Deep Circumflex Iliac Artery-vascularized Iliac Bone Graft for Femoral Head Osteonecrosis: Computed Tomography Anatomical Study.

BACKGROUND: Deep circumflex iliac artery (DCIA)-vascularized iliac graft transposition is a method for treating femoral head osteonecrosis but with inconsistent efficacy. We aim to improve the method of this surgery by recommending the optimal location of the iliac pedicle to satisfy the vascular length for transposition and the blood supply of the vascularized iliac graft. METHODS: The DCIA and its surrounding tissues were assessed on computed tomography angiography images for 100 sides (left and right) of 50 patients. The length of the vascular pedicle required for transposition and the length of the pedicle at different iliac spine positions were compared. The diameter and cross-sectional area of the DCIA and the distance between the DCIA and iliac spine were measured at different points to assess blood supply. We also compared differences in sex and left-right position. RESULTS: The diameter and cross-sectional area of the DCIA gradually decreased after crossing the anterior superior iliac spine (ASIS), and it approached the iliac bone. However, when the DCIA was 4 cm behind the ASIS (54 sides, 54%), it coursed posteriorly and superiorly away from the iliac spine. The vascular length of the pedicle was insufficient to transpose the vascularized iliac graft to the desired position when it was within 1 cm of the ASIS. The vascular length requirement was satisfied, and the blood supply was sufficient when the pedicle was positioned at 2 or 3 cm. CONCLUSION: To obtain a satisfactory pedicle length and sufficient blood supply, the DCIA pedicle of the vascularized iliac graft should be placed 2 to 3 cm behind the ASIS. The dissection of DCIA has slight differences in sex and left-right position due to anatomical differences.

Early warning of tipping in a chemical model with cross-diffusion via spatiotemporal pattern formation and transition.

The spatiotemporal pattern formation and transition driven by cross-diffusion of the Gray-Scott model are investigated for the early warning of tipping in this paper. The mathematical analyses of the corresponding non-spatial model and spatial model are performed first, which enable us to have a comprehensive understanding. Then, the linear stability analysis and the multiple scale analysis method exhibit that cross-diffusion is the key mechanism for the evolution of spatiotemporal patterns. Through selecting a cross-diffusion coefficient as the bifurcation parameter, the amplitude equations that can describe structural transition and determine the stability of different types of Turing patterns are derived. Ultimately, numerical simulations verify the validity of the theoretical results. It is demonstrated that in the absence of cross-diffusion, the spatiotemporal distribution of substances is homogeneous. Nevertheless, when the cross-diffusion coefficient exceeds its threshold value, the spatiotemporal distribution of substances will become inhomogeneous in space. As the cross-diffusion coefficient increases, the Turing instability region will be extended, leading to various types of Turing patterns: spots, stripes, and a mixture of spots and stripes.

Design of Stimuli-Responsive Phenothiazine Derivatives with Triplet-Related Dual Emission and High-Contrast Mechanochromism Guided by Polymorph Prediction.

The development of high-contrast stimulus-responsive materials with excited triplet emission is of great significance for anti-counterfeiting, sensor and memory applications, but remains a challenge. Here, we report a strategy for the rational design of stimulus-responsive phenothiazine derivatives with triplet-related dual emissions and high-contrast mechanochromism guided by Polymorph Prediction. The designed phenothiazine derivatives have the characters of simple structures, a facile synthetic procedure, and a good crystalline nature. We found that the crystals of those derivatives with the potential to form both quasi-axial (ax) and quasi-equatorial (eq) conformations could undergo conformation transition and show significant emission difference (Δλem >100 nm) under mechanical force. Meanwhile, all these phenothiazine derivatives exhibit aggregation-induced emission and emit room-temperature phosphorescence or thermally activated delayed fluorescence. The significant luminescent change of these materials under different stimuli gives them promise for applications in encryption and anti-counterfeiting.

Interfacial interactions and structures of protic ionic liquids on a graphite surface: A first-principles study and comparison with aprotic ionic liquids.

Protic ionic liquids (PILs) have currently been indicated as promising alternative electrolytes in electrical storage devices, such as lithium-ion batteries and supercapacitors. However, compared with the well-studied aprotic ionic liquids (AILs), the knowledge of the interface between PILs and electrode material surfaces is very rare to date. In this work, the adsorption behaviors of three groups of PILs, i.e. pyrrolidinium-based, imidazolium-based, and ammonium-based, on graphite was systematically investigated using first-principles calculations. The corresponding AILs were also taken into account for comparison. The adsorption mechanism of these ILs on the surface is controlled by the interplay of strong electrostatic interactions between adsorbed ions, weak vdW forces between ILs and substrate, and many aromatic interactions including π-π stacking and C-H/N-Hπ contacts. PILs do show quite different preferential interfacial interactions and structures on the graphite surface with respect to AILs, arising mainly from the anion-substrate interactions. Particularly, proton transfer takes place in the PILs consisting of the imidazolium/ammonium cation and the nitrate anion in the gas phase, but it tends to be attenuated or even disappears on graphite caused by interfacial interactions.

Triangular Interchalcogen Interactions: A Joint Crystallographic Data Analysis and Theoretical Study.

Noncovalent chalcogen-chalcogen interactions are being actively investigated from both crystallographic and theoretical viewpoints in recent years. According to our search of the Cambridge Structural Database (CSD), a huge number of crystal structures containing triangular Ch3 synthons were extracted. On the basis of the results of the CSD survey, a series of trimeric complexes of organic divalent chalcogen molecules were selected to model such interaction motifs. Similar to that in conventional chalcogen bonds, triangular interchalcogen interactions become gradually stronger along the sequence of Ch = S, Se, Te. Particularly, hydrogen bonds between the chalcogen centers and the H atoms in the substituents occur, which play a significant role in stabilizing the Ch3 motifs in the trimers. Through multibody energy calculations, the complexes under study exhibit no or only weak cooperativity. Finally, the differences between the Ch3 interaction motifs and the well-studied windmill X3 bonding (X means halogen and this is halogen bond) patterns were elucidated.

2Ch-2N Square Chalcogen Bonds between Pairs of Radicals: A Case Study of 1,2,3,5-Dichalcogenadiazolyl Derivatives.

Specific 2Ch-2N square interactions between pairs of heterocyclic rings have been the target of many recent crystallographic and computational studies. According to our search of the Cambridge Structural Database (CSD), a number of crystal structures of the derivatives of 1,2,3,5-dichalcogenadiazolyl (DChDA) radicals, which consist of 2Ch-2N square motifs in the dimer units, were extracted. On the basis of the CSD survey results, a set of dimeric complexes of DChDA-based radicals with diverse aryl substituents at the 4-position were selected to model such squares. Similar to that in conventional chalcogen bonds, 2Ch-2N square interactions become stronger as the atomic size of chalcogens increases. Both the orbital term and electrostatics contribute significantly to the attraction of these interactions, while the dispersion contribution is small but unneglectable. Some five-membered aryl substituents, such as imidazole, thiazole, and oxazole, produce markedly enhanced square interactions, leading to a pronounced influence on the distribution of spin populations on DChDA rings.

Effects of Cryopreservation and Replantation on Muscles: Application Scope of Limb Cryopreservation.

BACKGROUND: Wang successfully replanted the severed fingers of 2 patients after cryopreservation in 2002 and 2003, which has enabled us to share our own experience for the knowledge interests of our colleagues and to further develop this technology. METHODS: Fifteen healthy adult male Sprague-Dawley rats were selected and divided into 5 groups (group 1: normal control, group 2: cryopreservation with protectant, group 3: cryopreservation without protectant, group 4: 6-hour postoperative, and group 5: 72-hour postoperative). After harvesting the hind limbs, cryoprotectant was applied to 20 limbs, and the rest were cryopreserved without cryoprotectant for 15 days. After being thawed, the amputated limb was replanted in situ. Nerves, skins and gastrocnemius muscles were collected for hematoxylin and eosin staining, terminal deoxynucleotidyl transferase dUTP nick end labeling staining, and transmission electron microscopy observation. RESULTS: Muscle and skin tissues treated with cryoprotectant restored a better outline after being frozen than those not treated, whereas nerves were not significantly different between the 2 groups. After replantation, some of the myofibrils of the muscle were in disarray, but the sarcomere structure remained intact at approximately 6 hours postoperatively. At 72 hours, a transmission electron microscopy scan showed that the myofibrillar arrangement was disorderly, with segmental myofilament breakage, and the sarcomere structure was destroyed in some cases. In addition, the scan revealed increased apoptotic cells and collapse of basic structures in the skin and nerves. CONCLUSIONS: Relative to that of skin and neuronal tissue, the replantation of muscle tissues through the cryopreservation method is more difficult.

Description of noncovalent interactions involving π-system with high precision: An assessment of RPA, MP2, and DFT-D methods.

Efficient approaches with high precision are essential for understanding the formation and stability of noncovalent interaction complexes. Here, 21 noncovalent interaction complexes involving π-system are selected and grouped in three subsets according to ETS-NOCV method: dispersion-dominated, electrostatic-dominated, and mixed. We mainly focus on examining the performance of random-phase approximation (RPA) on these π systems. The tested RPA-based method includes standard RPA and its variants including the related single excitations (SEs), renormalized single excitations (rSEs), second-order screened exchange (SOSEX), and the renormalized second-order perturbation theory (rPT2). The routine second-order Møller-Plesset perturbation theory (MP2) and three popular DFT-D functionals (M06-2X-D3, ωB97XD, and PBE-D3(BJ)) are also assessed for comparison. In this work, besides the calculation of interaction energies at Dunning-type aug-cc-pVDZ and aug-cc-pVTZ basis set, we also present a larger database of interaction energies calculated using MP2 and RPA methods with Dunning-type aug-cc-pVQZ basis set. An accurate CCSD(T)/CBS scheme is used to provide benchmark database. In addition to the high-level results, we also provide potential energy surfaces (PES) of different interaction type. Among all the tested methods, MP2 has a satisfactory performance on electrostatic-dominated and mixed-type systems, except for dispersion-dominated systems. DFT-D functionals, especially ωB97XD functional, has a balanced performance across all the tested systems. Importantly, for RPA-based methods, the calculation accuracy can be dramatically improved by taking into account SE or exchange effects, especially in the mixed complexes. We conclude that rPT2 among all the test RPA-based methods gives an overall satisfactory performance across different interaction types. © 2019 Wiley Periodicals, Inc.

2Ch-2N square and hexagon interactions: a combined crystallographic data analysis and computational study.

In recent years, chalcogen bonding (ChB), a typical σ-hole interaction, has shown great potential as a bottom-up design approach for specific applications. According to our survey of the Cambridge Structural Database (CSD), a large number of crystal structures containing 2Ch-2N square and hexagon interaction motifs were extracted. On the basis of the CSD search results, the 2Ch-2N square interactions in the dimers of 2,1,3-benzochalcogenadiazole 1 and 2,1,3-pyridochalcogenadiazole 2, together with 2Ch-2N hexagon interactions in the dimers of chalcogenazolo-pyridine 3 and triazolo-chalcogenadiazole 4, were firstly studied. Then, substituent effects on these peculiar interactions were thoroughly examined by introducing a diversity of small, non-aromatic substituents at the 4,7-positions of the 1S scaffold and various aryl substituents at the 2-position of the 3Te scaffold. Our calculations showed that the major contribution to the attraction of such bidentate ChB interactions is electrostatics, while the orbital term also plays an important role. Some strong electron-withdrawing substituents, such as NO2, CN, and CF3, tend to enhance square ChB interactions, while C6F5 and CF3 substituents with a strong electron-withdrawing ability strengthen hexagon ChB interactions. Particularly, a good linear correlation has been established between the binding energies of the dimers under study and both the surface electrostatic potential (ESP) maxima for the Ch σ-holes and the minimum surface ESP of the N atoms, which provides reasonable models to evaluate these interactions. The results reported in this work will provide design guidance for the applications of 2Ch-2N cyclic motifs in materials science and biochemistry.

Endoplasmic reticulum stress-dependent ROS production mediates synovial myofibroblastic differentiation in the immobilization-induced rat knee joint contracture model.

Joint contracture is a common complication for people with joint immobility that involves fibrosis structural alteration in the joint capsule. Considering that endoplasmic reticulum (ER) stress plays a prominent role in the promotion of tissue fibrosis, we investigated whether the unfolded protein response (UPR) contributes to the fibrotic development in immobilization-induced knee joint contractures. Using a non-traumatic rat knee joint contracture model, twelve female Sprague-Dawley rats received knee joint immobilization for a period of 8 weeks. We found that fibrosis protein markers (type I collagen, α-SMA) and UPR (GRP78, ATF6α, XBP1s) markers were parallelly upregulated in rat primary cultured synovial myofibroblasts. In the same cell types, pre-treatment with an ER stress inhibitor, 4-phenylbutyric acid (4-PBA), not only abrogated cytokine TGFß1 stimulation but also reduced the protein level of UPR. Additionally, high reactive oxygen species (ROS) generation was detected in synovial myofibroblasts through flow cytometry, as expected. Notably, TGFß1-induced UPR was significantly reduced through the inhibition of ROS with antioxidants. These data suggest that ER stress act as a pro-fibrotic stimulus through the overexpression of ROS in synovial fibroblasts. Interestingly, immunohistochemical results showed an increase in the UPR protein levels both in human acquired joint contractures capsule tissue and in animal knee joint contracture tissue. Together, our findings suggest that ER stress contributes to synovial myofibroblastic differentiation in joint capsule fibrosis and may also serve as a potential therapeutic target in joint contractures.

A symptomatic cyamella in the popliteus tendon causing snapping knee: a case report and literature review.

BACKGROUND: Cyamella,the sesamoid bones of the popliteus muscle, are rare in humans. Snapping knee is an uncommon problem which can be difficult to diagnose. CASE PRESENTATION: In this case, we report a 24-year-old male with snapping knee caused by symptomatic cyamella in the popliteus tendon. A large cyamella was identified upon surgery and was removed. Postoperatively, the patient had immediate relief of preoperative symptoms, and there were no signs of recurrence after 1 years of follow-up. CONCLUSIONS: Although not previously suggested, symptomatic cyamella in the popliteus tendon should be considered as part of the differential diagnosis of the snapping knee.

Theoretical Exploration of Halogen Bonding Interactions in the Complexes of Novel Nitroxide Radical Probes and Comparison with Hydrogen Bonds.

In this work, halogen bonding interactions in the complexes of two new nitroxide radicals, which contain both a halogen-bond-donor group and an electron-spin-resonance-active radical unit, were investigated using density functional theory calculations. For comparison, the corresponding hydrogen-bonded complexes were also examined. Halogen bonds in these systems are predicted to be linear and much stronger than hydrogen bonds. To further understand the nature of these interactions, many theoretical methods, such as atoms in molecules, noncovalent interaction index, localized orbital locator, energy decomposition analysis, electron density difference, and electron spin densities, were employed. Compared with hydrogen bonds, halogen bonds have more open shell and covalent interaction components. Particularly, the formation of halogen bonds changes the ratio of different conformations, leading to spin density shift on certain atoms. The results reported herein will assist in the design of new functional probes for the detection of halogen bonding.

The Interactions between Imidazolium-Based Ionic Liquids and Stable Nitroxide Radical Species: A Theoretical Study.

In this work, the interactions between imidazolium-based ionic liquids and some stable radicals based on 2,2,6,6-tetramethylpiperidine-1-yloxyl (TEMPO) have been systematically investigated using density functional theory calculations at the level of M06-2x. Several different substitutions, such as hydrogen bonding formation substituent (OH) and ionic substituents (N(CH3)3(+) and OSO3(-)), are presented at the 4-position of the spin probe, which leads to additional hydrogen bonds or ionic interactions between these substitutions and ionic liquids. The interactions in the systems of the radicals containing ionic substitutions with ionic liquids are predicted much stronger than those in the systems of neutral radicals, resulting in a significant reduction of the mobility of ionic radicals in ionic liquids. To further understand the nature of these interactions, the natural bond order, atoms in molecules, noncovalent interaction index, electron density difference, energy decomposition analysis, and charge decomposition analysis schemes were employed. The additional ionic interactions between ionic radicals and counterions in ionic liquids are dominantly contributed from the electrostatic term, while the orbital interaction plays a major role in other interactions. The results reported herein are important to understand radical processes in ionic liquids and will be very useful in the design of task-specific ionic liquids to make the processes more efficient.

Guest-Induced Breathing Effect in a Flexible Molecular Crystal.

By introducing a flexible component into a molecular building block, we present an unprecedented alkyl-decorated flexible crystalline material with a breathing behavior. Its selective adsorption is derived from the breathing effect induced by a guest triggered alkyl transformation. This feature allows the crystal to take up 2.5 mmol g(-1) of chloroform with high adsorption selectivity (CHCl3 /EA >2000 for example), implying a potential application in sorption separation and chemical sensors.

The acidity/basicity of metal-containing ionic liquids: insights from surface analysis and the Fukui function.

Metal-containing ionic liquids (ILs) have been recognized as potential solvents, catalysts, catalyst precursors and reagents for many organic processes. In this work, several quantum-chemical parameters, including the surface electrostatic potential (Vs,max and Vs,min), the lowest surface average local ionization energy (I̅s,min), and the electrostatic potential at the position of an atom (EPnuc), were adopted to understand the acidity/basicity of metal-containing ILs. Chlorometallate-based ILs show stronger acidity than conventional ILs, because of the increased electron-deficiency of the imidazole ring upon the incorporation of metal chloride. For the ILs with the Ag-coordinated cations, the acidity tends to attenuate while the basicity becomes stronger, as compared to traditional ILs. In addition, the regional Fukui function was also used to assess the molecular distribution of the Lewis acidity/basicity of the ILs under study. Overall, the introduction of metals into either the cations or the anions influences the acidity/basicity of ILs to a large degree, which would be beneficial for their certain applications, such as catalysis and extraction. We hope that the results presented here will assist in the development of novel metal-containing ILs with desirable properties.

Tuning spin-states of carbynes and silylynes: a long jump with one leg.

The challenge motivating this paper is to induce, by chemical substitution, a silylyne, SiR, or a congeneric carbyne, CR, to adopt the high-spin quartet rather than the low-spin doublet as its ground state. The difficulty is seen in the preference for the doublet of the parent SiH (doublet-quartet energy difference ∼39 kcal/mol, favoring the doublet) or CH (∼17 kcal/mol). Strategies for having high-spin ground state parallel those for silylenes and carbenes: greater electropositivity (σ-donation) and π-acceptance of the single substituent favor the high-spin state. The electronegativity trend can be understood from an ions in molecules way of thinking already present in the literature in the works of Boldyrev and Simons, and of Mavridis and Harrison; i.e., the quartet ground state spin of some CR/SiR species is largely determined by the ground state spin of C(-)/Si(-). In this study, we provide a diabatization analysis that solidly confirms the ions in molecules picture and explains the difference in the equilibrium internuclear distances for the two spin states. In general, electronegativity dominates the ordering of spin states. π-Acceptors also help to lower the quartet state energy of the many carbynes (silylynes) examined, whose range of doublet-quartet differences calculated is impressive, 120 (100) kcal/mol. The qualitative understanding gained leads to the prediction of some quartet-ground state carbynes (CMgH, CAlH2, CZnH, CSiH3, CSiF3, etc.) and a smaller number of silylynes (SiMgH, SiMgF, SiBeH, etc.). A beginning is made on the energetics of approach geometries of the fragments in the highly exoergic dimerization of CH to acetylene; it should proceed for the ground state doublet CH through C2h-like trajectories, with no activation energy.

The cyanate and 2-phosphaethynolate anion congeners ECO- (E = N, P, As, Sb, Bi): prelude to experimental characterization.

Pioneering synthetic research by the groups of Grutzmacher and Goicoechea have made possible the preparation of 2-phosphaethynolates (PCO(-)). The obvious question arises: can progress be made toward AsCO(-), SbCO(-), and BiCO(-)? Here the properties of all five anion congeners ECO(-) (E = N, P, As, Sb, Bi) were systematically investigated using ab initio coupled-cluster methods with correlation-consistent basis sets cc-pVXZ (X = D, T, Q). These anions exhibit linear structures with significant natural bond orbital negative charge on both the E and O atoms. These species should react with electrophiles via attack at either center. On going from nitrogen to bismuth, with the atomic radius increasing, the bond between E and C becomes weaker, while the C-O bond tends to be slightly stronger. By the time one gets to BiCO(-), the C-O bond distance is 1.181 Å, indicating a very strong double bond. Relative to the PCO(-) anion, which is reactive toward several unsaturated compounds, the As/Sb/BiCO(-) anions may undergo cycloaddition more readily with unsaturated substrates. The dissociation energy of the E-C bond, except for that of NCO(-), is predicted to be much less than that of the C-O bond. These dissociation energies are 76 kcal/mol (P(-)-CO), 58 kcal/mol (As(-)-CO), 37 kcal/mol (Sb(-)-CO), and 28 kcal/mol (Bi(-)-CO). Even the BiCO(-) anion should be achievable in the laboratory. The vibrational frequencies for these anions are predicted, and our results should assist in the experimental characterization and exploration of the heavier congeners ECO(-).

Halogen bond: its role beyond drug-target binding affinity for drug discovery and development.

Halogen bond has attracted a great deal of attention in the past years for hit-to-lead-to-candidate optimization aiming at improving drug-target binding affinity. In general, heavy organohalogens (i.e., organochlorines, organobromines, and organoiodines) are capable of forming halogen bonds while organofluorines are not. In order to explore the possible roles that halogen bonds could play beyond improving binding affinity, we performed a detailed database survey and quantum chemistry calculation with close attention paid to (1) the change of the ratio of heavy organohalogens to organofluorines along the drug discovery and development process and (2) the halogen bonds between organohalogens and nonbiopolymers or nontarget biopolymers. Our database survey revealed that (1) an obviously increasing trend of the ratio of heavy organohalogens to organofluorines was observed along the drug discovery and development process, illustrating that more organofluorines are worn and eliminated than heavy organohalogens during the process, suggesting that heavy halogens with the capability of forming halogen bonds should have priority for lead optimization; and (2) more than 16% of the halogen bonds in PDB are formed between organohalogens and water, and nearly 20% of the halogen bonds are formed with the proteins that are involved in the ADME/T process. Our QM/MM calculations validated the contribution of the halogen bond to the binding between organohalogens and plasma transport proteins. Thus, halogen bonds could play roles not only in improving drug-target binding affinity but also in tuning ADME/T property. Therefore, we suggest that albeit halogenation is a valuable approach for improving ligand bioactivity, more attention should be paid in the future to the application of the halogen bond for ligand ADME/T property optimization.

Structures and electronic properties of transition metal-containing ionic liquids: insights from ion pairs.

Transition metal-containing ionic liquids (TM-ILs) have attracted a great deal of attention in recent years, due to their unique physical and chemical properties. In this work, several representative TM-ILs, such as the cations consisting of silver(I) center coordinated by two n-alkylimidazole ligands ([(C(n)(im))Ag(mim)](+)) and the anions involving mercury(II) (HgCl3(-)), zinc(II) (ZnCl3(-)), and rhenium(VII) (ReO4(-)), were investigated using density functional theory calculations. First, the structural and energetic properties of the ion pairs for these TM-ILs have been examined in detail and compared with properties for conventional ILs. It was found that the interactions between the cations and anions, including hydrogen bonds and electrostatic interactions, in TM-ILs become weaker in strength than those in traditional ILs. In particular, the calculated geometric and energetic features compare fairly well with the experimental results, such as melting points and X-ray crystal structures of these TM-ILs. Then, the structures and energetics of ion-pair dimers for three ILs containing HgCl3(-), ZnCl3(-), and ReO4(-) were also explored, to gain a deeper understanding of the properties of TM-ILs. Finally, a survey of the Cambridge Structural Database (CSD) was undertaken to provide some crystallographic implications of TM-ILs.

Stability and Dynamics Analysis of Time-Delay Fractional-Order Large-Scale Dual-Loop Neural Network Model With Cross-Coupling Structure.

In recent years, the analysis of the dynamics of annular neural networks has received extensive attention and achieved some achievements. However, most of the current research merely focuses on the single-ring, low-dimension, two rings sharing one neuron cases, without considering the rich coupling modes between rings. In this article, a large-scale time-delay fractional-order dual-loop neural network model with cross-coupling structure is established, in which two rings complete information interaction through two shared neurons. Moreover, the Caputo fractional derivative is introduced in this article to describe the neural network more accurately. First, the transmission time delay between each neuron is selected as the key parameter leading to the bifurcation, and the characteristic equation of the network is creatively derived using the Coates flow graph method. Subsequently, through the holistic element method and magnitude angle formula, we simplify the analytical process. Then, we obtain the stability and Hopf bifurcation criterion of the network. Finally, the conclusions of the theoretical analysis are verified by a series of numerical simulations. The results show that the stability region of the network is closely related to the fractional order, the number of neurons, the distribution of neurons, and the self-feedback coefficients. Moreover, the time delays have a significant effect on the amplitude and period of the Hopf bifurcation.