For the first time, an unconditionally stable finite-difference time-domain (FDTD) method for 3-D simulation of dispersive nonlinear media is presented. By applying a new adopted alternating-direction implicit (ADI) time-splitting scheme and the auxiliary differential equation (ADE) technique, the time-step in the FDTD simulations can be increased much beyond the Courant-Friedrichs-Lewy (CFL) stability limit. Thus, in comparison to the classical nonlinear FDTD method, the computational time for the proposed approach is decreased significantly while maintaining a reasonable level of accuracy. Numerical examples are presented to demonstrate the validity, stability, accuracy and computational efficiency of the proposed method.

<AbstractText>With ultrasonography or 2D magnetic resonance imaging (MRI) of the lateral ankle ligament, it is particularly difficult to show the entire calcaneofibular ligament (<em>CFL</em>). The purpose of this study was to evaluate the morphological characteristics of the lateral ankle ligaments in injured patients and uninjured controls using 3D MRI.</AbstractText><AbstractText>A total of 64 ankles of 59 healthy volunteers and lateral ligament injury patients (mean age of 32.4 years) were examined. The 64 ankles included a healthy group of 11 ankles, an acute injury group of 12 ankles that underwent MRI a month after injury, and a chronic injury group of 41 ankles that underwent MRI more than 3 months after injury. Using a 3.0-T MRI system, imaging was done with fast imaging employing steady-state acquisition cycled phases. Oblique sagittal images that most clearly depicted the entire anterior talofibular ligament (ATFL) and <em>CFL</em> were prepared manually and evaluated using a workstation.</AbstractText><AbstractText>In the healthy group, both the ATFL and <em>CFL</em> were clearly and entirely visualized. The mean width in the central portion was 4.0 ± 1.0 mm in the ATFL and 4.8 ± 0.6 mm in the <em>CFL</em>. 3D MRI in the acute injury group showed findings of diffuse swelling with hyperintensity in the ATFL of all patients. The <em>CFL</em> in 7 of 12 ankles showed findings of diffuse swelling with hyperintensity. In the chronic injury group, morphological abnormalities of the ATFL were seen in 19 of 41 ankles. The ligament signal disappeared in 2 ankles, thinned in 4 ankles, and showed swelling in 13 ankles. Morphological abnormalities of the <em>CFL</em> were seen in 17 of 41 ankles. The ligament signal disappeared in 1 ankle, thinned in 2 ankles, and showed swelling in 14 ankles.</AbstractText><AbstractText>3D MRI may be a useful modality to visualize both the ATFL and the <em>CFL</em>.</AbstractText>

Ankle sprains are a common injury that may need reconstruction and extensive physical therapy. The purpose of this study was to provide a description of the biomechanics of the ankle joint complex after anterior talofibular (ATFL) and calcaneofibular (CFL) ligament rupture to better understand severe ankle injuries. Envelope of motion of ten cadaveric ankles was examined by manual manipulations that served as training data for a radial basis function used to interpolate ankle mobility at flexion angles under load and torque combinations. Moreover, ankle kinematics were examined while tendons were loaded to identify how their performance is altered by ligament rupture. The force required to plantarflex the ankle following ligament rupture was measured by calculating the load through the Achilles. Following ATFL injury, the largest changes were to internal rotation (5°) in deep plantarflexion and anterior translation (1.5mm) in early plantarflexion. The combined ATFL and CFL rupture changed the internal/external rotation (3°), anterior/posterior translation (1mm), and inversion (5°) throughout flexion relative to the isolated ATFL rupture. The Achilles' load increased by 24% after the rupture of ligaments indicating a reduction in its efficiency. This study suggests that if patients demonstrate a primarily an increased laxity in internal rotation, the damage has solely occurred to the ATFL; however, if the constraint is reduced across multiple motions, there is likely damage to both ligaments. Higher loads in the Achilles suggest that it is overloaded after the injury; hence, targeting the calf muscles in rehabilitation exercises may reduce patients' pain.

BACKGROUND

Congenital fused labia (CFL) is defined as a failure or significant delay in the opening of the juvenile sealed labia majora. This phenotype is known to be variably common in adult captive female marmosets but has never been investigated in detail before.

METHODS

Here, we define, describe and quantify the variations in the degree of closure of the vulva in 122 captive marmosets (Callithrix jacchus) from 1.2 to 42 months old and include colony analysis.

RESULTS

There was a negative correlation between the degree of labial fusion and animal age after prepubertal period (P < 0.05). CFL females had higher number CFL relatives (4.3 ± 0.6 vs 2.4 ± 0.5 for non-CFL, P < 0.05) and more external ancestors compared to non-CFL (P < 0.05).

CONCLUSIONS

Our results therefore suggest that CFL phenotype is most likely associated with epigenetic effects induced by the captive environment and colony management strategy of extensive crossing of family lines to promote heterozygosity.

This study aimed to develop a numerical model capable of predicting changes in the cell-free layer (CFL) width in narrow tubes with consideration of red blood cell aggregation effects. The model development integrates to empirical relations for relative viscosity (ratio of apparent viscosity to medium viscosity) and core viscosity measured on independent blood samples to create a continuum model that includes these two regions. The constitutive relations were derived from in vitro experiments performed with three different glass-capillary tubes (inner diameter=30, 50 and 100 μm) over a wide range of pseudoshear rates (5-300 s(-1)). The aggregation tendency of the blood samples was also varied by adding Dextran 500 kDa. Our model predicted that the CFL width was strongly modulated by the relative viscosity function. Aggregation increased the width of CFL, and this effect became more pronounced at low shear rates. The CFL widths predicted in the present study at high shear conditions were in agreement with those reported in previous studies. However, unlike previous multi-particle models, our model did not require a high computing cost, and it was capable of reproducing results for a thicker CFL width at low shear conditions, depending on aggregating tendency of the blood.

A new type of deformable model is presented that merges meshes and level sets into one representation to provide interoperability between methods designed for either. This includes the ability to circumvent the CFL time step restriction for methods that require large step sizes. The key idea is to couple a constellation of disconnected triangular surface elements (springls) with a level set that tracks the moving constellation. The target application for Spring Level Sets (SpringLS) is to implement comprehensive imaging pipelines that require a mixture of deformable model representations to achieve the best performance. We demonstrate how to implement key components of a comprehensive imaging pipeline with SpringLS, including image segmentation, registration, tracking, and atlasing.

Purpose: Despite the evidence on the role of gravity stress test to access the instability of other ankle injuries, there is limited literature regarding gravity stress on the lateral ankle ligament's insufficiency. The objective of our study was to objectively measure the tibiotalar angular movement under gravity stress after progressive sectioning of the lateral ankle ligaments.

Methods: We performed sequential sectioning of the anterior talofibular (ATFL), calcaneofibular (CFL), and posterior talofibular ligaments (PTFL) in twelve ankle specimens. Under gravity stress, we measured the angular movement of the talus in relation to the tibia. The measuring device is based on a three-axis gyroscope and accelerometer.

Results: Comparing to the intact condition, the plantar flexion increased on average 1.78° (95% confidence interval [CI] 1.15;2.42), 5.13° (95%CI 3.10;7.16) and 8.63° (95%CI 6.05;11.22), the rotation increased by 1.00° (95 CI -0.51;2.51), 3.68° (95%CI 1.97;5.40) and 15.62° (95%CI 10.09;21.14), and the varus increased 2.89° (95% CI 1.39, 4.39), 8.12° (95% CI 5.16, 11.07) and 11.68° (95% CI 7.91, 15.46), after sectioning the ATFL, CFL, and PTFL, respectively. The overall changes were statistically significant.

Conclusions: There was a significant tibiotalar laxity after sectioning of lateral ankle ligaments when the foot position is influenced only by gravity. The tibiotalar angular displacement was significant when the CFL and PTFL were cut which suggests that the gravity test could be used to assess combined lateral ankle ligament injury. This evidence might be a step forward in the development of lateral ankle ligaments gravity stress tests.

Level of evidence: 5 (cadaver study).

Keywords: Ankle sprain; Anterior talofibular ligament; Diagnosis device; Instability test; Lateral ligaments; Talocrural joint axis.

The aim of the present study was to investigate the anatomical and morphological characteristics and the maximum elongation of the calcaneofibular ligament (CFL) in cadavers. In a sample of 72 cadaveric lower limbs the mean values of length, width, thickness, and angle with the sagittal plane were recorded for the CFL. The mean ligament's length was 31.8 mm, and the mean width and thickness were 4.4 mm and 1.5 mm respectively. The mean angle with the sagittal plane was 51.11°. In 72.2% of the lower limbs studied, the ligament presented one band, while 22.2% and 5.6% of them were two-banded and three-banded respectively. A common origin with the anterior talofibular ligament (TFL) was found in 24 of the feet (33%). There were also 4 cases in which the anterior TFL was absent. Finally, we measured the maximal elongation of the ligament during extreme inversion and simultaneous dorsal flexion and found it to be 2.88 mm on average. We noticed and statistically verified that women presented a greater elongation compared to men. A precise knowledge of the origin, insertion, direction, and morphology of CFL is critical for ligament injuries in ankle sprains and during ankle reconstruction. Ligament elasticity plays an important role in the range of ankle motion and ligament shearing. Male and female ankle joints differ in several anthropometric characteristics and thus the genre differences in ligament elongation are of great interest.

The advancement of modern lighting technologies has led to many revolutions in lighting efficiency and presentation. The progression from filament bulbs, to CFL, and now LED technologies have produced a bounty of energy-efficient lighting options for design engineers and consumers. As the light-producing elements of a lighting fixture improve, the limiting factor in efficient illumination is no longer the light source, but the optical system itself. There are many characterization methods and standards for defining light for illumination in terms of color and human response. With concerns of how things like light pollution and energy requirements impact our society and the world around us, it is critical to understand how well a lighting fixture can illuminate a desired area while minimizing light lost to the environment and maximizing the total radiative intensity (radiance) of a space. This work presents two figures of merit, one for over-illumination and another for under-illumination, to characterize the optics of a lighting system based on a ray tracing methodology. Five common simplified optical design, with four varying beam angles, were simulated to present these new figures of merit. Results showed that common imaging optical systems such as parabolic and ellipse reflectors struggled to produce a well-lit area without over illumination, while nonimaging alternatives like the compound parabolic and compound elliptical reflectors were able to reach the thermodynamic ideal of a fully illuminated area without light lost to the environment. This work hopes to inform illumination engineers and lighting designers to help improve their optical design to maximize performance and minimize waste.

BACKGROUND

We have already discovered 23 patients during the work of the outpatient department and operations whose unstable signs on the posterolateral ankle. The anterior drawer test demonstrated normal during the physical examinations while the spaces of the posterior tibiotalar joints increased in stress X-ray plain films. ATFL intact and posterolateral ligaments lax were found during operations too. It is important to make existence claims and illuminate the mechanism of posterolateral ankle instability.

METHODS

A finite element model of the ankle was established for simulating to cut off posterolateral ligaments in turn. Ankle movements with tibia rotation under load on five forefoot positions were simulated as well.

RESULTS

The difference values with tibia external rotation were negative, and the positive results occurred with tibia internal rotation. The tibia-talus difference values in some forefoot positions were 2 ~ 3 mm after PTFL together with CFL or/and PITFL were cut off. The tibula-talus difference values were 2.21 ~ 2.76 mm after both PTFL and CFL were cut off. The tibia-fibula difference values were small. The difference values increased by 2 ~ 5 mm after cutting off the PITFL.

CONCLUSIONS

Posterolateral ankle ligaments, especially CFL and PITFL, play a significant role in maintaining ankle stability. The serious injuries of both CFL and PITFL would affect posterolateral ankle stabilities. PITFL was important to subtalar joint stability.

Compact stars may contain quark matter in their interiors at densities exceeding several times the nuclear saturation density. We explore models of such compact stars where there are two first-order phase transitions: the first from nuclear matter to a quark-matter phase, followed at a higher density by another first-order transition to a different quark-matter phase [e.g., from the two-flavor color-superconducting (2SC) to the color-flavor-locked (CFL) phase]. We show that this can give rise to two separate branches of hybrid stars, separated from each other and from the nuclear branch by instability regions, and, therefore, to a new family of compact stars, denser than the ordinary hybrid stars. In a range of parameters, one may obtain twin hybrid stars (hybrid stars with the same masses but different radii) and even triplets where three stars, with inner cores of nuclear matter, 2SC matter, and CFL matter, respectively, all have the same mass but different radii.

We demonstrate the fabrication of diffractive optical elements (DOEs) on 3-Dimensional curved surfaces by capillary force lithography (CFL). Curved gratings with a period of 20mum and 820nm have been successfully fabricated in polymer on concave surfaces by CFL. The experiment results indicate that the capillary force lithography is an effective method to replicate DOEs on curved surfaces with a very high fidelity and a relatively fast speed. In addition, we found that the growth rate of the polymer in the sub-microfabrication is much faster and the step height is much closer to the master than that in the microfabrication for CFL, which makes CFL more attractive in the fabrication of DOEs with a sub-microscale or even nanoscale feature size than a microscale feature size.

More energy-efficient, readily dimmable, long-lasting and more affordable light-emitting diode (LED) lights are increasingly finding applications in poultry production facilities. Despite anecdotal evidence about the benefits of such lighting on bird performance and behavior, concrete research data were lacking. In this study, a commercial poultry-specific LED light (dim-to-blue, controllable correlated color temperature (CCT) from 4500 to 5300 K) and a typical compact fluorescent light (CFL) (soft white, CCT=2700 K) were compared with regards to their effects on growing performance, activity levels, and feather and comb conditions of non-beak-trimmed W-36 pullets during a 14-week rearing period. A total of 1280-day-old pullets in two successive batches, 640 birds each, were used in the study. For each batch, pullets were randomly assigned to four identical litter-floor rooms equipped with perches, two rooms per light regimen, 160 birds per room. Body weight, BW uniformity (BWU), BW gain (BWG) and cumulative mortality rate (CMR) of the pullets were determined every 2 weeks from day-old to 14 weeks of age (WOA). Activity levels of the pullets at 5 to 14 WOA were delineated by movement index. Results revealed that pullets under the LED and CFL lights had comparable BW (1140±5 g v. 1135±5 g, P=0.41), BWU (90.8±1.0% v. 91.9±1.0%, P=0.48) and CMR (1.3±0.6% v. 2.7±0.6%, P=0.18) at 14 WOA despite some varying BWG during the rearing. Circadian activity levels of the pullets were higher under the LED light than under the CFL light, possibly resulting from differences in spectrum and/or perceived light intensity between the two lights. No feather damage or comb wound was apparent in either light regimen at the end of the rearing period. The results contribute to understanding the impact of emerging LED lights on pullets rearing which is a critical component of egg production.

Lateral ankle instability is a complex condition that can, at times, prove difficult to evaluate and treat for general practitioners. The difficulty in evaluation and treatment is due in part to the ankle complex is composed of three joints: talocrural, subtalar, and tibiofibular syndesmosis. All three joints function in conjunction to allow complex motions of the ankle joint. The main contributors to the stability of the ankle joint are the articular surfaces, the ligamentous complex and the musculature - which allows for the dynamic stabilization of the joints. The lateral ankle is comprised of the anterior talofibular ligament (ATFL), the calcaneofibular ligament (CFL) and the posterior talofibular ligaments (PTFL). The anterior talofibular ligament originates from the along the anterior colliculus of the lateral malleolus and inserts on the lateral talar articular facet, with its course running in 45-90 degrees to the longitudinal axis of the tibia. The primary function of the ATFL is to resist inversion in plantarflexion and anterolateral translation of the talus in the mortise. The calcaneal fibular ligament originates from the anterior border of the fibula approximately 9mm proximal to the distal tip and inserts on the calcaneus approximately 13mm distal to the subtalar joint and rooted to the peroneal tendon sheath. The CFL crosses both the subtalar joint and the ankle joint. The primary functions of the CFL are to resist inversion in neutral and dorsiflexed position and also restrains subtalar inversion, which limits talar tilt within the mortise. Lastly, the posterior talofibular ligament is the strongest of the lateral ligaments but only plays a supplementary role in ankle stability. The PTFL originates on the posterior border of the fibula and inserts on the posterolateral tubercle of the talus and runs perpendicular to the longitudinal axis of the tibia. Of the three ligaments (ATFL, CFL, and PTFL) only the CFL ligament is extracapsular to the ankle joint.

Purpose: Anatomical reconstruction of the calcaneofibular ligament (CFL) is a common technique to treat chronic lateral ankle instability. A bone tunnel is used to fix the graft in the calcaneus. The purpose of this study is to provide some recommendations about tunnel entrance and tunnel direction based on anatomical landmarks.

Methods: The study consisted of two parts. The first part assessed the lateral tunnel entrance for location and safety. The second part addressed the tunnel direction and safety upon exiting the calcaneum on the medial side. In the first part, 29 specimens were used to locate the anatomical insertion of the CFL based on the intersection of two lines related to the fibular axis and specific landmarks on the lateral malleolus. In the second part, 22 specimens were dissected to determine the position of the neurovascular structures at risk during tunnel drilling. Therefore, a method based on four imaginary squares using external anatomical landmarks was developed.

Results: For the tunnel entrance on the lateral side, the mean distance to the centre of the CFL footprint was 2.8 ± 3.0 mm (0-10.4 mm). The mean distance between both observers was 4.2 ± 3.2 mm (0-10.3 mm). The mean distance to the sural nerve was 1.4 ± 2 mm (0-5.8 mm). The mean distance to the peroneal tendons was 7.3 ± 3.1 mm (1.2-12.4 mm). For the tunnel exit on the medial side, the two anterior squares always contained the neurovascular bundle. A safe zone without important neurovascular structures was found and corresponded to the two posterior squares.

Conclusion: Lateral landmarks enabled to locate the CFL footprint. Precautions should be taken to protect the nearby sural nerve. A safe zone on the medial side could be determined to guide safe tunnel direction. A calcaneal tunnel should be directed to the posterior inferior medial edge of the calcaneal tuberosity.

Keywords: Bone tunnel; Calcaneofibular ligament; Hindfoot instability; Ligament reconstruction; Neurovascular bundle.

A cariogenic situation was modeled by soft acidification by hydrochloric acid in vitro in mixed salivary pool of 10 subjects aged 16-18, and the values of pH and active concentration of sodium ions, optic density, and concentration of inorganic phosphorus were studied. Soft acidification of human mixed saliva was found to result in its structural disorders. The saliva of subjects with negligible caries was more stable to unfavorable exposure than mixed saliva of subjects with a higher CFL index. Experiments showed that pH of 6.2 is the critical value causing evident destruction of the saliva and reducing its mineralizing potential. These data may be used in studies of the molecular mechanisms of caries development.

Background. Both percutaneous and arthroscopic techniques have been introduced in anatomic ankle lateral ligaments reconstruction. The purpose of this study was to compare these two techniques in identifying the calcaneal insertion of the calcaneofibular ligament (CFL). Methods. Fifteen fresh-frozen human ankle cadaver specimens were used in this study. Each specimen was tested in three stages. For stage 1, each specimen was evaluated under arthroscopy. After debridement was performed, the insertion of the CFL on the calcaneus was identified, and a 1.5mm Kirschner wire was drilled at the center of the insertion. For stage 2, a percutaneous technique was used to identify the center of the insertion of the CFL. A second 1.5 mm Kirschner wire was drilled through the skin marker. For stage 3, the ankle was dissected, the footprint of the CFL was identified under direct vision, and the distances between the center of the CFL insertion on the calcaneus and the two Kirschner wires were measured, respectively. Results. In the arthroscopic technique group, the mean distance from the Kirschner wire to the center of the CFL insertion in the calcaneus was 3.4 ± 1.3 mm. In the percutaneous technique group, the mean distance from the Kirschner wire to the center of the CFL insertion was 3.2 ± 1.4 mm. No significant difference was found between the two groups. Conclusion. No difference in identifying the calcaneal insertion of the CFL was found between the percutaneous and the arthroscopic ankle lateral ligaments reconstruction technique. Both techniques can be used during anatomic ligaments reconstruction in treatment of chronic ankle instability.

Background: This study was performed to determine the sensitivity and specificity of ultrasound in the diagnosis of traumatic ankle injury in comparison with magnetic resonance imaging (MRI).

Materials and methods: This cross-sectional study was performed on 31 patients with soft-tissue injury or fracture, referring to the MRI imaging center of Alzahra and Kashani Hospitals in Isfahan from October 2018 to March 2019. After an MRI, an ultrasound of the affected ankle was performed for all patients. Sonography and MRI were performed by two radiologists who were blinded to the results of each other's reports. The sensitivity, specificity, positive predictive value, and negative predictive value of sonography were determined.

Results: In this study, 31 patients with ankle trauma were studied. The mean age of the patients was 30.73 ± 10.15 years; 32.3% were male and 67.7% were female. The sensitivity of ultrasound relative to MRI to detect damage to the anterior talofibular ligament (ATFL), posterior talofibular ligament (PTFL), and calcaneofibular ligament (CFL) was 66.67%, 50%, and 100%, respectively, and the corresponding specificity was 92.86%, 93.10%, and 93.10%, respectively. According to Kappa test, the agreement between ultrasound and MRI methods for detecting injury to ATFL (κ = 0.51), PTFL (κ = 0.35), and CFL (κ= 0.63) was statistically significant (P < 0.05).

Conclusion: Ultrasound is an appropriate modality for the diagnosis of injuries to CFL and ATFL and has shown acceptable results for PTFL. It could be used as an alternative in cases where access to MRI is not available.

Keywords: Ankle; diagnosis accuracy; magnetic resonance imaging; trauma; ultrasound.

Fibrocytes originate from the bone marrow monocyte lineage and participate in the pathogenesis of pulmonary fibrosis. Research providing a comprehensive picture of fibrocytes is still limited. Cofilin-1 (CFL-1) is an important protein that regulates cell proliferation, migration and differentiation. Whether CFL-1 can induce monocyte differentiation into fibrocytes and promote the process of pulmonary fibrosis is unknown. Compared with that of healthy controls, the expression of CFL-1 was significantly increased in the plasma and peripheral blood mononuclear cells (PBMCs) from idiopathic pulmonary fibrosis (IPF) and connective tissue disease-associated interstitial lung disease (CTD-ILD) patients (P < 0.05). The percentages of peripheral blood fibrocytes in the IPF group (4.2550 ± 0.3483%) and CTD-ILD group (4.7100 ± 0.4811%) were higher than that in the control group (1.6340 ± 0.2549%) (both P < 0.05). In vitro, PBMCs transfected with siRNA-CFL-1 showed lower expression of CFL-1, and the percentage of fibrocytes was lower than that of the control (P < 0.05). PBMCs transfected with Lv-CFL-1 to increase the expression of CFL-1 showed a higher percentage of fibrocytes than the control (P < 0.05). In mice with bleomycin-induced pulmonary fibrosis, the relative expression of CFL-1 was increased, and the percentage of fibrocytes was higher than that in the saline group (P < 0.05). In bleomycin-induced mice, interference with Lv-CFL-1 decreased the expression of CFL-1, the percentage of fibrocytes was lower, and the lung tissue showed less fibrosis (P < 0.05). The overexpression of CFL-1 is associated with pulmonary fibrogenesis. CFL-1 could promote the differentiation of fibrocytes from monocyte peripheral blood mononuclear cells and promote pulmonary fibrosis.

Keywords: Cofilin-1; Differentiation; Fibrocytes; Monocyte peripheral blood mononuclear cells; Pulmonary fibrosis.

Nanodrug transport in tumor microvasculature and deposition/extravasation into tumor tissue are an important link in the nanodrug delivery process. Considering heterogeneous blood flow, such a dual process is numerically studied. The hematocrit distribution is solved by directly considering the forces experienced by the red blood cells (RBCs), i.e., the wall lift force and the random cell collision force. Using a straight microvessel as a test bed, validated computer simulations are performed to determine blood flow characteristics as well as the resulting nanodrug distribution and extravasation. The results confirm that RBCs migrate away from the vessel wall, leaving a cell-free layer (CFL). Nanodrug particles tend to preferentially accumulate in the CFL, leading to increased concentration near the endothelial surface layer. However, shear-induced NP diffusion is diminished within the CFL, causing to a much slower lateral transport rate into tumor tissue. These competing effects determine the NP deposition/extravasation rates. The present modeling framework and NP flux results provide new physical insight. The analysis can be readily extended to simulations of NP transport in blood microvessels of actual tumors.

Federated learning (FL) is currently the most widely adopted framework for collaborative training of (deep) machine learning models under privacy constraints. Albeit its popularity, it has been observed that FL yields suboptimal results if the local clients' data distributions diverge. To address this issue, we present clustered FL (CFL), a novel federated multitask learning (FMTL) framework, which exploits geometric properties of the FL loss surface to group the client population into clusters with jointly trainable data distributions. In contrast to existing FMTL approaches, CFL does not require any modifications to the FL communication protocol to be made, is applicable to general nonconvex objectives (in particular, deep neural networks), does not require the number of clusters to be known a priori, and comes with strong mathematical guarantees on the clustering quality. CFL is flexible enough to handle client populations that vary over time and can be implemented in a privacy-preserving way. As clustering is only performed after FL has converged to a stationary point, CFL can be viewed as a postprocessing method that will always achieve greater or equal performance than conventional FL by allowing clients to arrive at more specialized models. We verify our theoretical analysis in experiments with deep convolutional and recurrent neural networks on commonly used FL data sets.

This study examined how the uneven influx of red blood cells (RBCs) from feeding vessels influences formation of cell-free layer (CFL) in the downstream vessel of a venular bifurcation. Spatio-temporal variations of the CFL width along the downstream vessel (19-41-μm inner diameter, D) were determined at 0.5D intervals from 0.5D to 3.0D away from the bifurcation. Upstream flow conditions were quantified by the ratio of volume flow rates (Q*=Q(High)/Q(Low)) between high flow (Q(High)) and low flow feeding (Q(Low)) vessels. The RBC aggregation level in the rats was adjusted to be at healthy human levels by infusing Dextran 500. Our results suggested that the CFL formation process could be seen only from 2.0D away from the bifurcating point. The mean CFL width at the wall adjacent to the feeding vessel with a higher flow rate was consistently greater than that at the opposite wall, leading to an asymmetric CFL formation in the vessel. A positive relation (P<0.05) between the asymmetry of the CFL width and the volume flow rate ratio (Q*) was found. Our numerical prediction showed that flow resistance in the venular network could be significantly increased by the asymmetric formation of CFL downstream and this effect might become more pronounced under pathological flow conditions such as hyper-aggregating and/or low shear conditions.