Levine's Model Research Articles

Family Caregiver Acceptance and Use of Environmental Strategies Provided in an Occupational Therapy Intervention

Statement: This article describes the specific environmental strategies that were accepted and used by 100 family caregivers who participated in a home-based occupational therapy intervention. The intervention was designed to enhance the skills of caregivers in using the physical and social environment to address troublesome behaviors and dependency associated with the progression of dementia. The intervention involved five 90-minute home visits by occupational therapists who worked with families to identify caregiving issues and generate environmental-based solutions. Solutions ranged from no cost recommendations (e.g., removing clutter, simplifying the environment), to resource dependent recommendations (e.g., installing grab bars or handrails).Method of Study: Study participants were interviewed at home prior to intervention to gather basic demographic information and level of functioning of the person with dementia. During intervention, the occupational therapist recorded the number and types of caregiver issues that were the focus of intervention, the number and types of strategies introduced for each care issue and whether each strategy was accepted and subsequently utilized by caregivers. Barris, Kielhofner, Levine and Neville's (1985) model of the environment (objects, tasks, social groups, culture)was used to organize treatment focus and categorize environmental strategies.Results: Of the nine problem areas that formed the focus of intervention, the issues most frequently identified by caregivers as problematic included caregiver-centered concerns, catastrophic reactions, wandering, and incontinence. Caregivers were willing to try a total of 1,068 strategies offered as part of intervention. Of the strategies, 869 (81%) were subsequently used independently by caregivers. Caregivers used a greater number of strategies that modified the task and social environments (with respectively 84% and 83% of tried strategies actually used by caregivers) than the objects layer of the environment (74% of tried strategies).Conclusions: Caregivers are receptive to and utilize environmental strategies offered by occupational therapists. Understanding which strategies were accepted and used by caregivers in this study provides important knowledge from which to enhance occupational therapy practice with this under-served population.

Family Caregiver Acceptance and Use of Environmental Strategies Provided in an Occupational Therapy Intervention

Statement: This article describes the specific environmental strategies that were accepted and used by 100 family caregivers who participated in a home-based occupational therapy intervention. The intervention was designed to enhance the skills of caregivers in using the physical and social environment to address troublesome behaviors and dependency associated with the progression of dementia. The intervention involved five 90-minute home visits by occupational therapists who worked with families to identify caregiving issues and generate environmental-based solutions. Solutions ranged from no cost recommendations (e.g., removing clutter, simplifying the environment), to resource dependent recommendations (e.g., installing grab bars or handrails).Method of Study: Study participants were interviewed at home prior to intervention to gather basic demographic information and level of functioning of the person with dementia. During intervention, the occupational therapist recorded the number and types of caregiver issues that were the focus of intervention, the number and types of strategies introduced for each care issue and whether each strategy was accepted and subsequently utilized by caregivers. Barris, Kielhofner, Levine and Neville's (1985) model of the environment (objects, tasks, social groups, culture)was used to organize treatment focus and categorize environmental strategies.Results: Of the nine problem areas that formed the focus of intervention, the issues most frequently identified by caregivers as problematic included caregiver-centered concerns, catastrophic reactions, wandering, and incontinence. Caregivers were willing to try a total of 1,068 strategies offered as part of intervention. Of the strategies, 869 (81%) were subsequently used independently by caregivers. Caregivers used a greater number of strategies that modified the task and social environments (with respectively 84% and 83% of tried strategies actually used by caregivers) than the objects layer of the environment (74% of tried strategies).Conclusions: Caregivers are receptive to and utilize environmental strategies offered by occupational therapists. Understanding which strategies were accepted and used by caregivers in this study provides important knowledge from which to enhance occupational therapy practice with this under-served population.

Time-dependent realization of the infinite-dimensional hydrogen algebra

We use the Hamiltonian formalism to investigate the Katzin–Levine model of a time-dependent Kepler problem. This formalism enables us to define Lie products in terms of Poisson brackets and obtain a time-dependent realization of centerless twisted (or standard) Kac–Moody algebras of so( N+1). We also show that the classical solutions of the model are modulated conic sections and derive a generalized Kepler equation for the time dependence.

Perioperative nursing: identification of the nursing diagnosis of risk for infection based on the Levine's conceptual model

The pre-operative visit consists in the first phase in the systematization of perioperative nursing care. This study aimed at identifying, during the pre-operative visit and more frequently, a nursing diagnosis of clients submitted to general surgery. The selected theoretical framework was Levine's conceptual model based on the four conservation principles, which are: energy conservation, structural integrity conservation, personal integrity conservation and social integrity conservation. In order to reach the proposed objective, an instrument was previously elaborated and validated for data collection. The sample consisted of 30 patients, males and females, who had been submitted to general surgery. The nursing diagnosis Infection Risk obtained 100% of frequency during the pre-operative visits to surgery patients. As to related factors that were identified, we point out: the site of invasion by organisms after the surgery and invasive procedures. Thus, the identification of this diagnosis can help nurses with the planning and implementation of preventive and infection control care, especially if risk factors are identified in the preoperative period.

Effects of neonatal hypoxia/ischemia on ganglioside expression in the rat hippocampus.

Neonatal Hypoxia-Ischemia (HI) triggers a cascade of biochemical events that result in neuronal injury, but the mechanisms underlying these processes are not completely understood, and information regarding the effect of HI on the synthesis of brain glycoconjugates is lacking. The present work evaluates the effects of neonatal HI on hippocampal ganglioside synthesis. Seven-day-old rat pups were exposed to HI for 2.5 h according to the modified Levine model and samples from hyppocampus were obtained at 30 min as well as at 1, 2 and 4 days later. The activity for synthesis of gangliosides was evaluated by determining the incorporation of N-acetyl [3H]neuraminc acid ([3H]NeuAc) into the endogenous gangliosides of Golgi membranes and by determining the activity of Sial-T2 (GD3 synthase) and GalNAc-T (GM2 synthase), the two enzymes acting on sialyllactosylceramide (GM3) at the branching point of synthesis of a- and b-ganglioside pathway. Northern blot experiments were also conducted to determine transcription levels of the mRNAs specific for these transferases. Neonatal HI caused a relative increase of in vitro [3H]NeuAc incorporation into endogenous lactosylceramide, which was most noticeable at 30 min and I day post-event and disappeared by day 2 and 4. The transient accumulation of [3H]GM3 correlated with decreases in the activities of GD3- and GM2 synthase measured at 30 min and at 1 day after the HI insult. No significant variations in the expression of the genes for these enzymes were observed. Results suggest that transient accumulation of GM3 may be due to post-translational events negatively modulating both GD3- and GM2 synthase activities.

The window of opportunity for neuronal rescue with insulin-like growth factor-1 after hypoxia-ischemia in rats is critically modulated by cerebral temperature during recovery.

Insulin-like growth factor (IGF-1) is induced in damaged brain tissue after hypoxia-ischemia, and exogenous administration of IGF-1 shortly after injury has been shown to be neuroprotective. However, it is unknown whether treatment with IGF-1 delayed by more than a few hours after injury may be protective. Hypothermia after brain injury has been reported to delay the development of ischemic neuronal death. The authors therefore hypothesize that a reduction in the environmental temperature during recovery from hypoxia-ischemia could prolong the window of opportunity for IGF-1 treatment. Unilateral brain damage was induced in adult rats using a modified Levine model of right carotid artery ligation followed by brief hypoxia (6% O2 for 10 minutes). The rats were maintained in either a warm (31 degrees C) or cool (23 degrees C) environment for the first 2 hours after hypoxia. All rats were subsequently transferred to the 23 degrees C environment until the end of the experiment. A single dose of IGF-1 (50 microg) or its vehicle was given intracerebroventricularly at either 2 or 6 hours after hypoxia. Histologic outcome in the lateral cortex was quantified 5 days after hypoxia. Finally, cortical temperature was recorded from 1 hour before and 2 hours after hypoxia in separate groups of rats exposed to the "warm" and "cool" protocols. In rats exposed to the warm recovery environment, IGF-1 reduced cortical damage (P < 0.05) when given 2 hours but not 6 hours after insult. In contrast, with early recovery in the cool environment, a significant protective effect of IGF-1 in the lateral cortex (P < 0.05) was found with administration 6 hours after insult. In conclusion, a reduction in cerebral temperature during the early recovery phase after severe hypoxia-ischemia did not significantly reduce the severity of injury after 5 days' recovery; however, it markedly shifted and extended the window of opportunity for delayed treatment with IGF-1.

Perinatal Brain Iron Deficiency Predisposes the Rat Hippocampus to Long-term Damage following Hypoxic-ischemic Insult • 1566

The offspring of pregnancies complicated by diabetes mellitus or intrauterine growth retardation are at increased risk for perinatal asphyxia and for long-term neurocognitive sequelae. Both gestational conditions are characterized by an increased prevalence of brain iron deficiency. The hippocampus is important for a variety of cognitive functions (e.g., recognition memory) and is susceptible to hypoxicischemic (HI) injury. To evaluate the hypothesis that brain iron deficiency increases the vulnerability of the hippocampus to HI injury and to assess whether iron induced reperfusion injury has any role in such injuries, we ligated the right common carotid artery in 15 perinatally iron-deficient and 15 iron-sufficient 7-day-old rat pups,and exposed them to 2.5 hours of 8% FIO2(Levine model). The non-ligated left side served as the undamaged internal control. On day 14, neuronal injury was quantified histochemically by assessing intensity of staining for Nissl substance in 4 hippocampal subareas in both hemispheres using optical densitometry in gray scale units (range: 1/white-254/black). To assess iron induced reperfusion injury, sections were stained for iron by modified Perl's reaction. The brain iron concentration of the iron-deficient group was 55% of control (p<0.001). In the iron-deficient group,there was significant loss of Nissl substance on the ligated right side in subareas CA1 (124 ± 14 v. 112 ± 15, p=0.002), CA3ab (144 ± 10 v. 129 ± 15, p=0.001) and the dentate gyrus (136 ± 14 v. 128 ± 13, p=0.012), when compared with the unligated left side.The iron-sufficient group had significant right sided Nissl loss only in CA1 (111 ± 14 v. 106± 15, p = 0.05). The mean number of subareas with detectable right sided Nissl loss per animal was greater in the iron-deficient group than the iron-sufficient group (2.9 ± 1.0 v. 2.0 ± 1.2, p<0.05). The degree of right-sided Nissl substance loss per animal in the iron-deficient group was also greater in CA1(p=0.042), CA3ab(p=0.003) and the dentate gyrus(p=0.037)when compared with the iron-sufficient group. There were no side-to-side differences in the number of iron stained cells in either group. Perinatal iron deficiency increases the vulnerability of hippocampal subareas of CA1, CA3ab and dentate to HI injury. Iron deposition is not involved in the pathophysiology of this injury. These findings may explain the increased risk of perinatal asphyxia and its neurocognitive sequelae in infants born of pregnancies complicated by perinatal iron deficiency.

Dynamic Diffusion and Perfusion MRI of Acute Experimental HIE † 1860

Introduction: The Levine model of hypoxic-ischemic encephalopathy(HIE) was investigated using dynamic interleaved diffusion MRI and perfusion weighted MRI, employing an intravascular iron containing blood pool contrast agent. Diffusion MRI yields maps of tissue apparent diffusion coefficient(ADC) which indicate the presence of cytotoxic edema. Perfusion MRI yields relative cerebral blood volume (CBV) information.

Ca2+ MACROIMAGING IN CEREBRAL CORTEX OF YOUNG RATS IN HYPOXIA-ISCHEMIA 39

Pertubation of intracellular Ca2+(Ca2+)i-regulation during hypoxia-ischemia (HI) is believed to be a critical event in the pathophysiology of brain injury. There is, however, no data available on in vivo changes of (Ca2+)i during or after HI in immature animals. Young rats (n=11) at postnatal day (PND)7-21 were anesthetized with isofluran/urethane. The skull was opened and the parietal cortex of the right hemisphere was exposed (6 × 6 mm window) and the Ca2+-sensitive fluorescence dye Rhod 2-AM (40 μM in 1% Agar gel in Ringer solution) was applied for 30 min and then replaced by Ringer solution in 1% gelatine for 1 h. Using the modified Levine model, the rat pups were subjected to 1h of HI and 3 h of recovery under urethane (1 mg/g ip) anesthesia. Point-analysis demonstrated small increments of(Ca2+)i during HI followed by an increase during reperfusion being more marked at PND 18-21 than in the younger (PND 7-13) rats. Color imaging showed that the cortical area with increase of (Ca2+)i was larger at PND 18-21 than at PND 7-13. Furthermore, differential analysis of images revealed a unidirectional or spreading movement of(Ca2+)i across the cortical surface during the early phase of HI in some animals.

PERINATAL BRAIN IRON DEFICIENCY INCREASES THE VULNERABILITY OF RAT HIPPOCAMPUS TO HYPOXIC ISCHEMIC INSULT. † 1419

Postnatally acquired dietary iron deficiency has adverse long-term effects on neurodevelopment. Recently, our laboratory has identified gestational conditions (diabetes mellitus, intrauterine growth retardation) which result in a significant prevalence of perinatal brain iron deficiency. These groups of infants have poorer long-term developmental outcome, but the role of iron deficiency is unknown. Loss of cytochrome oxidase (CytOx) activity in the region of the hippocampus, an area central to cognitive function (recognition memory), has been shown to be an early and sensitive indicator of neuronal damage following perinatal hypoxic-ischemic encephalopathy (HIE) in the rat. We hypothesized that perinatal iron deficiency enhances the vulnerability of the hippocampus to HIE injury. Twenty 7-day-old, iron-deficient rat pups and 20 iron-sufficient controls underwent right carotid artery ligation and were exposed to 2.5 hours of hypoxia (8% FIO2). In this model (the Levine model), both hypoxia and ischemia (right side), but not hypoxia alone (left side), are needed to induce changes in neuronal CytOx activity. The left side is thus the internal control. The mean ± SD brain iron concentration of the iron-deficient group was 40% lower than the iron-sufficient group (28.0± 6.8 v 51.0 ± 7.8; p<0.001). The CytOx activity, visualized with diaminobenzedine, in four different areas of hippocampus 24 hours after hypoxic-ischemic damage was measured in optical density (OD) units (range: 1 black/254 white) by computer-assisted densitometry. There was right-sided CytOx activity loss in the dentate gyrus (102 ± 16 v 89 ± 17 OD units; p=0.009), CA3c (105 ± 16 v 93 ± 19 OD units; p=0.003) and CA1 (108 ± 27 v 98 ± 17 OD units; p=0.06) compared to the unligated left side in the iron-deficient group. Side-to-to-side differences were seen only in CA1 in the iron-sufficient group. Overall, the iron-deficient group had more subareas with right-sided loss than the iron-sufficient group (p=0.04), and the magnitude of right-left differences was greater in the iron-deficient group (p=0.05). Perinatal iron deficiency enhances the vulnerability of the neonatal brain to HIE and may contribute to long-term neurodevelopmental delays in at-risk newborns. Supported by NICHD.

Quantitative analysis of contralateral hemisphere hypertrophy and sensorimotor performance in adult rats following unilateral neonatal ischemic-hypoxic brain injury

The immature nervous system is capable of considerable compensatory reorganization following injury. This has been studied extensively following many different types of injury in humans and laboratory animals. One common risk factor associated with perinatal brain injury that has been associated with such reorganization is an ischemic-hypoxic event. Using the established Levine model of neonatal ischemic-hypoxia (IH) to create unilateral striatal, cortical and hippocampal damage, we investigated anatomical changes in the undamaged hemisphere contralateral to the injury. Specifically, we measured cross-sectional area (mm 2) of brain sections at the level of + 1.20 and - 2.12 mm from bregma. In addition, we examined sensorimotor deficits in these animals during development and as adults by measuring the amount of time that the animals were able to remain on a rotating treadmill. Our results show that some animals exhibited hypertrophy in the hemisphere contralateral to the lesion as compared to measurements taken from normal control animals. Additionally, we have demonstrated that, following IH, animals that showed significant contralateral whole-hemisphere hypertrophy were able to remain on the Rota-Rod treadmill significantly longer than the animals that did not exhibit this hypertrophy. We conclude that there are compensatory reorganizational changes that occur in the undamaged hemisphere contralateral to injury in some animals following neonatal ischemic-hypoxic brain injury. Furthermore, our data suggest that this plasticity in the contralateral hemisphere may be functionally advantageous.

Fitting Polytomous Item Response Theory Models to Multiple-Choice Tests

This study examined how well current software implementations of four polytomous item response theory models fit several multiple-choice tests. The models were Bock's (1972) nominal model, Samejima's (1979) multiple-choice Model C, Thissen &amp; Steinberg's (1984) multiple-choice model, and Levine's (1993) maximum-likelihood formula scoring model. The parameters of the first three of these models were estimated with Thissen's (1986) MULTILOG computer program; Williams &amp; Levine's (1993) FORSCORE program was used for Levine's model. Tests from the Armed Services Vocational Aptitude Battery,the Scholastic Aptitude Test, and the American College Test Assessment were analyzed. The models were fit in estimation samples of approximately 3,000; cross-validation samples of approximately 3,000 were used to evaluate goodness of fit. Both fit plots and X2 statistics were used to determine the adequacy of fit. Bock's model provided surprisingly good fit; adding parameters to the nominal model did not yield improvements in fit. FORSCORE provided generally good fit for Levine's nonparametric model across all tests. Index terms: Bock's nominal model, FORSCORE, maximum likelihood formula scoring, MULTILOG, polytomous IRT.

“Experience-Sharing” As an Antidote to Dependence-Making Behavior of General Practitioners

This article explores how group-dynamic interventions can be used to teach health professionals to counter impulses to make clients dependent on them. The basic assumption, derived from Kohut's work on narcissism, is that dependence-making behavior is connected with deep-rooted feelings of insufficiency resulting from a defective autonomy. A part of the standard Dutch General Practice (GP) training program, experience-sharing in groups of 12 GP trainees, offers opportunities to explore these feelings. The format of this experience-sharing (well-defined boundaries, minimal structure, facilitating leaders) often evokes behavior in which the peculiarities of the dependence-making behavior of the GP's vis-à-vis patients are mirrored: that is, dependent behavior. In order to analyze and influence this behavior, use can be made of Levine's model of group psychotherapy, which focuses on enhancing autonomy. In this paper we show, by means of four group cases, how Levine's framework can be used to enhance autonomy, lessen dependence, and thus diminish the tendency of GP's toward dependence-making behavior.

Normative developmental challenges and dieting and eating disturbances in middle school girls

Three predictions based on Levine and Smolak's (1992) developmental model of dieting and eating disturbances were tested: (1) Changes in pubertal status and/or dating status increase the probability of nonpathological dieting in middle school girls; (2) concurrent change in pubertal status, dating status, and academic stress increases the probability of subclinical eating disturbances in girls with a slender body ideal; and (3) the co-occurrence of modeling cues and direct messages from peers and/or family about the importance of weight, shape, and dieting increases the probability of these effects. Three hundred eighty-two girls were asked about menarcheal status, dating status, and academic stress, as well as attitudes about shape, eating behavior, and perceptions of peer and family pressures for slenderness. Results confirmed several of the predictions, suggesting that the interaction among cumulative developmental changes in early adolescence, adherence to a slender body ideal, and sociocultural pressures for thinness may be useful in distinguishing middle schoolers at risk for subclinical eating disturbances from both girls who do not diet and girls whose dieting is or will be "normative."

Structure analysis of an alkali metal adsorbed Si(001)(2 × 1) surface by tensor LEED

The structures of the alkali metal (K, Cs) adsorbed Si(001)(2 × 1) surface have been studied by tensor LEED. A reliability factor ( R factor) analysis has been carried out for models having different sites for the alkali atoms, that is, a pedestal site model (so called Levine's model), a cave site model and a double-layer model. Although the difference between the numerical values of R is small for these models, the smallest R factor is obtained for the double-layer model with a symmetric dimer model for the topmost Si atoms.

Prediction of specific damage or infarction from the measurement of tissue impedance following repetitive brain ischaemia in the rat

The development of irreversible brain damage during repetitive periods of hypoxia and normoxia was studied in anaesthetized rats with unilateral occlusion of the carotid artery (modified Levine model). Rats were exposed to 10 min hypoxia and normoxia until severe damage developed. As indices of damage, whole striatal tissue impedance (reflecting cellular water uptake), sodium/potassium contents (due to exchange with blood). Evans Blue staining (blood-brain barrier [BBB] integrity) and silver staining (increased in irreversibly damaged neurons) were used. A substantial decrease in blood pressure was observed during the hypoxic periods possibly producing severe ischaemia. Irreversibly increased impedance, massive changes in silver staining, accumulation of whole tissue Na and loss of K occurred only after a minimum of two periods of hypoxia, but there was no disruption of the BBB. Microscopic examination of tissue sections revealed that cell death was selective with reversible impedance changes, but became massive and non-specific after irreversible increase of the impedance. The development of brain infarcts could, however, not be predicted from measurements of physiological parameters in the blood. We suggest that the development of cerebral infarction during repetitive periods of hypoxia may serve as a model for the development of brain damage in a variety of clinical conditions. Furthermore, the present model allows the screening of potential therapeutic measuring of the prevention and treatment of both infarction and selective cell death.

Optimized structures and electronic properties of alkali-metal (Na, K) -adsorbed Si(001) surfaces.

The Na and K adsorption on the Si(001)-2\ifmmode\times\else\texttimes\fi{}1 surface is studied by first-principles molecular dynamics based on the norm-conserving pseudopotential. The stable adsorption sites are determined for full coverage (\ensuremath{\Theta}=1.0) and half coverage (\ensuremath{\Theta}=0.5). At \ensuremath{\Theta}=0.5, the configuration with Na and K adsorbed along the trough is more stable than predicted by the Levine model. The coverage dependence of the absorption energy suggests that the saturation coverage should be \ensuremath{\Theta}=1.0 for both Na and K and that a qualitative difference between Na and K can be observed in the growth mode of the adsorbed layer. Supplementary calculations for \ensuremath{\Theta}=1/3 and 5/6 are performed in order to obtain an insight into the difference between Na and K in the coverage dependence of the adsorption energy. It is pointed out that the partial core correction for the pseudopotentials of Na and K is very crucial in the structural stability arguments.

Theoretical support to the double-layer model for potassium adsorption on the Si(001) surface.

K adsorption on the Si(001)-2\ifmmode\times\else\texttimes\fi{}1 surface is studied by first-principles molecular dynamics based on a norm-conserving pseudopotential. The theoretically optimized structure for full coverage (\ensuremath{\Theta}=1.0) agrees fairly well with the double-layer model analyzed by x-ray photoelectron diffraction. At \ensuremath{\Theta}=0.5, the configuration with K adsorbed along the trough is more stable than the Levine model. The mean desorption energies for the two peaks in the thermal desorption spectrum are well accounted for by the present calculation. The calculated work-function change also agrees quantitatively with the observed one. Based on these analyses, it is concluded that the double-layer model should be appropriate for the saturation coverage of K on the Si(001) surface.

Linear and nonlinear optical properties of quartz-type GaPO4.

The linear and nonlinear optical properties of quartz-type ${\mathrm{GaPO}}_{4}$ were studied. The indices of refraction (${\mathit{n}}_{\mathit{o}}$ and ${\mathit{n}}_{\mathit{e}}$) have been measured as a function of wavelength from 300 to 770 K. The second-harmonic-generation coefficient ${\mathit{d}}_{11}$ and the Miller ${\mathrm{\ensuremath{\Delta}}}_{11}$ have been determined experimentally in the temperature range from 300 to 1000 K. At higher temperatures, ${\mathit{n}}_{\mathit{o}}$, ${\mathit{n}}_{\mathit{e}}$, ${\mathit{d}}_{11}$, and ${\mathrm{\ensuremath{\Delta}}}_{11}$ decrease slightly (${\mathrm{\ensuremath{\Delta}}}_{11}$ by approximately 6% at 1038 K). Compared with quartz or the isomorph berlinite, ${\mathrm{GaPO}}_{4}$ shows very small variations with temperature. Theoretical calculations using Levine's bond-charge model have also been made for the temperatures 173, 293, 373, 773, and 1023 K. The results are in reasonable agreement with experiment and allow insight into the physical origin of the larger magnitude and considerably lower temperature dependence of ${\mathit{d}}_{11}$ and ${\mathrm{\ensuremath{\Delta}}}_{11}$, as compared with quartz and berlinite.

Structure of the K adsorbed Si(001)2 × 1 surface studied by LEED

The surface structures of K adsorbed Si(001))2 × 1 surfaces have been studied by the dynamical analysis of low-energy electron diffraction (LEED) beam intensity versus electron energy curves (the so-called I- V curves). A reliability factor ( R-factor) analysis has been carried out for three models of the site of the K atoms, that is, a pedestal site model (Levine's model), a double layer model, and a cave site model. Although the difference of the numerical value of R is not so large among these models, the double layer model indicates the smallest value within a symmetric dimer model of the topmost Si atoms.