Toe Joint Research Articles

Transcutaneous auricular vagus nerve stimulation mitigates gouty inflammation by reducing neutrophil infiltration in BALB/c mice

Gouty inflammation, caused by uric acid crystal deposition, primarily affects tissues around the toe joints and triggers potent inflammatory responses. Current treatments focus on alleviating inflammation and pain using pharmaceutical agents, which can lead to side effects and complications. This has generated interest in non-pharmacological interventions, such as non-invasive vagus nerve stimulation (VNS). In this study, we explored the anti-inflammatory mechanisms of transcutaneous auricular vagus nerve stimulation (taVNS) in a mouse model of acute gout. Gouty inflammation was induced by injecting monosodium urate (MSU) crystals into the ankle joints of BALB/c mice. The effects of taVNS on the expression of inflammatory cytokines and chemokines in the ankle joint tissue were assessed using real-time quantitative PCR (qPCR), western blotting, histological assessments (H&E staining), and immunohistochemistry (IHC). The role of α7 nicotinic acetylcholine receptors (α7nAChR) was also evaluated by signal blocking. Our findings revealed that MSU significantly elevated gout-associated inflammatory cascades and mediators in the ankle joint. Notably, taVNS at 200 µA and 25 Hz effectively reduced these inflammatory responses, decreasing neutrophil infiltration and chemoattraction within the tissue. taVNS showed significant anti-inflammatory properties by suppressing neutrophil activity, offering a novel therapeutic approach for gout beyond conventional pharmacological methods. Additionally, taVNS holds potential for managing various chronic joint diseases. These results highlight taVNS as a promising non-pharmacological therapy for chronic inflammation.

Cochrane Corner

The Cochrane Collaboration has produced three new reviews relevant to bone and joint surgery since the publication of the last Cochrane Corner. These are relevant to a wide range of musculoskeletal specialists, and include reviews in lateral elbow pain, osteoarthritis of the big toe joint, and cervical spine injury in paediatric trauma patients.

The diabetic sausage toe: Prevalence, presentation and outcomes.

Osteomyelitis (OM) in diabetic foot infection could have many presentations such as an infected ulcer spreading to the bone or superimposed to Charcot neuroarthropathy. However, the sausage toe as a diabetic OM presentation was very rarely investigated; therefore, this study aims to assess the prevalence and signs of this presentation along with treatment modalities and outcomes. This is a retrospective series of patients presenting a sausage toe on admission. Several methods were conducted to diagnose OM, and three treatment modalities were applied. Two groups were compared: acute and chronic sausage toes. Outcomes were defined as sausage toe prevalence, ulcer location, OM prevalence, and comparative treatment results. Out of 82 diabetic toe infection cases, 24 (30%) presented as 'sausage toe'. The side of the proximal interphalangeal joint of the lateral toes was the most frequent ulcer location (50%), mostly on the dorsal aspect followed by the side aspect. There were 15 (62.5%) acute cases and 9 (37.5%) chronic cases. MRI showed signs of OM in 21 (87.5%) cases and signs of septic arthritis in 3 (12.5%) cases. At the final follow-up, a successful treatment was recorded in five (20%) cases with antibiotics alone. Out of the 19 (42%) procedures, conservative surgery was performed successfully in 8 (58%) cases while amputation was needed in 11 (45.8%) cases. There was no significant difference in amputation frequency between acute and chronic groups. This is the first study documenting the sausage toe as a prevalent presentation of diabetic toe infection. The deformity is conclusive of deep infection with a very high osteomyelitis frequency. Surgery is often required for infection control and healing, mainly for chronic cases, and treatment outcomes did not differ between acute and chronic sausage toe groups. It could be beneficial to include this entity in the diabetic wound classification systems.

The effect of including a mobile arch, toe joint, and joint coupling on predictive neuromuscular simulations of human walking

Predictive neuromuscular simulations are a powerful tool for studying the biomechanics of human walking, and deriving design criteria for technical devices like prostheses or biorobots. Good agreement between simulation and human data is essential for transferability to the real world. The human foot is often modeled with a single rigid element, but knowledge of how the foot model affects gait prediction is limited. Standardized procedures for selecting appropriate foot models are lacking. We performed 2D predictive neuromuscular simulations with six different foot models of increasing complexity to answer two questions: What is the effect of a mobile arch, a toe joint, and the coupling of toe and arch motion through the plantar fascia on gait prediction? and How much of the foot’s anatomy do we need to model to predict sagittal plane walking kinematics and kinetics in good agreement with human data? We found that the foot model had a significant impact on ankle kinematics during terminal stance, push-off, and toe and arch kinematics. When focusing only on hip and knee kinematics, rigid foot models are sufficient. We hope our findings will help guide the community in modeling the human foot according to specific research goals and improve neuromuscular simulation accuracy.

Squat and tuck jump maneuver for single-legged robot with an active toe joint using model-free deep reinforcement learning

Squat and tuck jump maneuver for single-legged robot with an active toe joint using model-free deep reinforcement learning

Non-surgical interventions for treating osteoarthritis of the big toe joint.

Non-surgical interventions for treating osteoarthritis of the big toe joint.

Intrinsic toe joint stabilization in foot-slip turning motion of musculoskeletal robot with DSP-SLIP model

This paper introduces the foot-slip turning motion by combining a slider-like mechanism with the double-support parallel spring-loaded inverted pendulum model, in which the musculoskeletal robot uses the model to simplify the slip-turning motion with its compliant structure and utilizes the foot muscle to improve its postural stability. The slip-turning motion, characterized by slight movements for swift turning via foot slippage, is advantageous for musculoskeletal robots due to their limited range of movement. The challenge lies in the reduced support area during the motion, which impacts stability. In our previous study, the robot ‘PneuTurn-T’ successfully executed said motion, whereas the details of the turning mechanism were lacking. This study investigated the utilization of leg compliance in the motion and its static postural stability in the landing stance. Experimental results exhibited a leg compression rate derived from the collected data in the early phase of the motion and validated intrinsic toe joint stabilization with foot muscle for passive postural control. The ground reaction force proves the capability to maintain the posture for 130% longer in the foot with plantar intrinsic muscle. Despite structural challenges, this approach shows promise for musculoskeletal robots, highlighting their ability to handle a turning task with simple control.

#2387 Case study of a patient with gouty nephropathy treated with immunosorbent therapy

Abstract Background and Aims Gouty nephropathy is a kidney disease caused by chronic hyperuricemia, in which uric acid crystals are deposited in the kidneys leading to tubular and glomerular damage, which in turn affects kidney function. Patient female, 68 years old, 7 years ago, no obvious cause of the first toe joint of the right foot, the right ankle joint redness, swelling and pain, the local skin temperature increases, serious limitation of activities, had checked the high uric acid (specific unknown), diagnosed as “gout”, simple treatment after the symptoms are relieved, but did not have systematic treatment, and gradually appeared in the left foot, the first toe joint, the left ankle joint, double knee joint redness, swelling and pain, oral pain medication treatment, pain disappears after still no systematic treatment. After that, redness, swelling and pain appeared gradually in the first toe joint of the left foot, left ankle joint and both knee joints, and the pain disappeared without systematic treatment after taking pain-relieving medicines. He was admitted to our hospital as an outpatient with the diagnosis of “gout”. Method Immunosorbent therapy was given once/day on days 1-3, along with Jinshuibao and urotoxin clearing granules. Immunosorbent therapy was given again three times on the 8th-10th day of admission. Results Before admission, uric acid: 899.3 µmol/L; creatinine: 586.1 µmol/L, both seriously out of the normal range. 3 days later, uric acid: 770.4 µmol/L, creatinine: 468.7 µmol/L. At the time of discharge, serum uric acid: 298.5 µmol/L and creatinine: 182.6 µmol/L were detected and restored to the normal range. Conclusion The case demonstrated the presence of gout with arthritic symptoms, vascular damage, anemia, and hepatic and renal impairment. The patient's gout progressively worsened due to prolonged absence of systemic treatment. After admission, the levels of uric acid and creatinine were effectively controlled and restored by immunosorbent therapy. This indicates that immunosorbent therapy plays a positive role in removing uric acid from the body and improving renal function. Meanwhile, the management and control of gout was further strengthened by combining the comprehensive treatment with Jinshuibao and uremic acid granules.

Biomechanical effects of adding an articulating toe joint to a passive foot prosthesis for incline and decline walking.

Walking on sloped surfaces is challenging for many lower limb prosthesis users, in part due to the limited ankle range of motion provided by typical prosthetic ankle-foot devices. Adding a toe joint could potentially benefit users by providing an additional degree of flexibility to adapt to sloped surfaces, but this remains untested. The objective of this study was to characterize the effect of a prosthesis with an articulating toe joint on the preferences and gait biomechanics of individuals with unilateral below-knee limb loss walking on slopes. Nine active prosthesis users walked on an instrumented treadmill at a +5° incline and -5° decline while wearing an experimental foot prosthesis in two configurations: a Flexible toe joint and a Locked-out toe joint. Three participants preferred the Flexible toe joint over the Locked-out toe joint for incline and decline walking. Eight of nine participants went on to participate in a biomechanical data collection. The Flexible toe joint decreased prosthesis Push-off work by 2 Joules during both incline (p = 0.008; g = -0.63) and decline (p = 0.008; g = -0.65) walking. During incline walking, prosthetic limb knee flexion at toe-off was 3° greater in the Flexible configuration compared to the Locked (p = 0.008; g = 0.42). Overall, these results indicate that adding a toe joint to a passive foot prosthesis has relatively small effects on joint kinematics and kinetics during sloped walking. This study is part of a larger body of work that also assessed the impact of a prosthetic toe joint for level and uneven terrain walking and stair ascent/descent. Collectively, toe joints do not appear to substantially or consistently alter lower limb mechanics for active unilateral below-knee prosthesis users. Our findings also demonstrate that user preference for passive prosthetic technology may be both subject-specific and task-specific. Future work could investigate the inter-individual preferences and potential benefits of a prosthetic toe joint for lower-mobility individuals.

Dance-specific eligibility of vocational ballet students - examinations at a governmental training institution for classical ballet

During their training, pre-professional ballet students are confronted with physical stresses comparable to those of competitive sports. In competitive sports, there are mandatory and binding aptitude tests to ensure that the growing athlete meets the requirements. In ballet, there are no such mandatory examinations preceding the start of training. For adult professional dancers, musculoskeletal ideals could be isolated from the dance medicine literature. However, only a few studies describe musculoskeletal characteristics of pre-professional ballet students. It is neither known at what age a student should meet the ideal measurements for an adult nor what deviations from the ideal can be considered normal. This study aims to describe sociodemographic and musculoskeletal characteristics of pre-professional ballet students and discusses to what extent they already meet or deviate from dance-specific eligibility criteria for adult professional ballet dancers. In this study, n = 414 female and n = 192 male students of John Cranko School (JCS) were seen by an experienced orthopaedist and dance physician. Mean age was 13.9 years (SD 3.5, range 5-22 years). Their medical history was taken (age; nationality; start of ballet/training) and a physical examination was performed (height/weight; symmetry of shoulder girdle, spine, waist triangles; pelvic tilt; tibial torsion; range of motion of base of index finger joint, spine, hips, ankle and base of great toe joint). Subsequently, the results of this study were compared with suitability criteria for adult professional ballet dancers that had been isolated from the dance medicine literature for a previous article. Examinees were from 49 different nations. 34.6% of the female subjects (≥16 years) were between 165 and 170 cm and 33.3% of the male subjects (≥18 years) were between 178 and 185 cm tall. 45.0% of those examined showed low body weight (<10th percentile, BMI <18.5 kg/m²). The trunk of 61.0-84.8% of those examined was erect and symmetrical. 25.2% had scoliosis. Half (53.5%) were found to have a bilateral external rotation of the hips of at least 60°, and 68.7% had a bilateral internal rotation between 20 and 50°. 87.3% exhibited a bilateral tibial torsion between 15 and 40°. A bilateral en dehors of 90° was calculated for 25.0%. In 9.1% of those examined, the upper ankle joints presented a dorsiflexion of at least 25°, and in 70.2%, a plantarflexion of at least 70° was seen. In 88.0%, the metatarsophalangeal joint of the great toe was 90° (f) and 80° (m) on both sides. The results of this study showed that pre-professional ballet students fulfil many characteristics of adult professional ballet dancers. High values already among young age groups suggest a ballet-specific selection. Nevertheless, not all students fulfil the theoretical "ideal measurements" for professional classical ballet. These anatomical limits should be considered individually in training to protect the growing pre-professional ballet dancer. The high ballet-specific anatomical demands, but especially the large number of students with a low body weight, underline the necessity of mandatory aptitude tests at the beginning and regular check-ups in the course of training to avert compensatory mechanisms and their consequential damage and to screen for eating disorders and disorders of eating behaviour.

A toe-inspired rigid-flexible coupling wheel design method for improving the terrain adaptability of a sewer robot.

The human toe, characterized by its rigid-flexible structure comprising hard bones and flexible joints, facilitates adaptive and stable movement across varied terrains. In this paper, we utilized a motion capture system to study the adaptive adjustments of toe joints when encountering obstacles. Inspired by the mechanics of toe joints, we proposed a novel design method for a rigid-flexible coupled wheel. The wheel comprises multiple elements: a rigid skeleton, supporting toes, connecting shafts, torsion springs, soft tendons, and damping pads. The torsion springs connect the rigid frame to the supporting toes, enabling them to adapt to uneven terrains and pipes with different diameters. The design was validated through kinematic and dynamic modeling, rigid-flexible coupled dynamics simulation, and stress analysis. Different stiffness coefficients of torsion springs were compared for optimal wheel design. Then, the wheel was applied to a sewer robot, and its performance was evaluated and compared with a pneumatic rubber tire in various experiments, including movement on flat surfaces, overcoming small obstacles, adaptability tests in different terrains, and active driving force tests in dry and wet pipelines. The results prove that the designed wheel showed better stability and anti-slip properties than conventional tires, making it suitable for diverse applications such as pipeline robots, desert vehicles, and lunar rovers.

Free neurovascular toe-(joint)-transfers compared to alternative reconstructive procedures for amputation injuries of two and tripartite fingers with substance loss.

Complex injuries of the hand frequently result in loss of essential functional features. Common reconstructive procedures for soft tissue defects of the thumb or phalanges are locoregional flaps like Moberg-, Foucher-, Cross-Finger- or Littler flaps. Microneurovascular toe (joint-) transfers complete the arsenal of operative reconstructive procedures and allow for most detailed reconstructions. Our experiences with free toe transplants are reported and diversely discussed regarding contending procedures. From 2010 until 2019 14 patients who received emergency or elective partial or complete toe transfers were compared with a control group (n = 12) treated with contending reconstructive procedures. Aim of the reconstructions was to cover the defect with well-vascularized, sensate tissue, while preserving length and range of motion in a reliable manner. The Kapandji score showed a significant difference (p- value = 0.04) with a score of 9.8 in comparison to control group (Kapandji index = 8.0). In our heterogenic patient collective free toe transplants have proven to achieve comparable functional results for reconstruction of two and tripartite phalanxes as opposed to common local reconstructive procedures.

Pain in Parkinson disease: a deep phenotyping study.

In our prospective cross-sectional study, we comprehensively characterized Parkinson disease (PD)-related pain in monocentrically recruited patients with PD using standardized tools of pain assessment and categorization. One hundred fifty patients were systematically interviewed and filled in questionnaires for pain, depression, motor, and nonmotor symptoms. Patients with PD-related pain (PD pain), patients without PD-related pain (no PD pain), and patients without pain (no pain) were compared. Pain was present in 108/150 (72%) patients with PD, and 90/150 (60%) patients were classified as having PD-related pain. Most of the patients with PD (67/90, 74%) reported nociceptive pain, which was episodic (64/90, 71%), primarily nocturnal (56/90, 62%), and manifested as cramps (32/90, 36%). Parkinson disease-related pain was most frequently located in the feet (51/90, 57%), mainly at the toe joints (22/51, 43%). 38/90 (42%) patients with PD-related pain received analgesic medication with nonsteroidal anti-inflammatory drugs being the most frequently used (31/42, 82%) and opioids most effective (70% pain reduction of individual maximum pain intensities, range 22%-100%, confidence interval 50%-90%). All patients received oral PD treatment; however, levodopa equivalent dose showed no correlation with mean pain intensities (Spearman ρ = 0.027, P > 0.05). Our data provide a comprehensive analysis of PD-related pain, giving evidence for mainly non-neuropathic podalgia, which bears the potential to rethink assessment and analgesic treatment of pain in PD in clinical practice.

A case report on the bilateral absence of fourth tendinous slip of the flexor digitorum brevis muscle in the foot: Exploring evolutionary and surgical relevance

The flexor digitorum brevis (FDB) muscle extends across the central region of the sole, positioned deep beneath the plantar aponeurosis. It inserts into the lateral four toes through four slender musculotendinous slips. Functionally, this muscle reinforces the foot arch by facilitating flexion at the interphalangeal and metatarsophalangeal joints of the lateral toes. In clinical contexts, the FDB muscle serves as a musculocutaneous flap in reconstructive surgeries, addressing various foot deformities. Despite its small size, the FDB muscle carries significant evolutionary importance, indicating potential phylogenetic degeneration in humans due to adaptations to diverse lifestyles. The anatomical variation presented in this case report holds importance, as the presence or absence of the FDB muscle can play a crucial role in maintaining arch integrity and holds relevance from a surgical perspective.

Biomechanical effects of an articulating prosthetic toe joint during stair navigation for individuals with unilateral, below-knee limb loss

Stair navigation is an essential and demanding form of locomotion. During stair ascent and descent, persons with lower limb loss exhibit gait characteristics which may increase their risk of falls and joint degeneration of the intact limb. To reduce deviations from typically-able-bodied gait and overloading of the intact limb for this population, one potential intervention involves modifying passive prosthetic feet by incorporating a flexible toe joint that simulates the biological metatarsophalangeal joint. In this study, we aimed to assess the user preferences and biomechanical effects of a flexible prosthetic toe joint during stair ascent and descent for persons with unilateral lower-limb loss. Nine participants with unilateral lower-limb loss were recruited (Male; Medicare Functional Classification Level: eight K4, one K3; age: 41 ± 11 years; mass: 95 ± 13 kg; height: 1.84 ± 0.05 m; mean ± SD). No significant changes in lower-limb joint mechanics were identified. Five of nine participants preferred the unmodified prosthesis with a standard carbon fiber keel for both stair ascent and descent. Varied user preferences and inconsistent changes in lower-limb joint parameters between participants highlight the importance of subject-specific analyses and individualized device prescription.

Stack versus Te Technique for Central Slip Reconstruction during Vascularized Toe Proximal Interphalangeal Joint Transfer.

Significant extension deficit is a common problem after a vascularized toe proximal interphalangeal joint transfer. One of the main causes related to extensor lag is central slip deficiency of the donor toes. In their clinical practice, the authors performed both the Stack and Te techniques to reconstruct central slip function during a joint transfer. The aim of this study was to compare the long-term outcomes of vascularized joint transfers between these two techniques. From May of 2009 to October of 2021, 38 digits in 36 patients (28 men and 8 women) underwent free vascularized toe joint transfer requiring central slip reconstruction. Eight and 30 digits were reconstructed with the Stack technique and the Te technique, respectively. The median length of follow-up was 19 months (range, 5 to 78 months). The overall median extension lag was 20 ± 20 degrees and flexion was 80 ± 20 degrees. There were no significant differences in extension lag (25 ± 29 degrees versus 20 ± 15 degrees; P = 0.281), flexion (75 ± 10 degrees versus 85 ± 20 degrees; p = 0.13), or range of motion (53 ± 23 degrees versus 63 ± 15 degrees; P = 0.076) of the joints between the Stack and Te techniques after the transfers. From the limited number of cases, both the Stack and Te techniques provided similar outcomes in correcting extension lag in vascularized joint transfers. The Te technique is a simplified and effective method for central slip reconstruction, whereas caution is advised when using the Stack technique because of potential complications. Therapeutic, III.

Effects of Wearing Slippers While Obstacle Crossing in Healthy Young Adults: Strategy for Toe Clearance Enhancement and Prevention of Slipper Loss.

Wearing loose footwear, such as slippers, poses a risk factor for tripping. Previous studies have examined obstacle crossing to find strategies to avoid tripping. However, the effect of wearing slippers on the likelihood of tripping remains unclear. Therefore, this study aimed to determine whether wearing slippers while level walking and obstacle crossing affects kinematic characteristics and muscle activity. Sixteen healthy, young adults performed two tasks (a)while wearing slippers and (b)while barefoot: (1)level walking and (2)crossing a 10-cm obstacle. Toe clearance, joint angles, muscle activity, and cocontraction were measured for both the leading and trailing lower limbs. In the slipper-wearing condition, knee flexion and hip flexion angles were significantly increased in the swing phase for the leading limb (p < .001 and p < .001, respectively) and trailing limb (p < .001 and p = .004, respectively) compared with the barefoot condition. Tibialis anterior activity (p = .01) and muscle cocontraction of the tibialis anterior and the medial head of the gastrocnemius (p = .047) were significantly increased in the swing phase of the trailing limb for the slipper-wearing condition compared with the barefoot condition in the obstacle crossing task. Wearing slippers increased knee and hip flexion angles, and muscle cocontraction of the tibialis anterior and medial head of gastrocnemius increased during obstacle crossing. The results revealed that obstacle crossing while wearing slippers would require foot fixation adjustment in addition to increased knee and hip flexion to avoid toe collision.

Vascularized Toe Proximal Interphalangeal Joint Transfer in Posttraumatic Fingers: Analysis of Prognostic Factors for Suboptimal Outcomes.

Posttraumatic finger osteoarthritis of the proximal interphalangeal joint (PIPJ) is a difficult problem. Over the past decade, we have reported several methods for improving the outcomes of vascularized toe joint transfer (VJT). In this study, we focused on determining poor prognostic factors which lead to a suboptimal outcome. A consecutive series of patients with posttraumatic osteoarthritis of the PIPJ who received VJT between January 2008 and January 2021 were enrolled in this study. The senior surgeon (Y.-T.L.) performed the surgery in all cases. In this retrospective study, we reexamine the initial trauma-related soft tissue and bony structure injuries of the recipient finger, to assess the baseline tissue quality before VJT. The injuries were classified into five major categories according to their anatomic region. The functional outcome parameters (including range of motion, percentage of use, and extensor lag of the transferred PIPJ) were collected. Univariate and multivariate linear regression analyses were performed using the generalized estimated equation model to identify the correlation between the injury category involved and functional outcome. A total of 59 digits were enrolled. Our results revealed that the fingers with previous vascular injury that received revascularization procedures had relatively suboptimal functional outcomes. These fingers had a significantly lower percentage of use both before (β = -0.222, P = 0.006) and after (β = -0.177, P = 0.006) receiving secondary procedures to improve functional outcome. Patients with prior revascularization surgery were associated with a poor functional outcome after VJT.

A Bio-Inspired Arched Foot with Individual Toe Joints and Plantar Fascia.

This paper presents the design and testing of an arched foot with several biomimetic features, including five individual MTP (toe) joints, four individual midfoot joints, and plantar fascia. The creation of a triple-arched foot represents a step further in bio-inspired design compared to other published designs. The arched structure creates flexibility that is similar to human feet with a vertical deflection of up to 12 mm. The individual toe joints enable abduction-adduction in the forefoot and therefore a natural pronation motion. Adult female bone data was obtained and converted into a CAD model to accurately identify the location of bones, joints, and arches. An analytical model is presented that gives the relationship between the vertical stiffness and horizontal stiffness of the longitudinal arches and therefore allows the optimization of stiffness elements. Experimental tests have demonstrated a vertical arch stiffness of 76 N/mm which is similar to adult human feet. The range of movement of the foot is similar to human feet with the following values: dorsi-plantarflexion (28°/37°), inversion-eversion (30°/15°), and abduction-adduction (30°/39°). Tests have also demonstrated a three-point contact with the ground that is similar to human feet.

The experimental investigation of foot slip-turning motion of the musculoskeletal robot on toe joints.

Owing to their complex structural design and control system, musculoskeletal robots struggle to execute complicated tasks such as turning with their limited range of motion. This study investigates the utilization of passive toe joints in the foot slip-turning motion of a musculoskeletal robot to turn on its toes with minimum movements to reach the desired angle while increasing the turning angle and its range of mobility. The different conditions of plantar intrinsic muscles (PIM) were also studied in the experiment to investigate the effect of actively controlling the stiffness of toe joints. The results show that the usage of toe joints reduced frictional torque and improved rotational angle. Meanwhile, the results of the toe-lifting angle show that the usage of PIM could contribute to preventing over-dorsiflexion of toes and possibly improving postural stability. Lastly, the results of ground reaction force show that the foot with different stiffness can affect the curve pattern. These findings contribute to the implementations of biological features and utilize them in bipedal robots to simplify their motions, and improve adaptability, regardless of their complex structure.