A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Mechanical Properties and Failure Mode of Proximal Screw Fixation Technique Using Locking Compression Plate for Proximal Interphalangeal Arthrodesis in Horses: An Ex Vivo Study

OBJECTIVE

 The aim of this study was to measure the mechanical properties and failure mode of an ex vivo model of proximal interphalangeal arthrodesis in horses with different methods of proximal screw fixation using a locking compression plate.

STUDY DESIGN

 Pastern joint arthrodesis with a 3-hole 4.5-mm narrow locking compression plate was performed on 20 forelimbs of equine cadavers, randomized into four groups based on the fixation method and type of proximal screw used: unicortical cortex, bicortical cortex, unicortical locking, bicortical locking. Single-cycle axial compression testing was conducted until failure. The frequency of implant plastic deformation was recorded. Bone failure analysis was performed through computed tomography examinations and fractal analysis.

RESULTS

 There were no differences in the analysed mechanical variables and fractal dimension among the groups. Transarticular screws showed a higher frequency of deformation (75%) regardless of the group. Both unicortical locking and bicortical locking groups deformed the plate more frequently.

CONCLUSION

 The type of screw used in the proximal hole of the locking compression plate and its method of anchoring in the proximal phalanx do not affect the mechanical properties of pastern arthrodesis in equine cadavers subjected to single-cycle axial compression tests until failure.

Symmetry and asymmetry in atherosclerosis

Atherosclerosis remains the main cause of death worldwide. Most important issues concerning atherosclerosis are hemodynamics and how it affects plaque prevalence and distribution, as well as the symmetry and asymmetry of vasculature and plaques. To present the symmetry in the vascular system an analysis of PubMed and MEDLINE databases was performed. As of February 21, 2023, the results were as follows: for "symmetry" AND "atherosclerosis" there were 47 results; for "symmetry" AND "atherosclerotic lesions" - 20 results; for "symmetry" AND "artery stenosis" - 82 results; for "asymmetry" AND "atherosclerosis" - 87 results. Not without meaning are preventive measures. In the light of the Fourth Industrial Revolution artificial intelligence (AI) solutions help to develop new tools outperforming already existing cardiovascular risk scales. The aim of this paper is to present a current view on symmetry within vasculature and atherosclerosis as well as present a new approach to assess individuals' cardiovascular risk in accordance with precision medicine assumptions. Symmetry and asymmetry within the human vascular system play a crucial role in understanding of arterial diseases, including atherosclerosis. Moreover, it is unavoidable to use AI in cardiovascular risk stratification. Int J Occup Med Environ Health. 2023;36(6):693-703.

The Fractal Viewpoint of Tumors and Nanoparticles

Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.

Fractal dimension of the brain in neurodegenerative disease and dementia: A systematic review

Sensitive and specific antemortem biomarkers of neurodegenerative disease and dementia are crucial to the pursuit of effective treatments, required both to reliably identify disease and to track its progression. Atrophy is the structural magnetic resonance imaging (MRI) hallmark of neurodegeneration. However in most cases it likely indicates a relatively advanced stage of disease less susceptible to treatment as some disease processes begin decades prior to clinical onset. Among emerging metrics that characterise brain shape rather than volume, fractal dimension (FD) quantifies shape complexity. FD has been applied in diverse fields of science to measure subtle changes in elaborate structures. We review its application thus far to structural MRI of the brain in neurodegenerative disease and dementia. We identified studies involving subjects who met criteria for mild cognitive impairment, Alzheimer's Disease, Vascular Dementia, Lewy Body Dementia, Frontotemporal Dementia, Amyotrophic Lateral Sclerosis, Parkinson's Disease, Huntington's Disease, Multiple Systems Atrophy, Spinocerebellar Ataxia and Multiple Sclerosis. The early literature suggests that neurodegenerative disease processes are usually associated with a decline in FD of the brain. The literature includes examples of disease-related change in FD occurring independently of atrophy, which if substantiated would represent a valuable advantage over other structural imaging metrics. However, it is likely to be non-specific and to exhibit complex spatial and temporal patterns. A more harmonious methodological approach across a larger number of studies as well as careful attention to technical factors associated with image processing and FD measurement will help to better elucidate the metric's utility.

Myotendinous Junction: Exercise Protocols Can Positively Influence Their Development in Rats

The myotendinous junction (MTJ) is an interface that different stimuli alter their morphology. One of the main stimuli to promote alterations in the MTJ morphology is physical exercise. The present study aimed to investigate the morphology and molecular MTJ adaptations of biceps brachii muscle in adult Wistar rats submitted to different ladder-based protocols. Forty Wistar rats (90 days old) were divided into four groups: Sedentary (S), Climbing (C), Overload Climbing (OC), Climbing, and Overload Climbing (COC). The results of light microscopy demonstrated the cell and collagen tissue reorganization in the experimental groups. The sarcomeres lengths of different regions showed a particular development according to the specific protocols. The sarcoplasmic invaginations and evaginations demonstrated positive increases that promoted the myotendinous interface development. In the extracellular matrix, the structures presented an increase principally in the COC group. Finally, the immunofluorescence analysis showed the telocytes disposition adjacent to the MTJ region in all experimental groups, revealing their network organization. Thus, we concluded that the different protocols contributed to the morphological adaptations with beneficial effects in distinct ways of tissue and cellular development and can be used as a model for MTJ remodeling to future proteomic and genetic analysis.

Control and Anticontrol of chaos in Fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola Virus diseases

This work proposes new fractional-order (FO) models of six chaotic diseases whose fractional dynamics have not been studied so far in literature. Secondly, design and analysis of suitable controllers to control chaos where present, and that of anticontrollers to generate chaos where absent, for these newly proposed FO models of diseases, are put forward. The proposed controllers and anticontrollers address the problem of the health hazards arising from the dysfunctionalities due to the impact of chaos in these biological models. Controllers to supress chaos in four diseases, namely, FO Diabetes Mellitus, FO Human Immunodeficiency Virus (HIV), FO Ebola Virus and FO Dengue models are designed by Back-stepping, Adaptive Feedback and Sliding Mode Control strategies, whereas anticontrollers to introduce chaos in diseases, namely, FO Parkinson's illness and FO Migraine models, are carried out by Linear State Feedback, Single State Sinusoidal Feedback and Sliding Mode Anticontrol strategies. The equilibrium points, eigenvalues and Lyapunov Exponents of the FO disease models are evaluated and indicate the significance of chaos in them and necessitate upon the requirement of controllers and anticontrollers accordingly. The simulation results in terms of bifurcation diagrams, time series plots and phase portraits confirm the successful accomplishment of the control objectives.

Fractal Design Boosts Extrusion-Based 3D Printing of Bone-Mimicking Radial-Gradient Scaffolds

Although extrusion-based three-dimensional (EB-3D) printing technique has been widely used in the complex fabrication of bone tissue-engineered scaffolds, a natural bone-like radial-gradient scaffold by this processing method is of huge challenge and still unmet. Inspired by a typical fractal structure of Koch snowflake, for the first time, a fractal-like porous scaffold with a controllable hierarchical gradient in the radial direction is presented via fractal design and then implemented by EB-3D printing. This radial-gradient structure successfully mimics the radially gradual decrease in porosity of natural bone from cancellous bone to cortical bone. First, we create a design-to-fabrication workflow with embedding the graded data on basis of fractal design into digital processing to instruct the extrusion process of fractal-like scaffolds. Further, by a combination of suitable extruded inks, a series of bone-mimicking scaffolds with a 3-iteration fractal-like structure are fabricated to demonstrate their superiority, including radial porosity, mechanical property, and permeability. This study showcases a robust strategy to overcome the limitations of conventional EB-3D printers for the design and fabrication of functionally graded scaffolds, showing great potential in bone tissue engineering.

Fractal analysis of rat dermal tissue in the different injury states

Scar formation and chronic ulcers can develop following a skin injury. They are the result of the over- or underproduction of collagen. It is very important to evaluate the quality and quantity of the collagen that is produced during wound healing, especially with respect to its structure, as these factors are very important to a complicated outcome. However, there is no standard way to quantitatively analyse dermal collagen. As prior work characterised some potentially fractal properties of collagen, it was hypothesised that collagen structure could be evaluated with fractal dimension analysis. Small-angle X-ray scattering technology (SAXS) was used to evaluate the dermis of rats exposed to graft harvest, burn, and diabetic pathologic states. It was found that almost all collagen structures could be quantitatively measured with fractal dimension analysis. Further, there were significant differences in the three-dimensional (3-D) structure of normal collagen versus that measured in pathologic tissues. There was a significant difference in the 3-D structure of collagen at different stages of healing. The findings of this work suggest that fractal analysis is a good tool for wound healing analysis, and that quantitative collagen analysis is very useful for assessing the structure of dermal collagen.

Adaptive Capacities and Complexity of Heart Rate Variability in Patients With Chronic Obstructive Pulmonary Disease Throughout Pulmonary Rehabilitation

Introduction

The complexity of bio-signals, like R-R intervals, is considered a reflection of the organism's capacity to adapt. However, this association still remains to be consolidated. We investigated whether the complexity of R-R intervals at rest and during perturbation [6-minute walking test (6MWT)], yielded information regarding adaptive capacities in Chronic Obstructive Pulmonary Disease (COPD) patients during pulmonary rehabilitation (PR).

Methods

In total, 23 COPD patients (64 ± 8 years, with forced expiratory volume in 1 s of 55 ± 19% predicted) were tested three times at the start (T1), middle (T2), and end (T3) of 4 weeks PR. Each time, R-R intervals were measured at rest and during 6MWT. The complexity of R-R intervals was assessed by evenly spaced Detrended Fluctuations Analysis and evaluated by the fractal exponent α and deviation from maximal complexity |1-α|.

Results

The 6MWT distance was significantly increased at T2 and T3 compared to T1. Neither α nor |1-α| at rest and during perturbation significantly changed throughout PR, nor were they consistently associated with 6MWT distances at each time. Throughout the PR program, complexity during the 6MWT was significantly lower compared to the rest. The level of α during 6MWT at T1 was positively correlated with the improvement of the 6MWT distance throughout the PR program.

Discussion

Reduced complexity in COPD patients during acute perturbation at the beginning of PR supports a decreased improvement of the 6MWT distance throughout PR. This result seems consistent with the notion that the complexity reflects the patients' adaptive capacities and could therefore become a clinical indicator in an applied perspective.

Morphological Changes in the Motor Endplate and in the Belly Muscle Induced by Previous Static Stretching to the Climbing Protocol

Static stretching provides benefits to the range of motion, modulates intramuscular connective tissue, and is incorporated into warm-up exercises. In this study, we present the effects in the motor endplate and belly muscle resulting from previous static stretching to climbing training. Twenty-four adult male Wistar rats were divided into four groups (n = 6 each): Sedentary (Sed), Climbing (Clb), Static stretching (Ss), and Static stretching prior to climbing (Ssc). The animals (Clb, Ss, and Ssc groups) were subjected to a training protocol 3×/week for 8 weeks, and the Ssc group was subjected to the Ss and Clb protocols in the same session. Samples from the animals were processed for immunostaining, histochemistry, and light microscopy. The Clb group presented a higher motor endplate; the Ss group presented no changes in the motor endplate; and the Ssc group demonstrated a higher compactness. We concluded that static stretching prior to the climbing protocol maintained the density of the motor endplate and increased the compactness of the neuromuscular junction structure. Also, there was a reduction in the myofibers’ diameter (Type I and IIa), an increase in myofibrillar densities (Type I and IIx, and total), and the reorganization of the myonuclei and the interstitium.

Can fractal dimension analysis be used in quantitating collagen structure?

It is well known that collagen tissue, especially the collagen structure, plays an important role in wound healing. However, most research on collagen has been qualitative and morphological, based on sections, and cannot be used for real-time monitoring and clinical prediction. There are no standardized methods of quantitative analysis based on the whole skin sample in three dimensions (3-D). In order to explore a 3-D quantitative analysis, we developed a method that was derived from that of material science and physics, combined with our previous technique, X-ray scattering (SAXS). We hypothesized that the dermis might be analysed by fractal dimensions. To test this hypothesis, we performed the analysis in different pathological conditions, such as scar tissue, different time points after wounding, skin in different degrees of burns and skin in diabetes. The results showed that fractal dimension analysis could detect differences in different locations of the scar tissue, at different time points after wounding, and at a different extent of the severity of skin in diabetes. The research demonstrated that fractal dimension analysis can describe the 3-D structure of the collagen tissue of the skin, which will be beneficial for studying wound healing and finding new clinical treatments.

Drawing Inspiration from Developmental Biology for Cardiac Tissue Engineers

A sound understanding of developmental biology is part of the foundation of effective stem cell-derived tissue engineering. Here, the key concepts of cardiac development that are successfully applied in a bioinspired approach to growing engineered cardiac tissues, are reviewed. The native cardiac milieu is studied extensively from embryonic to adult phenotypes, as it provides a resource of factors, mechanisms, and protocols to consider when working toward establishing living tissues in vitro. It begins with the various cell types that constitute the cardiac tissue. It is discussed how myocytes interact with other cell types and their microenvironment and how they change over time from the embryonic to the adult states, with a view on how such changes affect the tissue function and may be used in engineered tissue models. Key embryonic signaling pathways that have been leveraged in the design of culture media and differentiation protocols are presented. The cellular microenvironment, from extracellular matrix chemical and physical properties, to the dynamic mechanical and electrical forces that are exerted on tissues is explored. It is shown that how such microenvironmental factors can inform the design of biomaterials, scaffolds, stimulation bioreactors, and maturation readouts, and suggest considerations for ongoing biomimetic advancement of engineered cardiac tissues and regeneration strategies for the future.

Controlling chaos by the system size

Despite the ubiquity of physical systems evolving on time-dependent spatial domains, understanding their regular and chaotic dynamics is still in a rudimentary state. While chaos implies that the system's behavior can be altered by small perturbations, this sensitivity proves to be useful for control purposes. Here we report on the experimental discovery of a novel mechanism to control chaos by time-variation of the system (spatial domain) size: depending upon the rate of the latter, the chaotic state may be completely prevented. Our experimental observations are disentangled with theoretical insights and numerical modeling, which also reveals the ability to control spatio-temporal chaos, thus making the findings relevant to a wide range of natural phenomena.

Period-doubling bifurcation analysis and chaos control for load torque using FLC

Chaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.