study introduces a novel integer ratio based 3D box-counting fractal analysis (IRBCFA) to quantify regional fractal dimensions (FDs) in structural magnetic resonance imaging (MRI) data. The innovative method overcomes limitations of conventional box-counting techniques by accommodating arbitrary box sizes, thereby enhancing the precision of FD estimation in small, yet neurologically significant, brain regions. RESULTS: The application of IRBCFA to two publicly available datasets, OASIS-3 and ADNI, consisting of 520 and 180 subjects, respectively. The method identified discriminative regions of interest (ROIs) predominantly within the limbic system, fronto-parietal region, occipito-temporal region, and basal ganglia-thalamus region. These ROIs exhibited significant correlations with cognitive functions, including executive functioning, memory, social cognition, and sensory perception, suggesting their potential as neuroimaging markers for SCD. The identification model trained on these ROIs demonstrated exceptional performance achieving over 93 % accuracy on the discovery dataset and exceeding 87 % on the independent testing dataset. Furthermore, an exchange experiment between datasets revealed a substantial overlap in discriminative ROIs, highlighting the robustness of our method across diverse populations. CONCLUSION: Our findings indicate that IRBCFA can serve as a valuable tool for quantifying the spatial complexity of gray matter, providing insights into cognitive aging and aiding in the automated identification of individuals with SCD. The demonstrated generalizability and robustness of this method position it as a promising tool for neurodegenerative disease research and offer potential for clinical applications.

Mechanical Properties and Stress-Strain Relationship of PVA-Fiber-Reinforced Engineered Geopolymer Composite.

In this study, seven Engineering Geopolymer Composite (EGC) groups with varying proportions were prepared. Rheological, compressive, flexural, and axial tensile tests of the EGC were conducted to study the effects of the water/binder ratio, the cement/sand ratio, and fiber type on its properties. Additionally, a uniaxial tension constitutive model was established. The results indicate that the EGC exhibits early strength characteristics, with the 7-day compressive strength reaching 80% to 92% of the 28-day compressive strength. The EGC demonstrates high compressive strength and tensile ductility, achieving up to 70 MPa and 4%, respectively. The mechanical properties of the EGC improved with an increase in the sand/binder ratio and decreased with an increase in the water/binder ratio. The stress-strain curve of the EGC resembles that of the ECC, displaying a strain-hardening state that can be divided into two stages: before cracking, the matrix primarily bears the stress; after cracking, the slope decreases, and the fiber predominantly bears the stress.

Robust arterial compliance estimation with Katz's fractal dimension of photoplethysmography.

Arterial compliance (AC) plays a crucial role in vascular aging and cardiovascular disease. The ability to continuously estimate aortic AC or its surrogate, pulse pressure (PP), through wearable devices is highly desirable, given its strong association with daily activities. While the single-site photoplethysmography (PPG)-derived arterial stiffness indices show reasonable correlations with AC, they are susceptible to noise interference, limiting their practical use. To overcome this challenge, our study introduces a noise-resistant indicator of AC: Katz's fractal dimension (KFD) of PPG signals. We showed that KFD integrated the signal complexity arising from compliance changes across a cardiac cycle and vascular structural complexity, thereby decreasing its dependence on individual characteristic points. To assess its capability in measuring AC, we conducted a comprehensive evaluation using both in silico studies with 4374 virtual human data and real-world measurements. In the virtual human studies, KFD demonstrated a strong correlation with AC (r = 0.75), which only experienced a slight decrease to 0.66 at a signal-to-noise ratio of 15dB, surpassing the best PPG-morphology-derived AC measure (r = 0.41) under the same noise condition. In addition, we observed that KFD's sensitivity to AC varied based on the individual's hemodynamic status, which may further enhance the accuracy of AC estimations. These in silico findings were supported by real-world measurements encompassing diverse health conditions. In conclusion, our study suggests that PPG-derived KFD has the potential to continuously and reliably monitor arterial compliance, enabling unobtrusive and wearable assessment of cardiovascular health.

Nonlinear dynamics of postural control system under visual-vestibular habituation balance practice: evidence from EEG, EMG and center of pressure signals.

Human postural control system is inherently complex with nonlinear interaction among multiple subsystems. Accordingly, such postural control system has the flexibility in adaptation to complex environments. Previous studies applied complexity-based methods to analyze center of pressure (COP) to explore nonlinear dynamics of postural sway under changing environments, but direct evidence from central nervous system or muscular system is limited in the existing literature. Therefore, we assessed the fractal dimension of COP, surface electromyographic (sEMG) and electroencephalogram (EEG) signals under visual-vestibular habituation balance practice. We combined a rotating platform and a virtual reality headset to present visual-vestibular congruent or incongruent conditions. We asked participants to undergo repeated exposure to either congruent (n = 14) or incongruent condition (n = 13) five times while maintaining balance. We found repeated practice under both congruent and incongruent conditions increased the complexity of high-frequency (0.5-20 Hz) component of COP data and the complexity of sEMG data from tibialis anterior muscle. In contrast, repeated practice under conflicts decreased the complexity of low-frequency (<0.5 Hz) component of COP data and the complexity of EEG data of parietal and occipital lobes, while repeated practice under congruent environment decreased the complexity of EEG data of parietal and temporal lobes. These results suggested nonlinear dynamics of cortical activity differed after balance practice under congruent and incongruent environments. Also, we found a positive correlation (1) between the complexity of high-frequency component of COP and the complexity of sEMG signals from calf muscles, and (2) between the complexity of low-frequency component of COP and the complexity of EEG signals. These results suggested the low- or high-component of COP might be related to central or muscular adjustment of postural control, respectively.

Evaluation of mandibular trabecular bone structure in growing children with Class I, II, and III malocclusions using fractal analysis: A retrospective study.

OBJECTIVE: The present study aimed to evaluate the mandibular bone structure of patients with different malocclusions by using fractal dimension (FD) analysis on dental panoramic radiographic images. MATERIAL AND METHODS: Pre-treatment panoramic radiographic images of 103 patients were included in the study and divided into 3 groups as Class I (group 1: 0

Study on energy evolution and fractal characteristics of sandstone with different fracture dip angles under uniaxial compression.

In order to investigate the failure modes and instability mechanism of fractured rock. Uniaxial compression tests were conducted on sandstone specimens with different dip angles. Based on rock energy dissipation theory and fractal theory, the energy evolution characteristics and fragmentation fractal characteristics in the process of deformation and failure of specimens were analyzed. The results show that the peak strength and elastic modulus of fractured rock mass are lower than those of intact samples, and both show an exponential increase with the increase of fracture dip angle. The energy evolution laws of different fracture specimens are roughly similar and can be classified into four stages based on the stress-strain curve: pressure-tight, elastic, plastic, and post-destructive. The total strain energy, elastic strain energy, and dissipated strain energy of the specimen at the peak stress point increased exponentially with crack inclination, and the dissipated strain energy and compressive strength conformed to a power function growth relationship. The distribution of the fragments after the failure of the fracture sample has fractal characteristics, and the fractal dimension increases with the increase of the fracture dip angle. In addition, the higher the compressive strength of the specimen, the greater the energy dissipation, the more serious the degree of fragmentation, and the greater the fractal dimension. The data fitting further shows that there is a power function relationship between the dissipated strain energy and the fractal dimension. The research results can provide a theoretical basis for the stability of rock mass engineering and structural deformation control.

The Pathologically Evolving Aggregation-State of Cells in Cancerous Tissues as Interpreted by Fractal and Multi-Fractal Dispersion Theory in Saturated Porous Formations.

A recent author's fractal fluid-dynamic dispersion theory in porous media has focused on the derivation of the associated nonergodic (or effective) macrodispersion coefficients by a 3-D stochastic Lagrangian approach. As shown by the present study, the Fickian (i.e., the asymptotic constant) component of a properly normalized version of these coefficients exhibits a clearly detectable minimum in correspondence with the same fractal dimension (d ≅ 1.7) that seems to characterize the diffusion-limited aggregation state of cells in advanced stages of cancerous lesion progression. That circumstance suggests that such a critical fractal dimension, which is also reminiscent of the colloidal state of solutions (and may therefore identify the microscale architecture of both living and non-living two-phase systems in state transition conditions) may actually represent a sort of universal nature imprint. Additionally, it suggests that the closed-form analytical solution that was provided for the effective macrodispersion coefficients in fractal porous media may be a reliable candidate as a physically-based descriptor of blood perfusion dynamics in healthy as well as cancerous tissues. In order to evaluate the biological meaningfulness of this specific fluid-dynamic parameter, a preliminary validation is performed by comparison with the results of imaging-based clinical surveys. Moreover, a multifractal extension of the theory is proposed and discussed in view of a perspective interpretative diagnostic utilization.

Dynamic mechanical response and failure characteristics of coal and rock under saltwater immersion conditions.

The stability of coal and rock masses in water-rich mines is affected by both mine water erosion and dynamic disturbances. Thus, it is necessary to study the dynamic mechanical response and failure characteristics of coal and rock under the combination of saltwater and a high strain rate. To this end, a split Hopkinson pressure bar device was employed to investigate the effects of impact velocity, water content, and immersion liquid on the dynamic mechanical behaviours of coal and rock. The results revealed that the weakening effect of saltwater on the dynamic mechanical properties of coal and rock is much greater than that of distilled water. With increasing moisture content, the dynamic compressive strength of the coal specimens decreases monotonically, while that of the rock shows a trend of first increasing and then decreasing. The failure process and destruction of coal and rock are comprehensively affected by both the external impact load and the physical and mechanical properties of the material. The degree of damage of the coal and rock specimens increases with increasing impact velocity and water content. Moreover, the influence of various factors on the impact fracture mechanism of coal and rock under saltwater immersion conditions was revealed. These findings are highly important for the design and maintenance of underground coal and rock building structures.

Use of fractals in determining the malignancy degree of lung nodules.

Introduction: A Computer-Assisted Detection (CAD) System for classification into malignant-benign classes using CT images is proposed. Methods: Two methods that use the fractal dimension (FD) as a measure of the lung nodule contour irregularities (Box counting and Power spectrum) were implemented. The LIDC-IDRI database was used for this study. Of these, 100 slices belonging to 100 patients were analyzed with both methods. Results: The performance between both methods was similar with an accuracy higher than 90%. Little overlap was obtained between FD ranges for the different malignancy grades with both methods, being slightly better in Power spectrum. Box counting had one more false positive than Power spectrum. Discussion: Both methods are able to establish a boundary between the high and low malignancy degree. To further validate these results and enhance the performance of the CAD system, additional studies will be necessary.

Enhancing Concrete Mechanical Properties through Basalt Fibers and Calcium Sulfate Whiskers: Optimizing Compressive Strength, Elasticity, and Pore Structure.

To study the effects of basalt fibers (BFs), calcium sulfate whiskers (CSWs), and modified calcium sulfate whiskers (MCSWs) on the compressive strength and dynamic modulus of elasticity of concrete, this paper utilizes Mercury Intrusion Porosimetry (MIP) to measure the microstructure of concrete and calculate the fractal dimension of pore surface area. The results indicate that both CSWs and BFs can increase the compressive strength of concrete. CSWs can enhance the dynamic modulus of elasticity of concrete, while the effect of BFs on the dynamic modulus of elasticity is not significant. The improvement in compressive strength and dynamic modulus of elasticity provided by MCSWs is significantly greater than that provided by CSWs. Both CSWs and BFs can effectively improve the pore structure of concrete and have a significant impact on the surface fractal dimension. CSWs inhibit the formation of ink-bottle pores, while BFs increase the number of ink-bottle pores. Due to the ink-bottle pore effect, the fractal dimension of the capillary pore surface is generally greater than three, lacking fractal characteristics. The compressive strength and dynamic modulus of elasticity of concrete have a good correlation with the fractal dimensions of large pores and transition pores.

Time-dependent complexity characterisation of activity patterns in patients with Chronic Fatigue Syndrome.

BACKGROUND: Chronic Fatigue Syndrome patients suffer from symptoms that cannot be explained by a single underlying biological cause. It is sometimes claimed that these symptoms are a manifestation of a disrupted autonomic nervous system. Prior works studying this claim from the complex adaptive systems perspective, have observed a lower average complexity of physical activity patterns in chronic fatigue syndrome patients compared to healthy controls. To further study the robustness of such methods, we investigate the within-patient changes in complexity of activity over time. Furthermore, we explore how these changes might be related to changes in patient functioning. METHODS: We propose an extension of the allometric aggregation method, which characterises the complexity of a physiological signal by quantifying the evolution of its fractal dimension. We use it to investigate the temporal variations in within-patient complexity. To this end, physical activity patterns of 7 patients diagnosed with chronic fatigue syndrome were recorded over a period of 3 weeks. These recordings are accompanied by physicians' judgements in terms of the patients' weekly functioning. RESULTS: We report significant within-patient variations in complexity over time. The obtained metrics are shown to depend on the range of timescales for which these are evaluated. We were unable to establish a consistent link between complexity and functioning on a week-by-week basis for the majority of the patients. CONCLUSIONS: The considerable within-patient variations of the fractal dimension across scales and time force us to question the utility of previous studies that characterise long-term activity signals using a single static complexity metric. The complexity of a Chronic Fatigue Syndrome patient's physical activity signal does not suffice to characterise their high-level functioning over time and has limited potential as an objective monitoring metric by itself.