Analysis of influencing factors and interaction of body weight and disease outcome in patients with prediabetes

BACKGROUND The trend of prediabetes progressing to type 2 diabetes mellitus(T2DM)is prominent,and effective intervention can lead to a return to prediabetes.Exploring the factors influencing the outcome of prediabetes is helpful to guide clinical intervention.The weight change in patients with prediabetes has not attracted much attention.AIM To explore the interaction between body weight and the factors affecting the progression of prediabetes to T2DM.METHODS We performed a retrospective analysis of 236 patients with prediabetes and 50 with normal glucose tolerance(NGT),and collected clinical data and follow-up results of all patients.Based on natural blood glucose outcomes,we classified 66 patients with progression to T2DM into the disease progression(DP)group,and 170 patients without progression to T2DM into the disease outcome(DO)group.We analyzed the factors that influenced prediabetes outcome and the influence of body weight on prediabetes blood glucose outcome by unconditional logistic regression.A general linear model(univariate)was used to analyze the interaction between body weight and independent influencing factors.RESULTS There were 98 cases of impaired fasting glucose(IFG),90 cases of impaired glucose tolerance(IGT),and 48 cases of coexistent IFG and IGT.The body weight,waist circumference,body mass index,fasting blood glucose,and 2 h plasma glucose of patients with IFG,IGT,and coexistent IFG and IGT were higher than those in patients with NGT(P<0.05).Logistic regression analysis showed that body weight,glycosylated hemoglobin,uric acid,fasting insulin,and homeostatic model assessment for insulin resistance were independent factors affecting progression of prediabetes to T2DM(P<0.05).Receiver operating characteristic curve analysis showed that the area under the curve predicted by the above indicators combined was 0.905[95%confidence interval(CI):0.863-0.948],which was greater than that predicted by each indicator alone.Logistic regression analysis with baseline body weight as an independent variable showed that compared with body weight 1,the odds ratio(95%CI)of body weight 3 was 1.399(1.142-2.126)(P=0.033).There was a multiplicative interaction between body weight and uric acid(β=1.953,P=0.005).CONCLUSION High body weight in patients with prediabetes is an independent risk factor for progression to T2DM,and the risk of progression is increased when coexisting with high uric acid level.

Risk factors and their interactive effects on severe acute pancreatitis complicated with acute gastrointestinal injury

BACKGROUND There are many risk factors for severe acute pancreatitis(SAP)complicated with acute gastrointestinal injury(AGI),but few reports on the interaction between these risk factors.AIM To analyze the risk factors for SAP complicated with AGI and their interactive effects.METHODS We selected 168 SAP patients admitted to our hospital between December 2019 and June 2022.They were divided into AGI group and non-AGI group according to whether AGI was present.Demographic data and laboratory test data were compared between the two groups.The risk factors for SAP with concomitant AGI were analyzed using multifactorial logistic regression,and an analysis of the interaction of the risk factors was performed.RESULTS The percentage of patients with multiple organ dysfunction syndrome,acute physiological and chronic health scoring system II(APACHE II)score,white blood cell count and creatinine(CRE)level was higher in the AGI group than in the non-AGI group.There was a statistically significant difference between the two groups(P<0.05).Logistic regression analysis indicated that an APACHE II score>15 and CRE>100μmol/L were risk factors for SAP complicating AGI.The interaction index of APACHE II score and CRE level was 3.123.CONCLUSION An APACHE II score>15 and CRE level>100μmol/L are independent risk factors for SAP complicated with AGI,and there is a positive interaction between them.

New insights of Helicobacter pylori host-pathogen interactions: The triangle of virulence factors, epigenetic modifications and non-coding RNAs

Helicobacter pylori(H. pylori) is a model organism for understanding host-pathogen interactions and infection-mediated carcinogenesis. Gastric cancer and H. pylori colonization indicates the strong correlation. The progression and exacerbation of H. pylori infection are influenced by some factors of pathogen and host. Several virulence factors involved in the proper adherence and attenuation of immune defense to contribute the risk of emerging gastric cancer, therefore analysis of them is very important. H. pylori also modulates inflammatory and autophagy process to intensify its pathogenicity. From the host regard, different genetic factors particularly affect the development of gastric cancer. Indeed, epigenetic modifications, Micro RNA and long non-coding RNA received more attention. Generally, various factors related to pathogen and host that modulate gastric cancer development in response to H. pylori need more attention due to develop an efficacious therapeutic intervention. Therefore, this paper will present a brief overview of host-pathogen interaction especially emphases on bacterial virulence factors, interruption of host cellular signaling, the role of epigenetic modifications and non-coding RNAs.

Effects of interactions between environmental factors and KIF1B genetic variants on the risk of hepatocellular carcinoma in a Chinese cohort

AIM: To examine the effect of the potential interaction between KIF1 B variants(rs17401966 and rs3748578) and environmental factors on the risk of hepatocellular carcinoma(HCC) in a high-risk region in China.METHODS: Three hundred and six patients with HCC and 306 hospital-based control participants residing in the Shunde region of Guangdong Province, China were enrolled. Clinical characteristics were collected by reviewing the complete medical histories from the patient archives, and epidemiological data were collected using a questionnaire and clinical examination. Two single nucleotide polymorphisms(SNPs) of KIF1B(rs17401966 and rs3748578) were chosen for the current study. All subjects were genotypedusing a Taq Man real-time polymerase chain reaction. Multiplicative and additive logistic regression models were used to evaluate various gene-environment interactions.RESULTS: Smoking, frequent consumption of raw freshwater fish, hepatitis B virus(HBV) infection, and a family history of HCC were important risk factors for HCC in this population. Chronic infection with HBV was the most important environmental risk factor for HCC [odds ratio(OR) = 12.02; 95% confidence interval(95%CI): 6.02-24.00]. No significant association was found between the KIF1 B variants alone and the risk of HCC. Nevertheless, a significant additive effect modification was observed between rs17401966 and alcohol consumption(P for additive interaction = 0.0382). Compared with non-drinkers carrying either the AG or GG genotype of rs17401966, individuals classified as alcohol consumers with the AA genotype of rs17401966 had a significantly increased risk of HCC(OR = 2.36; 95%CI: 1.49-3.74).CONCLUSION: The gene-environment interaction between the KIF1 B rs17401966 variant and alcohol consumption may contribute to the development of HCC in Chinese individuals.

An Updated Mini Review on Grapefruit: Interactions with Drugs, Obesity and Cardiovascular Risk Factors

The paper examines the effects of grapefruit consumption in relation to drugs, obesity and cardiovascular risk factors. The review includes the most updated studies found in Pub-Med. The grapefruit effect refers to the ability of grapefruit juice and supplements to interact with a wide variety of pharmaceuticals, either enhancing or limiting their systemic availability. Due to altering the active dosage of the pharmaceutical, Grapefruit juice is commonly not allowed to be used alongside with many drugs. Naringin is the most important one, which can inhibit absorption of some drugs but more commonly 6’7’-dihydroxybergamottin, which inhibits CYP3A4. Lately, grapefruit has been found both in rats and adults to reduce body weight, blood pressure, improve lipid and hepatic profile and decrease platelet aggregation. These promising results must be followed by additional studies in order to add to the importance of the role and effects of grapefruit as part of our diet.

The driving factors and their interactions of fire occurrence in Greater Khingan Mountains, China

Fire is an important disturbance in terms of forest management.A comprehensive understanding of the relationships between the spatial distribution of fire occurrence and its driving factors are critical for effective forest fire management.To reveal biogeoclimatic and anthropogenic influences,this study introduced a geographical detector model to quantitatively examine the effects of multiple individual factors and their combinations on spatial patterns of fire occurrence in the Greater Khingan Mountains between 1980 and 2009.The geographical detector computes the explanatory power(q value)to measure the connection between driving factors and spatial distributions of fire occurrence.Kernel density estimation revealed the spatial variability of fire occurrence which was impacted by bandwidth.30 km might be the optimal bandwidth in this study.The biogeoclimatic and anthropogenic effects were explored using topography,climate,vegetation,and human activity factors as proxies.Our results indicated that solar radiation had the most influence on the spatial pattern of fire occurrence in the study area.Meanwhile,Normalized Difference Vegetation Index,temperature,wind speed,and vegetation type were determined as the major driving factors.For various groups of driving factors,climate variables were the dominant factors for the density of fire occurrence,while vegetation exerted a strong influence.The interactions between the driving factors had a more significant impact than a single factor.Individually,the factors in the topography and human activity groups exhibited weaker influences.However,their effects were enhanced when combined with climate and vegetation factors.This study improves our understanding of various driving factors and their combined influences on fire occurrences of the study area in a spatial context.The findings of this study verify that the geographical detector is applicable in revealing the driving factors of fire occurrence.

“Do Big Hands Guide Small Hands?”or“do Small Hands Guide Big Hands”:The intergenerational interactions in environmental behaviors and family influencing factors

Families'large pollution and energy consumption cannot be underestimated.In order to realize and internalize environmental awareness as a social consensus,it is imperative for every member of a household to be involved in transforming everyday behavior.Intergenerational interactions are of paramount importance.Accordingly,the focus of this study was on parent-adolescent interactions,their reciprocal impact on environmental behaviors,and the factors that have an influence on these processes.Questionnaires were employed to collect information of 684 families in 10 districts of Jinan,the capital of Shandong Province.Subsequently,interviews were conducted with 15 of these families to comprehend the tangible reasons underlying intergenerational interactions in environmental behaviors.First,a paired sample T-test was employed to compare the frequency of these interactions.The data showed that while the T values were positive in all eight compared groups,there were significant differences in seven of them.These results suggest that the impact of intergenerational interactions on environmental behaviors is not symmetrical:parents'instructions are far more frequent than adolescents'back-feeding of ecological notions.The interviews revealed that this phenomenon was generated primarily by unequal experiences between parents and adolescents because the latter do not participate in housework and family projects.Furthermore,the traditional concept of intergenerational order appears to be permanent.Second,two linear regression models,a Parent-to-Adolescent model and an Adolescent-to-Parent model that encompassed several factors including family structure,intergenerational relationships,living environment,and families'social class were developed.Among these factors,the intergenerational relationship variable played a particularly significant role:the more equal and open-minded dialogs are incorporated into parent-adolescent communication,the more favorable interactions may occur for development of their environmental behaviors.Thus,when an environmental education system with families is constructed,it is imperative to promote a parent's ecological awareness with the help of grass-roots organizations by means of reasonable rewards and punishments to redress their former behaviors so as to let Big Hands Guide Small Hands.It is also crucial to enhance a more equal intergenerational relationship through parents'schooling or other relevant services so as to create a favorable atmosphere for Small Hands Guide Big Hands.

Interaction and Relationship Between Angiotensin ConvertingEnzyme Gene and Environmental Factors Predisposing toEssential Hypertension in MongolianPopulation of China

Objective To investigate the association of specific functional gene ACE (I/D) variants of the renin-angiotensin system with essential hypertension (EH) and interaction between ACE (I/D) gene and risk factors for EH in a genetically homogenous Mongolia rural population of China. Methods Individuals (n=1099) were recruited from general population of Kezuohouqi Banner in Inner Mongolian Autonomous Region. Results The association was found between ACE genotype DD plus ID and EH, with an interaction between ACE genotype DD plus ID and cigarette smoking in an additive model. Cigarette smoking index and ACE gene showed a low exposure-gene (LEG) effect on EH, with interaction indices from 7.10 to 1.16. Interaction between ACE genotype DD plus ID and alcohol drinking on EH appeared an additive model. Alcohol drinking index and ACE gene showed a low exposure-gene (LEG) effect on EH, with interaction indices from 1.66 to 1.09. BMI and ACE gene showed a low exposure-gene (LEG) effect on EH, with interaction indices from 6.15 to 2.49. Interactions between ACE genotype and WHR on EH showed a multiplicative model. In a short, there was an interaction between ACE gene and cigarette smoking, alcohol drinking and BMI on EH, especially in a low dose-exposure effect Conclusion It is important for individuals who carry ACE D allele gene to prevent EH, and furthermore, to prevent and control coronary heart disease, in a view of population-based prevention.

Glial cell line-derived neurotrophic factor and brain-derived neurotrophic factor regulate the interaction between astrocytes and Schwann cells at the trigeminal root entry zone

The trigeminal root entry zone is the zone at which the myelination switches from peripheral Schwann cells to central oligodendrocytes.Its special anatomical and physiological structure renders it susceptible to nerve injury.The etiology of most primary trigeminal neuralgia is closely related to microvascular compression of the trigeminal root entry zone.This study aimed to develop an efficient in vitro model mimicking the glial environment of trigeminal root entry zone as a tool to investigate the effects of glial cell line-derived neurotrophic factor and brain-derived neurotrophic factor on the structural and functional integrity of trigeminal root entry zone and modulation of cellular interactions.Primary astrocytes and Schwann cells isolated from trigeminal root entry zone of postnatal rats were inoculated into a two-well silicon culture insert to mimic the trigeminal root entry zone microenvironment and treated with glial cell line-derived neurotrophic factor and brain-derived neurotrophic factor.In monoculture,glial cell line-derived neurotrophic factor promoted the migration of Schwann cells,but it did not have effects on the migration of astrocytes.In the co-culture system,glial cell line-derived neurotrophic factor promoted the bidirectional migration of astrocytes and Schwann cells.Brain-derived neurotrophic factor markedly promoted the activation and migration of astrocytes.However,in the co-culture system,brain-derived neurotrophic factor inhibited the migration of astrocytes and Schwann cells to a certain degree.These findings suggest that glial cell line-derived neurotrophic factor and brain-derived neurotrophic factor are involved in the regulation of the astrocyte-Schwann cell interaction in the co-culture system derived from the trigeminal root entry zone.This system can be used as a cell model to study the mechanism of glial dysregulation associated with trigeminal nerve injury and possible therapeutic interventions.

Hypoxia-inducible factor-1αin myocardial infarction

Hypoxia-inducible factor 1(HIF1)has a crucial function in the regulation of oxygen levels in mammalian cells,especially under hypoxic conditions.Its importance in cardiovascular diseases,particularly in cardiac ischemia,is because of its ability to alleviate cardiac dysfunction.The oxygen-responsive subunit,HIF1α,plays a crucial role in this process,as it has been shown to have cardioprotective effects in myocardial infarction through regulating the expression of genes affecting cellular survival,angiogenesis,and metabolism.Furthermore,HIF1αexpression induced reperfusion in the ischemic skeletal muscle,and hypoxic skin wounds in diabetic animal models showed reduced HIF1αexpression.Increased expression of HIF1αhas been shown to reduce apoptosis and oxidative stress in cardiomyocytes during acute myocardial infarction.Genetic variations in HIF1αhave also been found to correlate with altered responses to ischemic cardiovascular disease.In addition,a link has been established between the circadian rhythm and hypoxic molecular signaling pathways,with HIF1αfunctioning as an oxygen sensor and circadian genes such as period circadian regulator 2 responding to changes in light.This editorial analyzes the relationship between HIF1αand the circadian rhythm and highlights its significance in myocardial adaptation to hypoxia.Understanding the changes in molecular signaling pathways associated with diseases,specifically cardiovascular diseases,provides the opportunity for innovative therapeutic interventions,especially in low-oxygen environments such as myocardial infarction.

A NOTE ON 2_(IV)^(m-p) DESIGNS WITH THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS

In this article, the authors obtain some theoretical results for 2_(IV)^(m-p) designs to have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2_(IV)^(m-p) designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration.

Risk factors for Parkinson's disease and interaction analysis in Chinese patients

BACKGROUND： The etiology of Parkinson＇s disease （PD） remains unclear. The majority of studies have focused on the correlation between various factors and PD, with very different conclusions. To date, there has been no study on the interaction between PD family history and other risk factors, and very few studies have reported on hedtability. OBJECTIVE： To explore the risk factors for PD, the interaction between family history and other risk factors, and the impact of genetic factors on PD. DESIGN, TIME AND SETTNG： A paired, retrospective, case-control study was performed at the Department of Neurology, Qilu Hospital of Shandong University from November 2006 to October 2008. PARTICIPANTS： The case group included 157 Chinese PD patients selected from the Department of Neurology, Qilu Hospital of Shandong University in China from 2006 to 2008. An additional 157 patients treated in the same department during the same period were selected as the control group, and they were paired with regard to gender, age, and nationality to the case group. METHODS： Various scored factors were investigated in all participants. The association between various factors and PD was analyzed using univariate and multivariate logistic regression analysis. Interaction analysis between family history and other risk factors was performed using a logistic regression model. Heritability analysis was performed with the Falconer method. MAIN OUTCOME MEASURES： Risk factors for PD, interaction between family history and other risk factors, and heritability. RESULTS： Logistic regression analysis showed that family history, mental work, insecticide exposure, alcohol, and depression positively correlated with PD （odds ratio = 6.75, 2.37, 2.42, 2.03, 5.20, P〈 0.05）, whereas smoking had a negative correlation with PD （odds ratio = 0.49, P 〈 0.001）. The proportions of the effect attributable to interaction of family history and insecticide exposure, alcohol, and depression were 55.2%, 34.0%, and 41.4%, respectively, with a relative excess risk due to interaction of 8.96, 3.31, and 7.85, respectively. PD heritability from first-degree relatives was （36.86 ± 5.76） % and from second-degree relatives was （20.66 ± 6.81） %. CONCLUSION： Family history, mental work, insecticide exposure, alcohol, and depression were determined to be risk factors for PD, whereas smoking was a protective factor. Family history had a positive interaction with coexisting risk factors. Genetic factors had a smaller action on PD than environmental factors.

Effects of three-body interaction on dynamic and static structure factors of an optically-trapped Bose gas

We investigate how three-body interactions affect the elementary excitations and dynamic structure factor of a Bose- Einstein condensate trapped in a one-dimensional optical lattice. To this end, we numerically solve the Gross-Pitaevskii equation and then the corresponding Bogoliubov equations. Our results show that three-body interactions can change both the Bogoliubov band structure and the dynamical structure factor dramatically, especially in the case of the two-body interaction being relatively small. Furthermore, when the optical lattice is strong enough, the analytical results, combined with the sum-rule approach, help us to understand that： the effects of three-body interactions on the static structure Ihctor can be significantly amplified by an optical lattice. Our predictions should be observable within the current Bragg spectroscopy experiment.

Analysis of Interaction Factors Between Two Piles

A rigorous analytical method is presented for calculating the interaction factor between two identi- cal piles subjected to vertical loads.Following the technique proposed by Muki and Sternberg,the problem is decomposed into an extended soil mass and two fictitious piles characterized respectively by Young's modulus of the soil and that of the difference between the pile and soil.The unknown axial forces along fictitious piles are determined by solving a Fredholm integral equation of the second kind,which imposes the compatibility condition that the axial strains of the fictitious piles are equal to those corresponding to the centroidal axes of the extended soil.The real pile forces and displacements can subequally be calculated based on the determined fictitious pile forces,and finally,the desired pile interaction factors may be obtained.Results confirm the validity of the proposed approach and portray the influence of the governing parameters on the pile interaction.

Effects of genetic and environmental factors and gene-environment interaction on expression variations of genes related to stroke in rat brain

To determine if genetic and environmental (dietary) factors and gene-environment interaction impact on the expression variation of genes related to stroke, we conducted microarray experiments using two homozygous rat strains SHRSR and SHRSP fed with high and low dietary salt levels. We obtained expression data of 8,779 genes and performed the ranking analysis of microarray data. The results show that the genetic difference for stroke in rat brain has a strong effect on expression variations of genes. At false discovery rate (FDR) ≤ 5%, 534 genes were found to be differentially expressed between the genotypes resistant and prone to stroke, among which 304 genes were up-regulated in the resistant genotype and down-regulated in the prone genotype and 230 were down-regulated in the former and up-regulated in the latter. In addition, 365 were functional genes for transcription and translation, receptors (in particular, neurotransmitter receptor), channels of ions, transportation, metabolism and enzymes, and functional and structural proteins. Some of these genes are pivotal genes that cause stroke. However, dietary salt levels and GE interaction do not strongly impact on the expression variations of these genes detected on arrays.

Interaction of methylenetetrahydrofolate reductase C677T,cytochrome P4502E1 polymorphism and environment factors in esophageal cancer in Kazakh population

AIM: To evaluate the association and interaction of genetic polymorphisms in methylenetetrahydrofolate reductase (MTHER) and cytochrome P4502E1 (CY-P4502E1), environment risk factors with esophageal cancer (EC) in Kazakh, a high EC incidence area of Xinjiang Uygur Autonomous Region, China.METHODS: A 1:2 matched case-control study was conducted with 120 cases of EC and 240 population-or hospital-based controls. The controls were matched for sex, nationality, area of residence and age within a 5-year difference. MTHER and CYP4502E1 genotypes were identified by PCR-based restriction fragment length polymorphism (RFLP). A conditional logistic regression model was established to identify risk factors. The strata method was adopted in interaction analysis. RESULTS: Low consumption of green vegetables and fresh fruits, alcohol drinking, and unsafe water (shallow well, or river) were found to be the risk factors for EC. Individuals with the MTHFR677 (C/T + T/T) genotype had a 2.62-fold (95% CI: 1.61-4.28) risk of developing EC compared with those who carried the C/C genotype. Individuals with the CYP4502E1C1/C1 genotype had a 3.00-fold (95% CI: 1.82-4.96) risk compared with those who carried the CYP4502E1 (C1/C2 + C2/C2) genotype.Gene-environment interaction analysis showed that MTHFR677 gene polymorphism was correlated with consumption of green vegetables and fresh fruit, while CYP4502E1 C1/C1 was correlated with alcohol drink-ing and unsafe drinking water. MTHFR and CYP4502E1 analysis of gene-gene interaction showed that individu-als with the MTHFR677 (C/T + T/T) and CYP4502E1C1/C1 genotypes had a 7.41-fold (95% CI: 3.60-15.25) risk of developing EC compared with those who carried the MTHFR677C/C and CYP4502E1 RsaI C1/C2 + C2/C2 genes, and the interaction rate was higher than that of the two factors alone. CONCLUSION: Low consumption of green vegetables and fresh fruits, alcohol drinking, and unsafe water (shallow well, or river) and polymorphisms in MTHFR and CYP4502E1 genes are important risk factors for EC. There is a synergistic interaction among polymorphisms in MTHFR and CYP4502E1 genes and environment factors. MTHFR and CYP4502E1 genes can be used as biomarkers for prevention of EC in Kazakh, Xinjiang Uygur Autonomous Region, China.

Interaction of Mechanical and Electrochemical Factors duringCorrosion Fatigue of Fe-26Cr-1Mo Stainless Steel in 1M H_2SO_4 Solution

The cyclic plastic straining electrode technique has been used to investigate the transient electrochemical behaviour of Fe-26Cr1Mo stainless steel in 1M H2SO4 solution at a passive potential.The influence of plastic strain amplitude and plastic strain rate on the dissolution current response was analysed. The experimental results showed that the transient current was dependent on the competitive process of the surface film rupture and repassivation of the new surface. The high plastic strain amplitude and the high plastic strain rate caused a change of electrochemical activity of specimen surface. In the condition of low strain amplitude and strain rate, the characteristics of current response was mainly relative tp the process of new surface repassivation.The competition kinetics has been analysed through the comparison of plastic strain rate and repassivating rate

Study on the interaction between polymorphisms of FOXO3A gene and environmental factors in longevity at Bama county,Guangxi province

Objective: To study the interaction between the polymorphisms of FOXO3A and the environmental factors in the longevity district of Bama county.Methods: Using Taqmaq probe,genotyping of FOXO3A gene was performed for 200 longevous elderly(aged 90-110)and 288 healthy controls(aged 48-89).The interaction between the polymorphisms of gene and environmental factors were analyzed by using conditional logistic regression.Results: Minor allele frequencies(MAF)of five known SNPs in FOXO3A gene were higher in cases than in controls(P<0.05).There was a positive interction between minority alleles of rs2764264 in FOXO3A gene and the environment factors in the longevity district(OR=11.08,γ=1.075).Conclusion: Five SNPs of FOXO3A gene would be closely correlated with human longevity in Bama.The interaction between the polymorphisms of FOXO3A genes rs2764264 and the environment factors in the longevity district had synergy to longevity.The longevity phenomenon in Bama probably was the result of the interaction between gene and environmental factors.

Analysis of Interaction Factors between Two Piles in Layered Soils

A rigorous analytical method is presented, which takes into account the pile stiffening effects, using the theory of the transfer matrix-bottom rigidity for calculating the interaction factor between two identical piles in multi-layered soils subjected to vertical loads. Following the technique proposed by Muki and Sternberg, the problem is decomposed into extended soil layers and two fictitious piles characterized respectively by Young's moduli of the layered soils and those of the differences between the piles and the layered soils. The unknown axial forces along fictitious piles are determined by solving a Fredholm integral equation of the second kind, which imposes the compatibility condition that the axial strains of the fictitious piles are equal to those corresponding to the centroidal axes of the extended layered soils. The real pile displacements can be calculated based on the determined fictitious pile forces, and finally, the desired pile interaction factors may be obtained. Selected results from parametrical studies are presented to confirm the validity of the proposed approach and portray the influence of the governing parameters on the pile interaction.