Monthly Archives: August 2022

Pattern of Head and Neck Cancer Presentation and Management in a Tertiary Hospital in Owerri, South- East Nigeria

DOI: 10.31038/SRR.2022511

Abstract

Background: Head and neck cancers are increasingly becoming a prominent part of oncological practice in Nigeria due to increasing awareness and advances in this area of practice. Tumours of the head and neck region make up about 5-30% of all tumours in the body and often constitute a burden that impacts their sufferers physically, socially, financially and psychologically. In addition, there has been enormous challenges in the management of these conditions in a developing setting such as ours. The study aimed at assessing the pattern of presentation and management of head and neck cancers cases that presented at Federal Medical Centre, Owerri, Nigeria.

Materials and methods: The study is a 5-year retrospective analysis of all head and neck cancer cases that presented to the ENT Department of Federal Medical Centre, Owerri, Nigeria between January 2015 and December 2019. Data was extracted from patients’ case files, sorted and analyzed with SPSS version 25.0.

Results: A total of sixty-eight (68) head and neck cancer cases were seen over the period, however fifteen (15) cases had incomplete records therefore only fifty-three (53) cases were analyzed. A M:F ratio of 1.3:1 was recorded with the mean age of the patients being 53.5±14.0 years. The mean duration of presenting complaints was 12.2±9.2months. The commonest site of cancer among the patients was the larynx (26.3%) while the commonest histological diagnosis was Squamous cell carcinoma (54.5%). Majority of patients (94.3%) presented with advanced disease (stages III and IV). \The commonest modalities of treatment were surgery alone (35.9%) and chemoradiation therapy (33.9%). Outcome of treatment at 3 months was satisfactory in 43.4%. About 15.1% of the patients did not attend follow up clinics after treatment while 3 patients (5.7%) died within 3 months of treatment.

Conclusion: The pattern of presentation and principles of management of head and neck cancers in Federal Medical Centre, Owerri over recent years are similar to those of contemporary facilities around the region and country. The challenges facing the management of these cases include late presentation, financial paucity, poor social support system and poor follow up culture.

Introduction

Head and neck cancers are increasingly becoming prominent in oncological practice in Nigeria owing to the attention given and the advances made in this area of clinical practice. Tumours of the head and neck make up 5-8% of all tumours in the human body in Europe and America. [1] In India, this figure can be as high as 30%. [2] The prevalence of head and neck cancers in Nigeria vary widely from 6.2% in southern Nigeria [3] to 30% in Northern Nigeria. [4] Worthy of note is that these figures were essentially derived from hospital-based studies and as such may represent only a tip of the iceberg of the real burden of disease. This observation notwithstanding, up to half a million cases of head and neck tumours are diagnosed yearly worldwide and a significant proportion of these are in developing countries. [5] The management of head and neck tumours in Africa and Nigeria in particular is still faced with many challenges due to relative paucity of treatment facilities and widespread ignorance of the nature of the disease among the population leading to late hospital presentation. The aim of this study was to assess the pattern of presentation and management of head and neck cancers that presented to a tertiary health centre, Federal Medical Centre, Owerri, Nigeria over a 5-year period (between January 2015 to December 2019).

Materials and Methods

The study was a retrospective analysis of all head and neck tumour cases that presented to the Ear, Nose and Throat/Head and Neck Department of Federal Medical Centre, Owerri in South-Eastern Nigeria between January 2015 and December 2019. A total of sixty-eight (68) head and neck cancer cases were seen over the period, however fifteen (15) cases had incomplete records and were excluded, therefore only fifty-three (53) cases were analyzed. The case files of all the patients were retrieved from the hospital records and data extracted and analyzed with SPSS software version 25.0. The data analyzed include the socio-demographic characteristics, presenting complaints, clinical and histological diagnoses, treatment and general outcome. The results are represented in tables and charts. Statistical significance was set at p < 0.05 (Tables 1-7).

Table 1: Sociodemographic characteristics of the patients

		Male	Female	Total (%)	p-value
Age of patients (years)	<10	1	0	1 (1.9)	p = 0.353
	11-20	1	1	2 (3.8)
	21-30	5	4	9 (16.9)
	31-40	4	3	7 (13.2)
	41-50	6	5	11 (20.8)
	51-60	5	3	8 (15.1)
	61-70	4	3	7 (13.2)
	71-80	3	3	6 (11.3)
	>80	1	1	2 (3.8)
	Total	30	23	53 (100.0)
Level of education	Primary	6	4	10 (18.9)	P = 0.671.
	Secondary	12	6	18 (33.9)
	Tertiary	10	11	21 (39.6)
	None	2	2	4 (7.6)
	Total	30	23	53 (100.0)
Occupation	Student	2	3	5 (9.4)	p = 0.127
	Unemployed	3	5	8 (15.1)
	Business	19	7	26 (49.1)
	Civil servant	6	8	14 (26.4)
	Total	30	23	53 (100.0)

Table 2: Duration of complaints prior to presentation

	Male	Female	Total (%)	p-value
< 2 months	3	1	4 (7.6)	0.202
2-6 months	9	13	22 (41.4)
7-12 months	12	6	18 (33.9)
13-24 months	4	0	4 (7.6)
25-48 months	1	2	3 (5.7)
> 48 months	1	1	2 (3.8)
Total	30	23	53 (100.0)

The mean duration of presenting complaints prior to presentation was 12.2+/-9.2 months

Table 3: Primary sites of tumours among the patients

	Male	Female	Total (%)	p-value
Larynx	12	2	14 (26.3)	0.001
Sinonasal	6	5	11 (20.7)
Nasopharynx	7	1	8 (15.1)
Parotid gland	1	4	5 (9.4)
Hypopharynx	0	4	4 (7.6)
Oesophagus	2	1	3 (5.7)
Submandibular gland	2	2	4 (7.6)
Thyroid gland	0	2	2 (3.8)
Parapharynx	0	2	2 (3.8)
Total	30	23	53 (100.0)

Table 4: Histological diagnosis of the tumours

	Male	Female	Total (%)	p-value
Squamous cell carcinoma	24	5	29 (54.5)	0.001
Adenocarcinoma	0	5	5 (9.4)
Lymphoma	1	3	4 (7.6)
Sarcoma	1	1	2 (3.8)
Mucoepidermoid carcinoma	2	1	3 (5.7)
Adenoid cystic carcinoma	0	3	3 (5.7)
Acinic cell carcinoma	1	0	1 (1.9)
Verrucous carcinoma	0	3	3 (5.7)
Others	1	2	3 (5.7)
Total	30	23	53 (100.0)

Table 5: Stages of tumours among the patients

	Male	Female	Total (%)
Stage I	0	0	0 (0.0)
Stage II	1	2	3 (5.7)
Stage III	11	7	18 (33.9)
Stage IV	14	18	32 (60.4)
Total	26	27	53 (100.0)

Table 6: Treatment modalities offered to the patients

	Male	Female	Total (%)	p-value
Surgery alone	12	7	19 (35.9)	0.210
Surgery & Radiotherapy	2	6	8 (15.1)
Chemotherapy and Radiotherapy	11	7	18 (33.9)
Surgery, Chemotherapy and Radiotherapy	5	3	8 (15.1)
Total	30	23	53 (100.0)

Table 7: Outcome of treatment 6 weeks after treatment

	Male	Female	Total (%)	p-value
Satisfactory	13	10	23 (43.4)	0.594
Persistent disease	3	2	5 (9.4)
Death	2	1	3 (5.7)
Lost to follow	9	5	14 (26.4)
No follow up	3	5	8 (15.1)
Total	30	23	53 (100.0)

Results

A total of 53 head and neck cancer cases were analyzed over the period (excluding ophthalmological, neurosurgical and oral tumours). This comprised 30 males and 23 females with a male to female ratio of 1.3:1. The ages of the patients studied ranged from 9 to 85 years with a mean age of 53.5±14.0 years. The largest proportion of the patients (39.6%) had tertiary level of education while 34.0% and 18.9% had secondary and primary levels of education respectively.

Discussion

Socio-demographic Characteristics

The study noted slight male predominance with a male to female ratio of 1.3:1. This difference was not statistically significant (p = 0.095). Similar pattern was recorded in similar studies notably by Forae et al, [6] Akinshipo et al [7] and Kanu et al. [8] A systematic review by da Lilly-Tariah et al also found M:F ratio ranging from 1.1:1 to 2.3:1 after reviewing 27 publications on the subject. [9] The reason for this pattern is not known however, it may partly be due to the overwhelming preponderance of the male gender in laryngeal cancers which have widely been reported to be among the commonest head and neck cancers in this part of the world. The mean age of patients in this study (53.5±14.0 years) was slightly higher than those found by other workers; Erinoso et al found 39.6±21.1 years, [10] Adeyemi et al found 43.8±19.6 years, [11] Fomete et al found 48.4±16.2 years [12] and Kodiya et al found 35.5±20.1 years. [13] This suggests that head and neck cancers is prevalent in the middle ages in our environment where life expectancy is not as high as in the developed world. Notably, some other similar studies recorded peak prevalence amongst patients between the 4^th and 5^th decades of life [14,15].

Presenting Features

The commonest presenting symptoms include hoarseness (34.0%), nasal obstruction (30.8%), epistaxis (28.3%), dysphagia (15.1%) and neck swelling (9.4%). This pattern is in keeping with patterns found by similar work where sinonasal and laryngeal malignancies were most predominant. [14,15] The mean duration between the onset of symptoms and presentation was 12.2±9.2 months with majority of the patients (33.9%) presenting after 7-12 months of having the symptoms. This relatively late pattern of presentation is not uncommon in our environment where self-medication with over-the-counter medication is often the first form of care. Only 17 (32.1%) of the patients had formal prior consultations by general practitioners before being referred for specialist attention. In majority of the cases, persistent and worsening symptoms prompted their eventual presentation, albeit in advanced stages. This delayed pattern of presentation was also reported in studies by Okwor et al and in the systematic review by da Lilly-Tariah et al. [9]

Tumour Sites/Clinical Diagnosis

Majority of the tumours were in the larynx (26.3%), Sinonasal region (20.7%) and the nasopharynx (15.1%) while the thyroid and the parapharyngeal area had the lowest proportions at 3.8% each. A systematic review of 27 similar studies found the nasopharynx to be the commonest site followed by the sinonasal region and the larynx.⁹ Identical pattern was recorded by Nwawolo et al, [14] in Lagos, south-west Nigeria however, about 300km northwards, Ologe et al in Ilorin, Nigeria found relatively low prevalence for the larynx (ranking 4th with 4.5%). [15] The reason for this discrepancy is not clear, however variation in social behaviours such as smoking and alcohol intake between these regions are thought to play a role. [16,17] Our study reveals significant male predominance among laryngeal cancer sufferers (M:F ratio of 6:1) with similar pattern widely reported in this part of the world and attributed largely to such social practices as smoking and alcohol intake which are commoner among men. [3,8,9,12] Similar trend applies for nasopharyngeal carcinoma with a M:F of 7:1 in this study.

Tumour Type/Histological Diagnosis

By far, the predominant cancer in this study was squamous cell carcinoma accounting for 54.5%. Less common types include adenocarcinoma (9.4%), lymphomas (7.6%), adenoid cystic carcinoma (5.7%), sarcomas (3.8%) and acinic cell carcinoma (1.9%). An overwhelming majority (82.9%) of head and neck cancers in this study are of epithelial origin which largely mirrors the pattern in several similar studies in Nigeria such as those by Nwawolo et al (carcinomas 91.0% and sarcomas 6.6%), [14] Forae et al (carcinomas 83.4%, lymphomas 7.7% and sarcomas 3.5%), [6] Akinshipo et al (carcinomas 70.0%, sarcomas 15.0% and sarcomas 15.0%) [7] and Ologe et al (carcinomas 70.8%, lymphomas 20.2% and blastomas 9.0%). [15] The predominance of epithelial cancers is understandable considering that majority of the surfaces of the upper aerodigestive tract where tumourigenesis generally occurs are lined by squamous cell and columnar epithelium. Furthermore, a Nigerian meta-analysis of head and neck cancers lends credence to the pattern. [9]

Tumour Stage

The cases were graded using the TNM group staging (UICC/AJCC) models. Stage III and IV tumours accounted for 33.9% and 60.4% of the tumours respectively and when combined, the two stages accounted for 94.3% of all cases. Similar results were obtained Okwor et al in Ibadan, southwest Nigeria (stages III and IV cancers accounted for 87.5% of all head and neck cancers) [16] and a systematic review of 27 studies by da Lilly-Tariah et al. [9] This underscores the rampant delayed presentation often experienced in the more deprived regions of sub-saharan/tropical Africa and brings to fore the challenges faced by clinicians managing head and neck cancers in this region of the world. Inadequate health knowledge and lack of efficient primary health care centres may be factors responsible for late presentation of head and neck cancers in Nigeria. More elaborate studies aimed at ascertaining these factors are desirable.

Treatment/Management

The modality of treatment adopted for each case was decided based on the nature/stage of the tumour and the available resources for treatment. Because of the lack of radiotherapy facility at the centre of study, patients who required radiation therapy were referred to centres where such facilities were available however, they were seen on follow up schedules at our centre, where feasible. Majority of the patients (35.9%) were treated with surgery alone while 33.9% had combined chemoradiation without surgery. Because majority of the patient presented with advanced disease, there was limited chance for complete surgical removal of the tumour in many patients who were then referred for chemoradiation therapy. This pattern of intervention described here have been reported by authors of similar works. [14,16] A systemic review by da Lilly-Tariah et al revealed that majority of all head and neck cancers in Nigeria presented late and only had palliative chemoradiation therapy. [9] The challenges precipitating this has been highlighted above.

Outcome

The outcome of head and neck cancers depend on a number of factors which include nature and stage of the disease as well as quality of intervention given. Beyond these factors are the peculiar considerations of financial paucity and poor social support systems among many patients such that even when appropriate treatment modalities are available, they are often unaffordable to many patients in our setting. The outcome of our treatment after 3 months was assessed in this study by comparing the symptoms and functionality of the patients pre- and post-management.

Eight patients (15.1%) did not show up for any follow up visits at the clinics in the initial 3 months after treatment while 26.4% were lost to follow up within 3 months (this group had only one follow up visit and defaulted on the next). Among these groups, the outcome of management could not be assessed. Of the patients seen on follow up, 9.4% were found to have features of persistent disease after treatment whereas 43.4% were deemed to have satisfactory outcome. Mortality was recorded in 3 patients (5.7%) within 3 months of follow up; all 3 had advanced cancer with metastasis. Accurate reports on outcome of head and neck cancers in Nigeria are few and far between as highlighted by da Lilly-Tariah et al in their systemic review. [9] A study by Okwor et al assessing the survivorship of head and neck cancer patients in University College Hospital, Ibadan, Nigeria found that the median survival duration after treatment was 7.8 years for stage 1 cancers and 1.9 years for stage 4 diseases. [16] In the same study, combined treatment modalities were found to increase survival rates significantly compared with single treatment modalities. [16] The dearth of advanced modalities for treatment of cancers in our region may account for relatively poorer outcomes when compared with figures from resource-rich climes even though our study did not follow up the patients for more than 3 months.

Follow up of head and neck cancers pose a big challenge to clinicians partly due to low socioeconomic status and poor enlightenment among the patients and their care givers in this part of the world. Many patients do not understand the impact of being seen at scheduled intervals following definitive treatment. Following the initial relief from symptoms it is not unusual for such patients to default check-ups thereby denying researchers the golden opportunity of measuring treatment outcome more accurately. Further researches, preferably prospective and multi-centre based are desirable to assess the survival and outcome of patients treated for head and neck cancers in our region.

Conclusion

To conclude, head and neck cancer patients have presented in significant numbers to Federal Medical Centre, Owerri in recent times and the case profiles mirror those of similar tertiary institutions. Although many of the patients presented with late diseases, concerted efforts were made at diagnosing, staging and treating the diseases. The challenges facing the management of these cases include late presentation, financial paucity, poor social support system and poor follow up culture.

References

Tobias JS (1994) Cancers of the Head and Neck. BMJ 308: 961-966. [crossref]
Sanghvi LD, Rao DN, Joshi S (1989) Epidemiology of Head and Neck Cancer. Semin Surg Oncol 5: 305-309.
Lilly Tariah da OB, Nwana EJC, Okeowo PA (2000) Cancers of the Ear, Nose and Throat. Nig J Surg Sci 10: 52-56.
Bhatia PL (1990) Head and Neck cancers in Plateau State, Nigeria. West Afr J Med 9: 304-310. [crossref]
Goldenberg D, Lee J, Koch WM, et al. (2004) Habitual risk factors for Head and Neck cancers. Otolaryngol Head Neck Surg 131: 986-993. [crossref]
Forae GD and Nwafor CC (2017) Pattern of occurrence of primary head and neck cancers presenting in Benin-City, Southern Nigeria. Saudi J Health Sci 6(1): 52-56. [crossref]
Akinshipo AO, Taiwo AO, Abdullahi K, et al. (2017) Head and neck cancers: A histopathologic review of cases seen in three tertiary hospitals in Northwestern Nigeria. J Clin Sci 14(3): 113-118. [crossref]
Kanu OO, Nnoli MA, Asoegwu CA (2015) Prevalence of head and neck tumours in Calabar, Southeastern Nigeria. Asian J Med Sci 7(1): 142-146. [crossref]
Lilly Tariah da OB, Somefun OO, Adeyemo WL (2009) Current evidence on the burden of head and neck cancer in Nigeria. Head Neck Oncol 1: 14-17. [crossref]
Erinoso OA, Okoturo E, Gbotolorun OM, et al. (2016) Emerging trends in the epidemiological pattern of Head and Neck Cancers in Lagos, Nigeria. Ann Med Health Sci Res 6(5): 301-307. [crossref]
Adeyemi BF and Lawoyin JO (2008) Head and neck cancer – A clinicopathological study in a tertiary care centre. J Nat Med Assoc 100(6): 690-697. [crossref]
Fomete B, Adeola DS (2017) An epidemiological study of 270 cases of carcinomas of head and neck region in Nigeria tertiary healthcare facility. Egypt J Ear Nose Throat Allied Sci 18(3): 251-255. [crossref]
Kodiya AM, Adamu AI, Nggada HA, et al. (2016) Epidemiology of head and neck cancers in Maiduguri-Northeastern Nigeria. British J Med Med Res 11(5): 1-7. [crossref]
Nwawolo CC, Ajekigbe AT, Oyeneyin JO, et al. (2001) Pattern of head and neck cancers among Nigerians in Lagos. West Afr Med 20(2): 111-116. [crossref]
Ologe FE, Adeniji KA, Segun-Busari S (2005) Clinicopathological study of Head and Neck cancers in Ilorin, Nigeria. Trop Doct. 35(1): 2-4. [crossref]
Okwor VC, Fagbamigbe AF, Fawole OI (2017) Survivorship of patients with head and neck cancer receiving care in a tertiary health facility in Nigeria. Cancer Man Res. 9(1): 331-338. [crossref]
Adeloye D, Auta A, Fawibe A (2019) Current pattern of tobacco smoking in Nigeria: a systematic review and meta-analysis. BMC Pub Health. 19: 1719-1721. [crossref]

Older People Living with HIV and Antiretroviral Therapy: The Prevalence of Dysglycemia and Risk Factors

Leave a reply

DOI: 10.31038/EDMJ.2022612

Abstract

Objective: To assess the prevalence and factors associated with dysglycemia (diabetes and prediabetes) in older people living with HIV infection.

Method: This was a cross-sectional, analytical study with 59 older people living with HIV and using antiretroviral therapy, recruited by convenience sampling in two HIV referral hospitals in Recife (PE), between May/2018 and February/2020. The prevalence and factors associated with dysglycemia were analyzed by Chi-square, Fisher Exact, Kruskal-Wallis and Mann-Whitney tests.

Results: The mean age of the 59 older people 64.3 years and 66.1% were male. The prevalence of diabetes and prediabetes was 20.3% and 35.6%, respectively, and the significant risk factors were physical activity, coronary disease, risk of cardiovascular disease in ten years, HDL cholesterol levels and glycemia.

Conclusion: A high prevalence of diabetes and prediabetes was observed in older people living with HIV. Interventions aimed at older people with HIV and the risk of diabetes and prediabetes are necessary, especially those with a sedentary life style, with a relevant cardiovascular risk and biochemical changes that participate in metabolic syndrome.

Keywords

Older people with HIV, Diabetes, Prediabetes, Cardiovascular disease, Physical activity, Premature Aging

Introduction

The control of human immunodeficiency virus (HIV) infection has enabled an increase in life expectancy and has progressively incorporated chronic non-communicable diseases (NCDs), especially dysglycemia (prediabetes (PD) and type 2 diabetes (T2DM) and their complications [1,2].

Dysglycemia represents a major worldwide concern, especially when it affects older people living with the human immunodeficiency virus (OPLHIV), for whom there are specific risks such as the duration of infection, the degree of immunosuppression, cumulative exposure to antiretroviral therapy (ART) and co-infection with hepatitis C [3,4]. On the other hand, conventional risk factors have increased their participation in the impaired glucose tolerance process in this group, such as senescence, obesity, sedentary lifestyle and family history [5].

Associations have been reported between HIV infection and T2DM, particularly with the use of ART, with variation over time, mirroring an unequal repercussion among the many antiretroviral drugs that have emerged. Thus, the careful choice of ART regimens in those individuals facing a higher risk of developing T2DM and the selection and monitoring of antidiabetic medications in older people living with HIV targeted in drug interactions and possible comorbidities are challenges that should be part of the practice of those who deal with OPLHIV [6].

Chronic non-communicable diseases are more prevalent in older people, and HIV infection is on the increase in this population resulting from both new cases and a higher survival rate due to ART [7]. The process of senescence in older people shares pathways in the aging process promoted by HIV [8]. This reality faces prejudice, stereotypes and particularly invisibility among health professionals and society. The complexity of this research is to work on two public health problems in people aged 60 years or older, who, in developing countries, are considered to be old.

Therefore, the diagnosis and management of dysglycemia require a thorough understanding and approach, although the true prevalence of this disorder in older people remains uncertain [9]. More sensitive diagnostic tools are essential for the prevention of T2DM complications, since these are people submitted to conditions that promote aging through many mechanisms, thereby emphasizing their vulnerability and hindering a successful aging process [10].

Methods

This was a cross-sectional, analytical study that assessed the prevalence and factors associated with dysglycemia (PD and T2DM) in older people living with HIV and being treated with ART, attended at two of the three main referral services in Recife (PE) for patients with HIV and AIDS infection, recruited by convenience sampling, from May/2018 to February/2020.

The inclusion criteria applied were: aged 60 years or over, attended at specialized outpatient clinics at the selected tertiary hospitals, with a confirmed diagnosis of HIV infection. Exclusion criteria were: impaired cognition and/or communication (the Mini Mental State Examination applied by the researcher), untreated syphilis and neurological sequelae (data obtained from medical records). Each participant was personally interviewed by the researcher to complete the research instrument and additional information was collected from a review of their medical records.

Variables investigated for the sociodemographic profile: a) personal: gender, chronological age, self-reported skin color, fixed partner, schooling, monthly income of the participant; b) life habits: physical activity [11], classifying the participant as sedentary (no) or active (yes), alcohol consumption [12], considering abstention (no) or drinker (yes), current smoking [13] (yes or no) and current cannabis user (yes or no). Health of the older people: a) comorbidities (hypertension, coronary artery disease and hepatitis C categorized as “yes” if participants had a documented diagnosis of these conditions or were taking medications or self-reporting); b) geriatric dimension (urinary and fecal incontinence, visual and auditory deficits, sleep, fall, polypharmacy. For the evaluation of functionality, the Barthel Index for basic activities of daily living (ADL) was used, composed of ten functions (feeding, bathing, grooming, dressing, bowel control, bladder control, toileting, chair transfer, ambulation, stair climbing), with a score ranging from zero to 100, whereby a total score equal to 100 was considered independent [14]. For the cognition analysis, the Mini Mental State Examination (MSE) was used, with 19 items distributed in the following domains: orientation (time and place), memory, attention and calculation, recall and language. Because it is influenced by schooling, different cutoff points were proposed to minimize this problem: 18 points for illiterate people, 21 points for individuals with 1 to 3 years of schooling, 24 points for those with 4 to 7 years of schooling and 26 for participants with more than 7 years of schooling [15]. The nutritional status was analyzed through the Mini Nutritional Assessment (MAN), the only instrument validated in Brazil for the older population. It is divided into 2 modules: the first focuses on questions A to F, and may be considered as screening, with 14 being the maximum score. At the end of this first module, if the score is equal to or greater than 12 points, it is not necessary to proceed, since the participant is considered nourished. If it is less than or equal to 11 points, the assessment moves on to the second module, which is composed of 12 questions (G to R), with 16 being the maximum score. If ≥ 24 points- normal; 17 to 23.5 points – risk of malnutrition; < 17 points: malnourished [16].

The estimate of biological age (BA) was calculated by the researcher by applying an artificial intelligence algorithm [17] that includes 19 laboratory tests taken from the patient’s medical records (albumin, glucose, urea, total cholesterol, total protein, sodium, creatinine, hemoglobin, total bilirubin, triglycerides, HDL, LDL, calcium, potassium, hematocrit, CHCM, VCM, platelets and erithrocytes), weight, height and smoking information. The BA is the result obtained from the following mathematical subtraction operation: chronological age (CA) minus the age predicted by artificial intelligence. If the result is negative (CA lower than expected), there is premature biological aging. On the other hand, if the result is positive (chronological age greater than expected), there is no premature biological aging. To assess adherence to ART, the Morisky scale of four questions was applied by the researcher [18].

Medical records were used in order to collect data on diagnosis (HIV-positive serology), the use of statins [19] (Silva16) and results of complementary tests (viral load: the current and highest load; CD4+ T lymphocyte count: current and nadir; the most recent biochemical and hematological dosages in relation to the interview), details on ART (start date, number and types of regimens used) and HIV/AIDS-related diseases (toxoplasmosis, syphilis, tuberculosis).

A cardiovascular risk at 10 years was estimated using the Framingham online risk calculator based on age, sex, total cholesterol, HDL cholesterol, LDL cholesterol, smoking, diabetes mellitus and blood pressure. Individuals at low risk present 10% or less risk of cardiovascular disease (CVD) in 10 years, with an intermediate risk of 10-20% and a high risk of 20% or more [20] (Latufo17).

Glucose homeostasis disorders were defined by the ADA 2020 [21] criteria as PD (fasting plasma glucose level of 100-125 mg/dl) and T2DM (fasting plasma glucose level of at least 126 mg/dl) [22].

The research is in accordance with Resolution No. 466/2012 and Resolution No. 510/2016. The research was approved by the Research Ethics Committee of the Center for Health Sciences at the Universidade Federal de Pernambuco, under Report Number: 2.545.05. All participants signed an informed consent form.

For data analysis, a spreadsheet database was produced and exported to a database validation program. To characterize patients with regard to their profile: personal, socioeconomic, life habits, metabolic condition, ART use, disease time and disease inventory, frequency distributions were constructed. To assess which of these factors were associated with the classification of blood glucose level, the contingency table was constructed and the Chi-square test for independence was applied. In cases where the assumptions of the Chi-square test were not satisfied, the Fisher Exact test was applied. In assessing the influence of the blood glucose classification on the clinical dimension, health indicators, viral load and medication use, the contingency table was constructed and the Chi-square test was applied for homogeneity. For laboratory measurements, normality was assessed and, in cases where normality was not indicated, the distribution of the measure between the groups was made by the Kruskal-Wallis test, for comparison between the three blood glucose classification groups. In the comparison of measurements between the blood glucose classification groups, two to two, the Mann-Whitney test was applied. All conclusions were drawn considering a significance level of 5%.

Results

This study included 59 older people aged between 60 and 77 years, of whom 39 (66.1%) were male. All participants were on ART and 26 (44.1%) received 3 or more regimens. Most had an undetectable viral load (91.5%) and a CD4 T lymphocyte count above 350 cells/mm³ (71.2%). Hepatitis C virus co-infection was present in 6 of the 59 participants (10.2%) and the adherence rate to ART was 62.7%. Around 10.2% of the older people had received no formal education and 67.8% had no partner. Most had a monthly income ≤1 minimum wage (76.8%) and a normal nutritional status (91.5%). With regard to the ART groups used throughout the follow-up, nucleoside analogue reverse transcriptase inhibitors (NRTI) were dispensed for 98.3% of the older people, non-nucleoside reverse transcriptase inhibitors (NNRTI) for 61% and protease inhibitors (PI) for 57.6%. A total of 39% of the participants presented with more than 10 years of infection.

Table 1 demonstartes that chronological and biological ages did not present significant results regarding the prevalence of dysglycemia, but we observed that chronological age behaved with a higher prevalence of T2DM for participants aged between 66 and 70 years. With regard to biological age, in the groups with premature aging (BA>CA) the dysglycemic state of PD predominated and in the group without premature aging there was a higher prevalence of T2DM. Physical activity presented a difference (p=0.01), with the same prevalence of T2DM and PD (25.6% for both) in the sedentary group, while in those physically active, PD prevailed (62.5%). The independence test was not significant for the other factors assessed: sex, skin color, having a steady partner, schooling, and monthly income of the participant, alcohol consumption, smoking and cannabis use.

Table 1: Distribution of blood glucose classification according to the sociodemographic profile and life habits of participants

table 1

¹Qui-square test p-value for independence. ²p-value of fisher’s exact test

Table 2 presents a higher prevalence of dysglycemia in the three groups of the calendar year of initiating ART, the sum of PD and T2DM (50.0%, 57.1% and 57.1%), in relation to normal, although the homogeneity test was not significant (p-value = 0.975). For the group of patients currently using statins, there was a higher prevalence of T2DM (60%). Despite the differences in blood glucose classification for the groups of participants with certain characteristics, the independence test was not significant.

Table 2: Distribution of blood glucose classification according to disease time, ART, adect and statin

table 2

Nota: Median (Interquartile Amplitude) .¹p-value of chi-square test for independence.²p-value of fisher’s exact test. Kruskal-Wallis test ³p-value

Table 3 presents the distribution of the blood glucose classification according to the disease inventory, viral load and CD4 T lymphocyte count of the participants. The majority had normal blood glucose levels except for those with coronary heart disease, where the prevalence of diabetes was 100.0%. In the group with a history of hepatitis C, PD was more prevalent (66.6%), but was not significant. The independence test was significant only for the coronary disease factor (p-value = 0.039).

Table 3: Distribution of glycemia classification, according to the inventory of diseases of the assessed patients, viral load and CD4 T lymphocyte count

table 3

¹p-value of the chi-square test for independence. ²p-value of Fisher’s exact test

Table 4 presents the scales and geriatric clinical dimension, the Framingham score and laboratory tests of the participants according to the blood glucose classification. The Framinghan score demonstrated a higher prevalence of high-risk CVD in the T2DM (91.7%) and PD (52.4%) groups of patients. For the normal group, the highest prevalence was intermediate risk (42.3%). The homogeneity test was significant for the classification of the Framingham score (p-value = 0.020), indicating that the risk of cardiovascular events differs between the glycemic groups, being higher for those with diabetes. For the metabolic measurements, there was a difference for HDL cholesterol (p-value = 0.038) and for the last blood glucose value (p-value < 0.001). When comparing the HDL cholesterol levels between the groups, two by two, there was a significant difference only in the comparison between the group with T2DM and the normal group (p-value = 0.038). When comparing the blood glucose distribution between the classification groups, two by two, there was a significant difference between all comparisons: diabetic x pre-diabetic, diabetic x normal and pre-diabetic x normal (all comparisons with p-value < 0.001).

Table 4: Geriatric scales, geriatric clinical dimension, Framingham score and laboratory tests of participants according to blood glucose classification

table 4

Note: Median (Interquartile Range) ¹p-value of Fisher’s exact test. ²p-value of the Kruskal-Wallis test. 3p-value of the chi-square test for homogeneity

Table 5 presents the distribution of the current ART regimen according to blood glucose classification. It appears that the most commonly used drugs by patients with diabetes are Efavirenz (NNRTI), Lavimudine (NRTI) and Zidovudine (NRTI). For the pre-diabetic groups of and normal participants, the most commonly used drugs were Lamivudine (NRTI), Ritonavir (IP) and Tenofovir (NRTI).

Table 5: Distribution of current ART regimen according to blood glucose classification

table 5

Table 6 presents the mean and standard deviation of the time (in months) of using ART according to the classification of glycemia. It was verified that in the group of participants with T2DM, the drugs that had been used for the longest mean period of time were Zidovudine (NRTI), Lamivudine (NRTI) and Ritonavir (PI). For the PD group, the drugs that had been used for the longest mean period of time were Saquinavir (PI), Ritonavir (PI) and Lamivudine (NRTI). In the normal group, the drugs that had been used for the longest mean period of time were Saquinavir (PI), Zidovudine (NRTI) and Indinavir (PI).

Table 6: Mean and standard deviation of time (in months) of using ART according to blood glucose classification

table 6

Note: Media ± standard deviation

Discussion

In this study, we evidenced a high prevalence of dysglycemia and a high risk of cardiovascular disease estimated by the Framingham score among older people living with HIV and receiving antiretroviral therapy. We observed an association between a sedentary lifestyle, coronary heart disease, HDL cholesterol levels and high current blood glucose in the T2DM and PD groups.

The prevalence of dysglycemia in older people living with HIV was 55.9%, 20.3% and 35.6% for T2DM and PD, respectively. Among adults with HIV in the US, a prevalence of diabetes was observed of 10.3%, with a higher incidence of younger individuals and no obesity [22]. Duncan, Golf et al. [23] recruited a group of ethnically diverse adults with HIV who were twice treated as outpatients in London in a cohort separated by ten years. T2DM prevalence in the initial cohort was 6.8% and 15.1% in the final cohort, with a higher risk of dysglycemia associated with time of infection, ART toxicity, increasing age and body mass index. In Africa, few studies have been conducted on the subject, with prevalences of 3.5 to 26.5% for T2DM and 20.2 to 43.5% for PD, among adults with HIV on ART [24]. In Sub-Saharan Africa, data on T2DM are scarce and the high prevalence of anemia compromises the usefulness of glycated hemoglobin in the diagnosis of dysglycemia [25]. The prevalence of T2DM and PD in our study was higher than that observed in the literature, probably because it is a sample with a CA equal to or greater than 60 years in which most presented premature aging [26]. (Pathai23).

Additionally, persistent inflammation in PLHIV (inflammaids) and senescence (inflammaging) also contribute to multiple diseases such as diabetes, CVD, kidney disease and others. Although the specific mechanisms of each process – HIV, aging, comorbidities – may be unique or shared, biomarkers of immune activation and inflammation (IL-6, CD14, CD163, D-dimer, Tumor Necrosis Factor) are known to be associated with the development and progression of pathologies in PLHIV. Inflammation is also linked to comorbidities in older people with no HIV [8,27]. A cohort assessed twice in a period separated by a peirod of 10 years, identified that the longer duration of HIV status and exposure to ART were determinants for dysglycemia [23]. In our research, the participants in the group with less biological aging and a greater frequency of T2DM had a longer period of time of a diagnosis of HIV infection and exposure to ART.

A sedentary lifestyle is a risk factor for the development of dysglycemia. In the sedentary participants of this study there was an equal prevalence of DT2 and PD, while in those physically active, the state of PD prevailed. Physical activity is linked to a reduction in the risk of diabetes in the general population, therefore, it is of express relevance for OPLHIV in view of the reduced practice of exercises observed in this population [19,23]. Segatto, Freitas et al. [28] demonstrated the protective effect of physical activity in the context of HIV, by verifying a lower incidence of lipodystrophy and an inverse relationship between physical activity and the concentration of central adiposity, which represent risk factors for the development of dysglycemia. Additionally, research conducted by Mutimura, Stewart et al. [29] reported that physically active individuals had higher CD4 levels. As in our study, Hoffmann et al. [30] assessing a cohort, concluded that there was a robust prevalence of coronary atherosclerosis in HIV patients and that glycemic levels were higher among those with atherosclerotic plaques and in the population with adequately controlled HIV, markers of immune activation were evidenced innate and arterial inflammation related to coronary artery disease (CAD). Endothelial dysfunction is the fundamental element of atherogenesis and represents the confluence of different processes. The endothelium is injured by the immunological, pharmacological release of particles secondary to the destruction of CD4+ T lymphocytes and an increased expression of adhesion molecules. Thus, an inflammatory cascade damages the vessel and promotes premature atherosclerosis. However, there are intricate specific viral mechanisms that promote sustained immunodeficiency, immune dysregulation/activation, and inflammation despite ART. Within this scenario, ART promotes a reduction of endothelial damage by controlling HIV infection, but harms this same endothelium through its involvement in glucose and lipid metabolism. Unquestionable conclusions on the role of ART in cardiovascular risk do not yet exist, since the regimens used make use of different class associations [31]. Currently, the recommendation for minimizing cardiovascular risk relies on the early initiation of ART and controlling traditional risk factors such as smoking, obesity, sedentary lifestyle, inadequate diet, among others [32].

The Framingham Risk Score is a widely used tool to estimate the absolute risk of developing cardiovascular disease over a 10-year period [33]. In this study, 91.7% of patients with T2DM and 52.4% of PD presented a high risk of CVD, according to the Framingham score, while most normal patients (42.3%) presented an intermediate risk. This finding is justified because it is a chronologically older population and with a prevalence of premature aging in 68.7% of the participants. While this score is easy to use, it may not be ideal for people with HIV because it does not include antiretroviral drugs, a fact that might generate a different risk. The duration of treatment and the large number of possible drug combinations make it difficult to assess the individual effects [34].

With regard to the metabolic measures, there was a difference for HDL cholesterol and blood glucose. Metabolic syndrome is an element of considerable importance in PLHIV, although estimates vary, partly due to the use of different diagnostic criteria and also due to the duration of the prescribed antiretroviral regimen and the differences between the populations studied. We observed a result with significance for two important components of the metabolic syndrome, with lower HDL and higher blood glucose in patients with T2DM followed by PD. Bezerra and Burgos [35], analyzing the lipid profile in PLHIV with coronary atherosclerosis, identified the protective role of HDL and its importance in preventing unfavorable early CAD outcomes, including death.

There are limitations to be observed in this study. The cross-sectional design is able to appreciate associations but frustrates the assessment of causality. The limited sample size associated with geographic restriction and male predominance generate results that cannot be extended to all OPLHIV. However, it provides a significant contribution because it is a chronologically older population, which is growing worldwide, bringing together people who are aging with HIV and those who are acquiring HIV infection from the age of 60. Another relevant point is the use of biological age estimated with the use of artificial intelligence, which confirms previous studies on premature aging in HIV carriers. Moreover, since the study was conducted at two university hospitals with a specialized HIV service, we observed a greater commitment of the participants to their treatment associated with the multiprofessional follow-up, which probably did not distort the sample and corroborated the functional and cognitive preservation of the group. In Brazil, there are few studies with national representation that indicate the prevalence of dysglycemia in older people with HIV. Thus, this work may generate perspectives on the issue.

Responding to the objectives of the study, we evidenced a high prevalence of dysglycemia among older people living with HIV infection and receiving antiretroviral therapy and the high risk of cardiovascular disease in 10 years estimated by the Framingham score. We also found differences in the variables of physical activity, coronary heart disease and levels of HDL cholesterol and blood glucose. Prospective studies are needed in order to clarify any associations, and assess the relevance of pharmacological actions and lifestyle changes to prevent the development of PD and its progression to T2DM. Faced with the great challenge of human aging, screening and preventive measures need to be created and applied to older people. Health professionals need to pay attention to the possibility of HIV in this age group, thus avoiding late diagnosis. Physicians should minimize drug interactions by understanding aspects of the geriatric prescription and the possible weaknesses of this age group.

References

Guaraldi G, Orlando G, Zona S, et al. (2011) Premature Age-Related Comorbidities Among HIV-Infected Persons Compared With the General Clin Infect Dis. 53(11):1120-1126. [crossref]
Kalra S, Kalra B, Agrawal N, et al. (2011) Understanding diabetes in patients with HIV/AIDS. Diabetol Metab Syndr. 3(1): 2. [crossref]
Monroe AK, Glesby MJ and Brown TT (2015) Diagnosing and Managing Diabetes in HIV-Infected Patients: Current Concepts. Clin Infect Dis. 60(3):453-462. [crossref]
Hulgan T (2018) Factors Associated with Insulin Resistance in Adults with HIV receiving Contemporary Antiretroviral Therapy: A Brief Update. Curr HIV/AIDS Rep. 15(3):223-232. [crossref]
Samad F, Harris M, Puskas CM, et al. (2017) Incidence of diabetes mellitus and factors associated with its development in HIV-positive patients over the age of 50. BMJ Open Diabetes Res Care. 5(1): e000457. [crossref]
Noubissi EC, Katte JC, Sobngwi E (2018) Diabetes and HIV. Curr Diab Rep. 18(11):1-8.
Lopez-Otín C, Blasco MA, Partridge L, et al. (2013) The hallmarks of aging. Cell. 53(6):1194-1217. [crossref]
Dalzini A, Petrara MR, Ballin G, et al. (2020). Biological Aging and Immune Senescence in Children with Perinatally Acquired HIV. J Immunol Res. 2020: 8041616. [crossref]
Cunha GH, Franco KB, Galvão MTG, et al. (2020) Diabetes mellitus in people living with HIV/AIDS: prevalence and associated risk factors. AIDS Care. 32(5):600-607. [crossref]
Coelho AR, Moreira FA, Santos AC, et al. (2018) Diabetes mellitus in HIV-infected patients: fasting glucose, A1c, or oral glucose tolerance test – which method to choose for the diagnosis?. BMC Infect Dis. 18(1):309. [crossref]
Matsudo S, Araujo T, Matsudo V, et al. (2001) Questionario Internacional De Atividade Fisica (Ipaq): Estudo De Validade E Reprodutibilidade No Brasil. Rev Bras Atividade Física Saúde. 6(2): 5-18. [crossref]
Defined DL. National Institute on Alcohol Abuse and Alcoholism (NIAAA). [crossref]
Ariyothai N, Podhipak A, Akarasewi P, et al. (2004) Cigarette smoking and its relation to pulmonary tuberculosis in Southeast Asian J Trop Med Public Health. 35(1):219-227. [crossref]
Mahoney FI and Barthel DW (1965) Functional evaluation: the barthel Md State Med J. 14: 61-65. [crossref]
Folstein MF, Folstein SE and McHugh PR (1975) “Mini-mental state”: A practical method for grading the cognitive state of patients for the J Psychiatr Res. 12(3):189-198. [crossref]
Vellas B, Guigoz Y, Garry PJ, et al. (1999) The Mini Nutritional Assessment (MNA) and its use in grading the nutritional state of elderly patients. Nutr Burbank Los Angel Cty Calif. 15(2):116-122. [crossref]
Mamoshina P, Kochetov K, Putin E, et al. (2018) Population Specific Biomarkers of Human Aging: A Big Data Study Using South Korean, Canadian, and Eastern European Patient Populations. J Gerontol A Biol Sci Med Sci. 73(11):1482-1490. [crossref]
Morisky DE, Green LW and Levine DM (1986) Concurrent and predictive validity of a self-reported measure of medication adherence. Med Care. 24(1):67-74. [crossref]
Silva SP and Monteiro N (2016) Uso de estatinas e o risco de Diabetes Mellitus tipo 2: Revisão Baseada na Evidência. Rev Bras Med Fam Comunidade. 11(38): 1-8. [crossref]
Lotufo PA (2008) O escore de risco de Framingham para doenças Rev Med. 87:232-237. [crossref]
Association (2020) Standards of Medical Care in Diabetes-2020 Abridged for Primary Care Providers. Clin Diabetes. 38(1):10-38. [crossref]
Hernandez-Romieu AC, Garg S, Rosenberg ES, et al. (2017) Is diabetes prevalence higher among HIV-infected individuals compared with the general population? Evidence from MMP and NHANES 2009-2010. BMJ Open Diabetes Res Care. 5(1):e000304. [crossref]
Duncan AD, Goff LM, Peters BS (2018) Type 2 diabetes prevalence and its risk factors in HIV: A cross-sectional study. PloS One. 13(3):e0194199. [crossref]
Rhee JY, Bahtila TD, Palmer D, et al. (2016) Prediabetes and diabetes among HIV‐infected adults in Cameroon. Diabetes Metab Res Rev. 32(6):544-549. [crossref]
Hodel NC, Hamad A, Reither K, et al. (2020) Assessment of diabetes and prediabetes prevalence and predictors by HbA1c in a population from sub-Saharan Africa with a high proportion of anemia: a prospective cross-sectional BMJ Open Diabetes Res Care. 8(1): e000939. [crossref]
Pathai S, Lawn SD, Gilbert CE, et al. (2013) Accelerated biological ageing in HIV-infected individuals in South Africa: a case-control AIDS Lond Engl. 27(15):2375-2384. [crossref]
Rinaldi S, Pallikkuth S, George VK, et al. (2017) Paradoxical aging in HIV: immune senescence of B Cells is most prominent in young age. Aging. 9(4):1307-1325. [crossref]
Segatto AFM, Freitas Junior IF, Santos VR dos, et al. (2011) Lipodystrophy in HIV/AIDS patients with different levels of physical activity while on antiretroviral Rev Soc Bras Med Trop. 44(4): 420-424. [crossref]
Mutimura E, Stewart A, Crowther NJ, et al. (2008) The Effects of Exercise Training on Quality of Life in HAART-Treated HIV-Positive Rwandan Subjects with Body Fat Redistribution. Qual Life Res. 17(3):377-385. [crossref]
Hoffmann U, Lu MT, Foldyna B, et al. (2021) Assessment of Coronary Artery Disease With Computed Tomography Angiography and Inflammatory and Immune Activation Biomarkers Among Adults With HIV Eligible for Primary Cardiovascular JAMA Netw Open. 4(6):e2114923. [crossref]
Carvalho A, Valente R, Almeida-Morais L, et al. (2017) VIH e doença coronária – quando a prevenção secundária é insuficiente. Rev Port Cardiol. 36: 569. [crossref]
Kumar S and Samaras K (2018) The Impact of Weight Gain During HIV Treatment on Risk of Pre-diabetes, Diabetes Mellitus, Cardiovascular Disease, and Mortality. Front Endocrinol. 9:705. [crossref]
Cesarino CB, Borges PP, Ribeiro R de CHM, et al. (2013) Avaliação do risco cardiovascular de pacientes renais crônicos segundo critérios de Framingham. Acta Paul Enferm. 26(1):101-107. [crossref]
Friis-Møller N, Thiebaut R, Reiss P, et al. (2010) Predicting the risk of cardiovascular disease in HIV-infected patients: the data collection on adverse effects of anti-HIV drugs Eur J Cardiovasc Prev Rehabil. 17(5):491-501. [crossref]
Bezerra LA and Burgos UMMC (2021) Analise do perfil lipídico de pacientes HIV- positivo com aterosclerose coronariana/ Analysis of the lipid profile in HIV- positive patients with coronary atherosclerosis. Braz J Health Rev. 4(2):9094-9102. [crossref]

A Living System

Leave a reply

DOI: 10.31038/JCRM.2022541

Introduction

A living system is a structure that arises in order to solve the dissatisfaction of its elements – also living systems. It cannot arise over “inanimate” elements, only thanks to their properties it itself becomes a living structure.

In the course of modeling work on economic series, some properties were found that could be understood as properties of a living system. They were therefore verified on systems that were reasonably assumed to be live systems. It was about structural knowledge from the field of animal physiology (primarily human) and similar, albeit smaller, in the field of plant physiology. Using the “per analogiam” method, a common, systemic solution – the structure and principle of functioning of a living system – was found with a certain degree of objectivity.

For whom?

The basic question of every organizing system is – for whom it is built, who or what benefits from it. As detective lovers say – qui bono?

For man, it is completely conceivable and logical that, for example, society, as a living system, is created for man, to fulfill his interests. But for whom is a living system built an order lower, namely man himself? Who or what is its element?

The answer was usually the saying that for no one, that in short, evolutionarily asserted itself as the most successful. But for control theory this is not a sufficient answer. So what is its element?

Model works and the approach via analogies offer only one solution. The element of the so-called multicellular living systems is water! This is apparently not such a world-shattering statement, but it has its fundamental and world-shattering 😉 consequences.

The needs of water, its interests and dissatisfactions are therefore solved through it. And just as human society develops under the pressure of its elements, i.e. under the social pressure of man’s ideas and interests, other analogous living systems must also develop.

Dissatisfaction

The system evaluates the dissatisfaction of its elements for a simple reason – its existence rests on the elements, and if they become too dissatisfied, they will leave the system with all the resulting consequences. The system must be able to identify the dissatisfaction of the elements and must be able to respond to it adequately. The degree of satisfaction of all elements of a living system is the degree of its existence.

Elements

The whole scheme of a living system is based on the reason for which it arises. It is a solution to the dissatisfaction of the elements to an extent that is unattainable for the element itself.

The higher-level solution given by the new situation is given by the specialization ability of the elements. Specialized elements are involved in specialized production units. And these are divided from the point of view of the system into two basic groups: the production of food and the creation of suitable conditions for production and consumption.

Production units made of specialized elements – but extended by a more or less complex production structure (technique 😉) created in other production units – are companies in the case of human society and cells in the case of multicellular organisms. A cell is therefore not a living object, but only a productive, specialized unit.

The task of a living system simultaneously defines its two parts. Part of the regenerating, satisfying, not involved in the activity of the system of elements, and the part that creates the conditions for this regeneration, generally the solution of dissatisfaction. These two parts are in a constant process of overflowing. Each element “works” for some time, creates assumptions, but at the same time it is exhausted, its dissatisfaction changes and then it goes to the part for regeneration, where it consumes these created assumptions. The living system then has to ensure that the drawdown of the element during regeneration corresponds to the degree of its involvement and merit in the creation of assumptions.

In the text, the terms dissatisfaction and satisfaction will be used randomly, their meaning is identical – except for the sign.

Regeneration and Dark Matter

An element of a living system, having created common products within the framework of its specialization and received the corresponding remuneration (in society it is money), temporarily leaves these production units and relationships. It enters the “dark part, matter” – that is, a state where it cannot be seen from the living system. Only his activity aimed at solving his own dissatisfaction is observable. It restores its exhausted production possibilities and, as part of this regeneration, prepares to rejoin the system.

For regeneration, for some reason, it is necessary for the element to leave the system, to leave its specialized production relations, e.g. in a company or a cell. This part of the regeneration partly does not correspond to the terminology, it is not a restoration of a previously existing state. It is about the emergence of a new quality, especially in the area of finding new strategies for solving dissatisfaction. The element evaluates past experience and adjusts its past strategies to match possibly changing conditions. This specific part of regeneration – one could perhaps say sleep and its dream – is a completely irreplaceable part of regeneration.

In society, it is a person in the work process and a person in non-working time. In animals, it is the water that is active in the cells and the water that is in the cerebrospinal fluid and the lymphatic system, generally in the intercellular space. Similarly, in plants, it is water, when it is in living cells in an active process, regeneration occurs mainly in the vessels of plants (xylem).

In the case of the least studied – that is, astronomical systems – the essence of this division seems to be normal and dark matter.

In the following text, the term regeneration will be used in this broad, innovative sense. Like restoring elements not necessarily at the previous level.

Evaluation of the Element

In order for the element to subsequently and completely regenerate, it goes out of production. It is therefore necessary to somehow ensure in the system that it “takes away” indisputable information about its involvement in the creation of regeneration assumptions – some evaluation. For a person in a company it is money, for water in cells it is apparently some property in the distribution and dynamics of the charge of its package.

Production units generally operate independently. They have their own control mechanisms, evaluate the involvement of elements in production, solve their evaluation, etc. However, they are also under the influence of a system that moves their activity in the desired directions. In the case of the living system best known to us – human society – it is fiscal, monetary or economic policy.

Raman Enhancement Factor (EF) Calculations for Hot Spots at Two Metallic Spheres

Leave a reply

DOI: 10.31038/NAMS.2022514

Abstract

The interaction between two metallic spheres with radius R with external electromagnetic (EM) field polarized in the symmetric direction is described Solutions of Laplace equation with bi-spherical coordinates are developed Hot spots are obtained under the condition that the shortest distance between the two spheres surfaces is very small relative to their radius. Boundary conditions are applied which assume very large real negative value for the dielectric constant of the metallic spheres. Under these conditions the EM field is amplified by many orders of magnitudes relative to the incident EM field. Analytical results for maximal Raman enhancement factor (EF) are obtained as function of various parameters. The present study can be applied to surface-enhanced Raman spectroscopy (SERS) and two-photon induced illumination (TPI-PL) in which the amplification is proportional to the fourth power of the incident EM field.

Introduction

An electromagnetic (EM) mechanism for surface enhanced Raman spectroscopy (SERS) involves the localization and amplification of incident light fields by a surface plasmon resonance. Motivated by the need to quantify the EM enhancement within such structures, computational studies using the finite element method (FEM), the finite-difference time domain (FDTD) method, discrete dipole approximation, and the generalized multipole Mie (GMM) analysis appeared as ideal complement to experimental studies [1,2]. The ability of SERS to obtain single-molecule sensitivity relies on the formation of regions with ultra-highly enhancement called hot spots. These highly enhancement sites occur at the junction between two and more plasmonic structures separated by a very small gap. In the limit of very small particles, the EM interaction between different parts of the metal is instantaneous. Then Maxwell equations are leading to the condition that the electric and magnetic fields are longitudinal (). The magnetic response of the particles is negligible at optical frequencies for very small particles so that the electric field is the gradient of the scalar electric potential, [3]. In the present work analytical results are developed for maximal SERS enhancement factor ( EF ) under such conditions for two nearby metallic spheres. It is of much importance to find the conditions under which the EF is maximal so that spectroscopic effects on one molecule level can be observed. Although we treat a very special system one can learn from this case about the general conditions for getting maximal EF.

We consider two metallic spheres of equal radius R described in Figure 1. We choose the vertical z-axis along the line passing through the centers of the spheres. The perpendicular x, y plane contains the midpoint between the two spheres. We assume that the distance from the center of one sphere with radius, R (the upper one) to the center of the coordinate system along the Z coordinate is +D and that for the other sphere with the same radius R (the lower one) is -D.

We define

(1)

The shortest distance between the two spheres surfaces is given by: 2δ. For simplicity we treat mainly the case where the incoming EM field is homogenous and the electric field 2δ is along the Z axis. Assuming certain values for the dielectric constants [4,5] (for the two spheres ε(ω) which are function of the frequency ω and for the surrounding medium ε1) we present the solutions of the Laplace equation for the limiting case for which δ<1. The two focuses F₁and F₂ are located at a distance α from the center of the coordinate system along the symmetric axis, in upper and lower directions, respectively.

Laplace equations solutions for the upper and lower spheres are given by Ψ₊ and Ψ_– , respectively, and Laplace equation solution for the surrounding medium is given by Ψ1. The present system has a cylindrical symmetry under rotation around the Z axis. Thus, the two focuses are not changed by this rotation. It was shown [6-9] that Raman signals are strongly amplified when the molecules are inserted in the interstitial gaps between nanoparticles due to the very strong EM fields induced in these gaps (“hot spots”). Special studies were made on Raman signals enhancement in dimers (two nanoparticles) [10,11]. It was found that the Raman signals of spherical dimers are strongly enhanced when the incident polarization is parallel to the inter particle axis of the dimer (parallel polarization) [12]. In this case the opposite charges of polarization are facing each other at the small gap and by their interaction generate a huge EM field. On the other hand, when the incident EM field is polarized in direction perpendicular to the inter particle axis (perpendicular polarization) the induced charges are in directions different from that of the gap. In this case, individual local surface plasmons (LSP) in the dimer do not interact strongly with each other. As a result, EM field interaction is approximately compared in this case with that of isolated particles. It was found that the signal in SERS is proportional to the fourth power of the amplified EM field for parallel polarization. Similar results are obtained by two-photons-induced luminescence (TPI-PL) [13]. Raman scattering and TPI-PL phenomena are increased by many orders of magnitude relative to that of the ordinary ones, for molecules inserted in these hot spots.

In the present work we study the solutions of Laplace equation solutions for dimers with bi-spherical coordinates [14,15] which are developed under the condition 2δ<1. Hot spots are produced in the system of two metallic spheres interacting with external homogeneous EM field. While important results (mainly for the potential) for the present system were developed by solving Laplace equation with the use of bi-spherical coordinates the analysis for the hot spots remained problematic due to convergence problems. By using boundary conditions various authors [16] obtained after some tedious algebra set of recursion relations (or equivalently infinite set of linear equations) for the Laplace equation superposition solutions. Such system was truncated by taking finite set of linear equations and was solved on computers. Special care was taken to make sure its convergence i e , that the number of recursion relations is not too small (especially for nearby spheres where very high number of recursion relations is needed). We give here an alternative for deriving the EM fields at the hot spots by using bi-spherical coordinates with certain approximations. We develop in the present work a relatively simpler model for analyzing the properties of the EM fields by using approximations which are suitable for treating the hot spots with the use of bi-spherical coordinates. Analytical results for maximal enhancement factor (EF) are developed. The bi-spherical coordinates are a special three-dimensional orthogonal coordinates system defined by coordinates η, α, Φ.

The two poles with η = ±∞ are located on the Z axis at z = ±a and denoted in Figure 1 by F₁ and F₂. Surfaces of constant η are given by spheres (described in Figure 2).

Figure 1: Two spheres with metallic dielectric constant ε(ω) with radius R and the surrounding medium with dielectric constant ε₁, under homogenous external EM field propagating in the x direction and polarized in the Z direction where E_z= E₀. Various parameters are described in the present x, z coordinates system.

In the present system the electrostatic potential has cylindrical symmetry about the Z axis. It is therefore independent of the angle Φ and only the term m=0 is retained. In Figure 2 we describe the coordinates η for certain values of η as function of the x, z coordinates. The large circles represented by small values of η are truncated in this figure. The surfaces of the spheres in the present system are given by bi-spherical coordinates ±η₀ given by:

Figure 2: Bi-spherical coordinates in the x, z plane showing circles of constant bi-spherical radial coordinate η where curves of constant polar angular α with α =π ,π / 2,π / 3,π / 6 are perpendicular to these curves [3]. EM field polarized in the Z direction propagates in the x direction. The curve for α =π is along the Z axis.

This equation for η = η₀( η = – η₀) represents in Figure 1 the upper (lower) sphere with radius R where its center is moved from the center of the coordinate system by a distance D in the positive (negative) Z direction. In Figure 2 η₀ should be chosen for a special value of η which is related by Eq (3) to the parameters of Eq (1). The distance between the surfaces of the two spheres along the Z axis becomes very small relative to their radius for small values of η ( η = η₀< 1). The two poles F₁and F₂ are obtained at Ψ₊ ,Ψ_– .

Laplace-Equation Solutions for Two Metallic Spheres with Incident EM Field Parallel to the Symmetric Z Coordinate

We define Ψ₊ ,Ψ_– and Ψ₁, respectively, as the potentials (with the condition m=0 ) inside the upper sphere, the lower sphere, and the surrounding medium, respectively. The potential due to the external field is assumed to be given by . In the present article the external field is written in short notation as E₀. It is antisymmetric with respect to reflections through the xy plane: Z → – Z or η → – η.

The potential Ψ₁outside the spheres is given with the same symmetry as that of the external field potential:

where P_n are Legendre polynomials and A_n are certain constants. Using the relation [16-20]:

where the upper (lower) sign holds for positive (negative) Z, Eq (8) is transformed to:

For η = η₀ , and positive Z, Eq (6) is transformed to:

From the fact that Ψ₊and Ψ_– have to be finite at the points: x = y = 0; z = ±a, where: η = ±∞, we obtain [16-20].

One should notice that the function is antisymmetric with respect to reflections through the xy plane i.e. Z → – Z or η → – η in agreement with the symmetry of the external electric field. The general solutions for the potentials in the surrounding medium, and in the upper sphere are given by Eqs (6) and (8), respectively. But the coefficients A_n and B_n should be obtained from the boundary conditions.

Using Eqs (6-9) we get the EM potentials as function of the bi-spherical coordinates. Transformation of these equations to be functions of the x, y, z coordinates can be made by using Eqs (2). The coefficients A_n and B_n are calculated as follows:

We use the first boundary condition given as:

By using the equality (10) and comparing the corresponding expressions (7) and (8) for η = η₀we obtain:

A second boundary condition can be used as [16-20]:

Using Eq (6) we get:

The derivatives include the local plasmons charges induced on the surfaces of the spheres. In the present work we follow the idea, that for treating the limits of large field enhancement in hot spots we can use the following approximation which will simplify very much the analysis:

a) Derivatives in Eqs (13) and (14) include derivatives according to η of (cosh η – cos α )^½in addition to the derivatives of the terms in the summations of these equations. Under the condition that δ is much smaller than R there are many B_nand A_n terms including exponential terms with derivatives proportional to the integer n which are very large relative to the derivatives of (cosh η – cos α )^½so that the latter derivatives can be neglected for hot spots. The terms with larger value of n for represent more rapid decay of the local surface plasmons.

b) In the present analysis for hot spots we assume that A_n and B_n are very large numbers so that for the purpose of using the boundary condition (12) the small term can be neglected.

By substituting Eqs (13) and (14) into Eq (12) and using the above approximations we get for the relation between A_n and B_n:

Here the common factors: (cosh η – cos α )^½ , P_n( cos α ) , and the term of order n proportional to E₀were neglected Eq (15) shows that for larger values of −ε (ω) the term B_nbecomes smaller. One should notice that while Eq (15) represents an approximate relation for hot spots, Eq (11) is exact one. One might notice that the above approximation b) was not included in [3]. We find now that although the derivative of (cosh η – cos α )^½ is small relative to the derivatives of exponential terms its contribution might be not small relative to the term with external field. So only by using both approximations the new relation (15) between B_n and A_n is approximately valid at hot spots.

By substituting Eq (15) for B_n into Eq (11) we get:

By rearranging the terms in Eq (16) we get:

One might notice that the expression for A_n derived in [3] included the same denominator as in Eq (17) but the numerator becomes now different due to the use of the approximate relation of Eq (15). In the following analysis we develop new analytical results for EF which were not obtained in previous works as they ended there only with numerical calculations.

By transforming the hyperbolic functions of Eq (17) to exponential terms we get:

We divide both numerator and denominator of this equation by . Then we get

We note that the calculation of the coefficients A_nby the use of Eq (19) becomes quite simple as it can be derived in a straight forward way by the use of the parameter ε (ω ) and the experimental parameters: ε (ω), and ε₁. The use of the present approach is limited, however, by the validity of Eq, (15) appropriate to hot spots. For more accurate calculations we should add the contribution of the derivatives of (cosh η – cos α )^½but this will complicate very much the analysis so that new results for EF were not obtained [17-20].

For getting maximal EF one uses metals of the type of Au or Ag which at certain frequencies ε(ω) is very large real negative value (taken as experimental parameter) with negligible imaginary value. In the following Section we will develop the equations with bi-spherical coordinates for the electric field at the hot spots. We will develop further our equations by bi-spherical coordinates in Section 4 for the limit of enhancement factor (EF) under the above conditions and approximations. The requirement of having large negative real value for the metals dielectric constant will be found to be a crucial parameter for large EF [21-30].

The EM Field in Bi-Spherical Coordinates at the Hot Spots

The normal component of the EM field for which m=0 [16] is related in the space outside of the two spheres to the gradient in bi-spherical coordinates given as:

where , are unit vectors in the directions, respectively, i e in the bi-spherical radial direction and in direction perpendicular to .

Since the potential Ψ₁ in bi-spherical coordinates is given in Eq (10) by sum of n terms, the gradient in the normal η direction is given by:

In the derivation for gradient of the potential for the normal component (in the radial direction) only derivatives relative to η are taken into account while η₀ and α remain certain constants. By operating with Eq, (21) on Ψ₁( η , α ) of Eq (10) we take into account only the derivatives of the terms proportional to A_n representing the amplified potential which is very large relative to the external potential terms -E₀Z. Then we get:

Since the derivative of (cosh η – cos α )^½ relative to η is very small relative to the derivatives of the sinh functions (for δ <1 where the number of coefficients A_nis very large) we neglect this derivative and get

Eq (23) gives the general solution for the radial EM field in bi-spherical coordinates for hot spots for which δ <1 and for which the coefficient A_n are given by Eq (19).

Following Figure 2 and previous analysis we find that the hot spot is produced in a region for which the bi-spherical coordinate α satisfy approximately the relation α =π →c osα = −1. One should notice that the curve α = π coincides with the z axis, connecting the two poles with η = ±∞ and it is perpendicular to all η curves. It leads to special values of the Legendre polynomials on the symmetric Z axis given by [3]:

By substituting the value cos α = −1 and Eq (24) into Eq (23) we obtain the result for the EM field in bi-spherical coordinates on the symmetric coordinate Z including the hot spot:

We are interested in calculations of the total EM field intensity at the hot spot given by E_spot². We notice that in the calculation of E_spot² we have non-diagonal products E_nE_n, (n ≠ n^`’) with alternating signs so that their total contribution approximately vanishes. We consider therefore only the diagonal incoherent elements. Then for the electric field amplified factor E_spot² and for the SERS measurements which are proportional to E_spot⁴ we get:

We should take into account that E_spot² gives the electric field squared at the hot spot where products of E_n with E_n, ( n ≠ n^`’ ) vanish due to the approximation made after Eq (24). We should consider also that SERS measurements depend on E_spot⁴ so it is obtained by the square of the sums of Eq (26) (as demonstrated later in Section 4). We inserted in Eqs (26) the maximal value n_max which guarantees summation convergence but in the analytical calculations we allow this value to tend to ∞. Transformations of the η coordinate to be a function of the Z coordinate were developed in previous work but here we develop the explicit results for EF at the center of the hot spot for which η = 0. Then Eq (26) is transformed to simpler form as:

The η coordinates for the hot spots are in the range 0 ≤ η ≤ η₀ so that we expect that for larger values of η we will get larger values of corresponding to larger values of the functions. While such effect might be important, for cases for which η₀< 1 such effect will be relatively small so that Eq (27) still gives an approximate order of magnitude to Eq (26).

Analytical Results for Maximal Field-Enhancement (EF) at the Center of the Hot Spot

The electric field at the center of the hot spot is obtained by inserting Eq (19) into Eq (27) with summation over η. Then we get:

We define the light intensity as . Then the amplification of the light intensity at the center of the hot spots is given by:

One might notice that the parameter G(ω) in the present analysis is based on the new equation (15)

Eq (29) can be converted approximately to the following integral:

Eq (30) was transformed by using the definitions:

and given approximately as

By assuming a very large real negative value of ε (ω) we get from Eq (29) the approximation G(ω) → −1, Then by using this approximation in Eq (32) we get:

The integral in Eq (33) is obtained by using the corresponding integral from Gradshtein and Ryzhik book [31] where Γ(n) is the Gamma Function and ς (n) is the Riemann Zeta Function with the values.

Inserting these values in Eq (33) we get:

As the amplified field in SERS measurements is proportional to the fourth power its field enhancement factor (EF) is given by the square of Eq (35) i e ,

Eqs (35-36) represent very fundamental results by which the maximal enhanced light amplification factor for symmetric metallic dimers is proportional to η₀^-5 and the EF for SERS measurements is proportional to η₀^-10 . These analytical results are valid under the conditions 2δ <1, and G (ω) = [ε₁ −ε (ω)] / [ε₁ +ε (ω ) ] ) → −1 For cases in which G (ω) = | [ε₁ −ε (ω)] / [ε₁ +ε (ω ) ] )| >1 the integral in Eq. (32) is changed reducing much its value. It is verified by our calculations by which:

For example, for G (ω) = [ε₁ −ε (ω)] / [ε₁ +ε (ω ) ] ) = −1.1, -1.2, -1.3 we get, respectively, F(ω) = 0.707,0.232,0.159 so that the integral in Eq (32) becomes smaller and the light intensity of Eq (35) is decreased by the function F(ω). The EF of Eq (36) is decreased by this function squared (The changes in the coefficient ε (ω) / ( ε₁ + ε (ω ) ) are relatively smaller). An important conclusion from the present analysis is that for getting maximal EF we need to use metals which have large real negative value for ε (ω) i.e. using metals like A_u or A_g at certain frequencies. For hot spots for which we have the condition 2δ <1 we can use the approximations:

We find that the critical parameter η₀ for the symmetric spherical dimers is where d = 2δ is the shortest distance between the two spheres. We estimate that in more general nano particles gaps the critical parameter will be the ratio between the length of the gap and the metallic curvature around it.

Conclusion

In the present work we treated the mechanism by which “hot spots” are produced in the system of two metallic spheres with the same radius R interacting with incident homogeneous EM field polarized in the symmetric Z direction. Hot spots with huge EM field are produced by local plasmons at a small gap with nanoscale dimensions. Such hot spots are measured by surface enhanced Raman spectroscopy (SERS) and two-photon induced luminescence (TPI-PL). These effects depend on the fourth power of the EM field at the hot spot where the measured molecules are inserted. The present analysis is based on theoretical solution of Laplace equations using bi-spherical coordinates with certain values for the dielectric constants of noble metals. In the present system the fourth power of the EM fields at the hot spot turns to have extremely large values when the shortest distance between the spheres surfaces 2δ is very small i e , when 2δ <1. We developed in the present article certain approximations suitable for hot spots. In the present system in which the external EM is in the symmetric Z axis the potential has cylindrical symmetry about the Z axis. Therefore the potential Ψ₁ (η,α) at the hot spot developed in Eq (10) is function of the bi-spherical coordinates η, α , where represents the distance from the bi-spherical coordinates center and η,α represents an angle from this reference direction. The coordinates η,α can therefore be described as bi-spherical polar coordinates in the x, z plane of Figure 1, and these coordinates are not changed by rotation around the z axis. The potential Ψ₁ (η,α) is proportional to summation of Legendre polynomials P_n (α) with proportionality coefficients A_n and sinh function. The last term on the right side of Eq, (10) represents the external potential V_ext = – EZ where Z is defined in bi-spherical coordinates in Eq (2), and E₀ denotes, in short notation, the external EM field. By using the boundary conditions, we obtained after some calculations and certain approximations a general equation for the coefficients A_n in Eq (19). General solution for the EM field in the bi-spherical radial direction η is derived in Eq (23). Amplified EM field is found to be proportional to sum of products of the coefficients A_n with Legendre polynomial P_n (cos α) and with cosh function. As the hot spots in dimers are produced on (or near) the symmetric Z axis, for which x=y=0 we simplified the calculations by using this condition and used the relation: cos α = -1 simplifying the expression for Legendre polynomials. The use of bi-spherical coordinates is demonstrated in Figure 2. In Section 4 we developed analytical results for the field enhancement factor (EF) at the center of the hot spot. Although the electric field has a complicated dependence on the coordinate Z for simplicity of calculation we used Eq (27) for the hot spot center. The final results are given in Eq (35) in which the maximal light amplification factor is proportional to η₀^–5 and in Eq (36) in which the maximal EF for SERS measurements is proportional to η₀^-10 where and d = 2δ is the shortest distance between the two spheres. The present article is based on classical model but when the gap length is of an atomic scale quantum effects become important [32].

References

Kleinman SL, Frontiera RR, Henry A-I, Dieringer JA, Van Duyne RP (2013)Creating, characterizing, and controlling chemistry with SERS hot spots. Phys ChemChem Phys 15: 21-36. [crossref]
Sonntag MD, Klingsborn JS, Zrimsek AB, Sharma B, Ruvuna LK et al. (2014) Molecular plasmonics for nanoscale spectroscopy. Chem Soc Rev 43: 1230 [crossref]
Ben-Aryeh. (2021)Hot spots in two metallic spheres system related to Laplace equation solutions with bi- spherical coordinates. Applied Physics B 127: 157. [crossref]
Johnson PB, Christy R W (1972) Optical constants of the noble metals. Phys Rev B 6: 4370-4379.
Joh Johnson PB, Christy RW (1974) Optical constants of transition metals: Ti, V, Mn, Fe, Co, Ni, and Pd. Phys Rev B 9: 5056-5070.
Le Ru EC, Etchegoin PG (2009) Phenomenological local field enhancement factor distributions around electromagnetic hot spots. J Chem Phys 130: 181101. [crossref]
Ding SY, You E M, Tian ZQ, Moskovits M (2017) Electromagnetic theories of surface-enhanced Raman spectroscopy. Chem Soc Rev 46: 4042-4076. [crossref]
Inoue M, Ohtaka K (1983) Surface enhanced Raman scattering by metal spheres. I. cluster effect. J Phys Soc Japan 52: 3853-3864.
Jiang J, Bosnick K, Maillard M, Brus L (2003) Singe molecule Raman spectroscopy at the junctions of large Ag nanocrystals. J Phys Chem B 107: 9964-9972.
Nikoobakht B, El-Sayed MA (2003) Surface-enhanced Raman scattering studies on aggregated gold nanorods. J Phys Chem A 107: 3372-3378. [crossref]
Lee HM, Lee JH, Jin SM, Suh YD, Nam JM (2013) Single-molecule and single-particle-based correlation studies between localized surface plasmons of dimeric nanostructures with 1 nm gap and surface-enhanced Raman scattering. Nano Letters 13: 6113-6121. [crossref]
Li W, Camargo PHC, Lu X, Xia Y (2009) Dimers of silver nanospheres: Facile synthesis and their use as hot spots for surface-enhanced Raman scattering. Nano Lett 9: 485-490.
Imura K, Okamoto H, Hossain MK, Kitajima M (2006) Visualization of localized intense optical fields in single Gold nanoparticle assemblies and ultrasensitive Raman active sites. Nano Letters 6: 2173-2176. [crossref]
Aravind PK, Nitzan A, Metiu H (1981) The interaction between electromagnetic resonances and its role in spectroscopic studies of molecular adsorbed on colloidal particles or on metal surfaces. Surface Science 110: 189-204.
Morse PM, Feshbach H (1953) Methods of Theoretical Physics.
Stoy RD (1989) Solution procedure for the Laplace equation in bi-spherical coordinates for two spheres in a uniform external field: Parallel orientation. J Appl Phys 65: 2611-2615.
Stoy RD (1989) Solution procedure for the Laplace equation in bi-spherical coordinates for two spheres in a uniform external field: Perpendicular orientation. J ApplPhys 66: 5093-5095.
Ruppin R (1978) Surface modes of two spheres. Phys Rev B 26: 3440-3444.
Goyette A, Navon A (1978) Two dielectric spheres in an electric field. Phys Rev B 13: 4320-4327.
Levine HB, McQuarrie DA (1968) Dielectric Constants of simple gas. J ChemPhys 47, 4181-4187.
Yan BX, Zhu YY, Wei Y, Pei H (2021) Study on surface enhanced Ramanscattering of and sphericl dimers based on 3D finite element method. Scientific Reports 11: 8391. [crossref]
D DePrince AE, Hinde RJ (2010) Accurate computation of electric field enhancement factors for metallic nanoparticles using the discrete dipole approximation. Nanoscale Res Lett 5: 592-596. [crossref]
Drai Draine BT, Flatau PJ (1994) Discrete-dipole approximation for scattering calculations. J Opt Soc Am A 11: 1491-1499.
Camargo PHC, Au L, Rycenga M, Li W, Xia Y (2010) Measuring the SERS enhancement factors of dimers with different structures constructed from silver nano-cubes. Chem Phys Lett 484: 304- 308.
Le Ru EC, Blackie E, Meyer M, Etchegoin PG (2007) Surface enhanced Raman scattering enhancement factors: A comprehensive study. J Phys Chem C 111: 13794.
Stiles PL, Dieringer JA, Shah NC, Van Duyne RP (2008) Surface enhanced Raman spectroscopy. Annu Rev Anal Chem 1: 601-626.
Etchegoin PC, Le EC (2011) Basic electromagnetic theory. In Surface -Enhanced Raman -Spectroscopy. Wiley
Yu H, Peng Y, Yang Y, Li ZY (2019) Plasmon-enhanced light-matter interactions and application. Computational Materials 5: 45.
Jensen T, Kelly L, Lazarides A, Schatz GC (1999) Electrodynamics of noble nanoparticles and dimers. J Cluster Science 10: 295-317.
McMahon JM, Li S, Ausman LK, Schatz GC (2012) Modelling the Effects of small gaps in surface-enhanced Raman Spectroscopy. J Phys Chem C 116: 1627-1637. [crossref]
Gradshtein IS, Ryzhik IM (1980) Table of Integral, Series and Products New York, Academic Press p: 330.
Zhu W, Esteban R, Borisov AG, Baumberg JJ, Nordlander P, et al. (2016) Quantum mechanical effects in plasmonic structures with sub-nanometer gaps. Nature Communications 17: 11495. [crossref]