Modeling patchy saturation of fluids in nanoporous media probed by ultrasound and optics.

Nanoporous materials provide high surface area per unit mass and are capable of fluids adsorption. While the measurements of the overall amount of fluid adsorbed by a nanoporous sample are straightforward, probing the spatial distribution of fluids is nontrivial. We consider literature data on adsorption and desorption of fluids in nanoporous glasses reported along with the measurements of ultrasonic wave propagation. We analyze these using the so-called dynamic equivalent medium approach, which is based on Biot's theory of dynamic poroelasticity with coefficients that are continuous random functions of position. When further constrained by optical scattering data for similar systems, the calculations show that on adsorption the characteristic patch size is of the order of 100 pore diameters, while on desorption the patch size is comparable to the sample size. Our analysis suggests that one can employ ultrasound to probe the uniformity of the spatial distribution of fluids in nanoporous materials.

Ultrasonic study of water adsorbed in nanoporous glasses.

Thermodynamic properties of fluids confined in nanopores differ from those observed in the bulk. To investigate the effect of nanoconfinement on water compressibility, we perform water sorption experiments on two nanoporous glass samples while concomitantly measuring the speed of longitudinal and shear ultrasonic waves in these samples. These measurements yield the longitudinal and shear moduli of the water-laden nanoporous glass as a function of relative humidity that we utilize in the Gassmann theory to infer the bulk modulus of the confined water. This analysis shows that the bulk modulus (inverse of compressibility) of confined water is noticeably higher than that of the bulk water at the same temperature. Moreover, the modulus exhibits a linear dependence on the Laplace pressure. The results for water, which is a polar fluid, agree with previous experimental and numerical data reported for nonpolar fluids. This similarity suggests that irrespective of intermolecular forces, confined fluids are stiffer than bulk fluids. Accounting for fluid stiffening in nanopores may be important for accurate interpretation of wave propagation measurements in fluid-filled nanoporous media, including in petrophysics, catalysis, and other applications, such as in porous materials characterization.

The Effect of the Method of Downhole Deployment on Distributed Acoustic Sensor Measurements: Field Experiments and Numerical Simulations.

Distributed acoustic sensing (DAS) is a promising technology for seismic data acquisition, particularly in downhole applications. However, downhole DAS measurements can be affected by the deployment method of the fibre-optic cable. These effects were explored in a field trial in two wells (one vertical and one deviated) drilled at the Otway International Test Centre. The trial in the vertical well shows that (1) fibre-optic cables cemented behind the casing provide data of the highest quality due to the best coupling to the formation, and (2) tubing-conveyed cable shows only slightly weaker coupling, but the data quality can be severely degraded by source-generated noise. A cable loosely suspended in the deviated well provided data quality comparable to that of the cemented DAS cable. To better understand the nature of the observed effects, the field experiments were supplemented by numerical modelling with a 1.5D full wave reflectivity algorithm (3D wave propagation in a 1D model), where cement, casing and wellbore were represented by infinite vertical layers. The results show that (1) a cement layer has only a slight effect (<5%) on the DAS amplitude; (2) the vertical strain in a liquid-filled borehole is comparable to that in the formation; and (3) the strain amplitude in the cable is of the same order of magnitude both in the formation and in the fluid. The strain in the cable is zero both when the cable's Poisson's ratio is zero and when the borehole fluid is air. The results confirm the feasibility of borehole DAS measurements with fibre-optic cables suspended in a borehole liquid (but not gas!).

Evidence of Nonlinear Seismic Effects in the Earth from Downhole Distributed Acoustic Sensors.

Seismic velocities and elastic moduli of rocks are known to vary significantly with applied stress, which indicates that these materials exhibit nonlinear elasticity. Monochromatic waves in nonlinear elastic media are known to generate higher harmonics and combinational frequencies. Such effects have the potential to be used for broadening the frequency band of seismic sources, characterization of the subsurface, and safety monitoring of civil engineering infrastructure. However, knowledge on nonlinear seismic effects is still scarce, which impedes the development of their practical applications. To explore the potential of nonlinear seismology, we performed three experiments: two in the field and one in the laboratory. The first field experiment used two vibroseis sources generating signals with two different monochromatic frequencies. The second field experiment used a surface orbital vibrator with two eccentric motors working at different frequencies. In both experiments, the generated wavefield was recorded in a borehole using a fiber-optic distributed acoustic sensing cable. Both experiments showed combinational frequencies, harmonics, and other intermodulation products of the fundamental frequencies both on the surface and at depth. Laboratory experiments replicated the setup of the field test with vibroseis sources and showed similar nonlinear combinations of fundamental frequencies. Amplitudes of the nonlinear signals observed in the laboratory showed variation with the saturating fluid. These results confirm that nonlinear components of the wavefield propagate as body waves, are likely to generate within rock formations, and can be potentially used for reservoir fluid characterization.

Monitoring Injected CO2 Using Earthquake Waves Measured by Downhole Fibre-Optic Sensors: CO2CRC Otway Stage 3 Case Study.

Monitoring changes of formation properties along the well bore associated with the presence of carbon dioxide can be important for both tracking the plume inside of the primary containment and detecting leakage into the zone located above the reservoir. This can be achieved with time lapse wireline logging, but this approach requires well intervention and is not always possible. If the well is permanently instrumented with an optical fibre, it can be used as a distributed seismic receiver array to detect gas behind the casing by monitoring changes in amplitude of the seismic waves generated by active or passive seismic sources. Previous research showed the efficacy of this technique using continuous seismic sources. The Stage 3 Otway Project presented an opportunity to test this technique using passive seismic recording, as downhole fibre-optic arrays recorded numerous regional earthquakes over the period of nearly 2 years before, during, and after CO2 injection. Analysis of P-wave amplitudes extracted from these downhole gathers shows a consistent amplitude anomaly at the injection level, visible in all events that occurred after the start of injection. This indicates that the anomaly is caused by changes in elastic properties in the reservoir caused by CO2 saturation. However, extracted amplitudes show significant variability between earthquakes even without subsurface changes; thus, multiple events are required to distinguish the time-lapse anomaly from time-lapse noise. Ubiquity of these events even in a tectonically quiet region (such as Australia) makes this technique a viable and cost-effective option for downhole monitoring.

Optimal bounds for attenuation of elastic waves in porous fluid-saturated media.

Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions.

Effect of estrogens on blood glutamate levels in relation to neurological outcome after TBI in male rats.

PURPOSE: Estrogen has been shown to possess neuroprotective properties both in vitro and in vivo. Traumatic brain injury (TBI) in ovulating females results in favorable neurological outcomes when compared to males with similar insults. The brain-to-blood glutamate gradient removes excess glutamate from brain extracellular fluids (ECF). Enhancing this gradient leads to improved neurological outcomes following TBI. In this study we investigate the effect of female gonadal steroids on blood glutamate levels and neurological outcomes. METHODS: Forty male Sprague-Dawley rats were assigned to one of five groups: (1) sham, (2) Premarin treatment, (3) TBI, (4) TBI + Premarin treatment, and (5) TBI + Premarin pretreatment. TBI was induced, and estrogen and glutamate levels were determined at 0, 60, 120, 135, and 150 min. Neurological recovery was evaluated using the Neurological Severity Score (NSS) at 1 h and reassessed at 24 h post TBI. RESULTS: Premarin treatment groups demonstrated a decline in blood glutamate levels by 60 min. This decline was found to be more pronounced in the TBI + Premarin group, which maintained the decline throughout the experiment. At 120 min, the difference between groups was most pronounced (TBI + Premarin 99 ± 36 µM/l vs. control 200 ± 46 µM/l, p < 0.01). Neurological recovery was significantly better in the Premarin treatment group (NSS at 24 h 6 ± 1 vs. control 11 ± 1). CONCLUSIONS: Premarin injected into male rats significantly decreases blood glutamate levels in rats suffering TBI. This decrease is associated with improved neurological outcomes, thus implicating the role of estrogen in neuroprotection.

The effect of hyperthermia on blood glutamate levels.

INTRODUCTION: Glutamate neurotoxicity is determined by the balance between glutamate release within the brain and efflux of excess glutamate from the brain. Brain-to-blood efflux of glutamate is increased by decreasing the concentration of glutamate in blood. Little is known about the effect of hyperthermia on blood glutamate concentrations, and the effectiveness of blood glutamate-decreasing mechanisms in these conditions. Although hyperthermia is hypothesized to decrease blood glutamate concentrations by activation of stress mechanisms, blunting the stress response by blocking ß-adrenergic receptors should prevent this decrease. Furthermore, during hyperthermia there should be a concurrent process of leakage of glutamate from muscle tissue into blood, resulting in a contradictory increase of blood glutamate concentrations. In this study we investigated the effects of hyperthermia on blood glutamate levels and studied the effects of the ß-adrenergic receptor antagonist propranolol on stress-induced changes in glutamate levels. We then studied the effectiveness of the blood glutamate scavenger oxaloacetate on hyperthermia-induced increases of glutamate levels. MATERIALS AND METHODS: Twenty-four rats were randomly divided into 3 groups. Rats' body temperatures were increased (by 1°C every 40 minutes) from 37°C to 42°C. The first group received 1 mL per 100 g of isotonic saline (control). The second group received 1 mL per 100 g of 1M oxaloacetate when the temperature reached 39°C. The third group received 10 mg/kg of propranolol before initiation of the warming. RESULTS: Warming the rats from 37°C to 39°C decreased the blood glutamate levels in the control group (P < 0.01) and oxaloacetate treatment group (P < 0.0001), whereas further increases in temperature from 40°C to 42°C increased the blood glutamate levels (P < 0.01 and P < 0.0001, respectively). Pretreatment with propranolol prevented the decrease in blood glutamate concentrations seen in mild hyperthermia and did not affect the increase in blood glutamate levels seen at temperatures of 41°C and 42°C (P < 0.005). DISCUSSION: The results of this study demonstrated that hyperthermia leads to decreases in glutamate levels in the blood, presumably by activation of the sympathetic nervous system. Oxaloacetate, previously reported to reduce blood glutamate levels at 37°C, was ineffective at temperatures over 40°C. Propranolol pretreatment blunted the initial decrease in blood glutamate, and thereafter had no effect when compared with control and treatment groups. Understanding the mechanisms underlying glutamate regulation in the blood during states of hyperthermia and stress has important clinical implications in treating neurodegenerative conditions.

Pain specialists' evaluation of patient's prognosis during the first visit predicts subsequent depression and the affective dimension of pain.

OBJECTIVE: To examine the predictive value of physician's prognosis after patient's first visit to a pain specialty clinic. DESIGN: This is a prospective-longitudinal study in which patients completed questionnaires regarding their pain and psychological constructs before their first visit to a pain specialist and again after an average of 5 months. Physicians rated patient's prognosis immediately after the first visit. SETTING: This study was conducted at the outpatient specialty pain clinic at Soroka University Medical Center. PATIENTS: Forty-five chronic pain patients suffering from a range of nonmalignant pain conditions. OUTCOME MEASURES: Sensory and affective pain measured by the Short-Form McGill Pain Questionnaire and depressive symptoms measured by the Center for Epidemiological Studies-Depression Scale. RESULTS: Multiple regression analysis revealed that physician's rating of patient prognosis at Time 1 uniquely predicted subsequent depressive symptoms and affective pain but not sensory pain at Time 2 even after controlling for Time 1 levels of these variables. CONCLUSION: Physician's pessimistic evaluation of patient's prognosis after the first visit was longitudinally associated with an increase in depression and in the affective dimension of pain over time, but not with changes in the sensory component of pain. Referring to physician pessimism as a marker for pre-depressed patient may lead to early preventive interventions.

Modeling of axisymmetric wave modes in a poroelastic cylinder using spectral method.

Algorithm and code are presented which solve the dispersion equation for cylindrical poroelastic structures. The algorithm is based on the spectral method, which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. The results are illustrated for the case of a fluid-saturated free cylinder with open- and closed-pore boundary conditions on its surface. The computed dispersion curves are in good agreement with analytical results, which confirms the accuracy of the method.

Modeling of wave dispersion along cylindrical structures using the spectral method.

Algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wave numbers of different modes. The advantage of this technique is that it is easy to implement, especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelastic media. The application of the new approach is illustrated using models of an elastic cylinder and a fluid-filled tube. The dispersion curves so produced are in good agreement with analytical results, which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.

The contribution of the blood glutamate scavenging activity of pyruvate to its neuroprotective properties in a rat model of closed head injury.

The removal of excess glutamate from brain fluids after acute insults such as closed head injury (CHI) and stroke is expected to prevent excitotoxicity and the ensuing long lasting neurological deficits. Since blood glutamate scavenging accelerates the removal of excess glutamate from brain into blood and causes neuroprotection, we have evaluated here whether the neuroprotective properties of pyruvate could be partly accounted to its blood glutamate scavenging activity. The neurological outcome of rats after CHI improved significantly when treated with intravenous pyruvate (0.9 mmoles/100 g) but not with pyruvate administered together with glutamate. Pyruvate, at 5 micromole/100 g rat was neither protective not able to decrease blood glutamate but displayed the latter two properties when combined with 60 microg/100 g of glutamate-pyruvate transaminase. Since the neurological recovery from CHI was correlated with the decrease of blood glutamate levels, we conclude that pyruvate blood glutamate scavenging activity contributes to the spectrum of its neuroprotective mechanisms.

Patients' self-criticism is a stronger predictor of physician's evaluation of prognosis than pain diagnosis or severity in chronic pain patients.

UNLABELLED: The experience of pain is influenced by patients' personality, social and cultural background, and patient-doctor interaction. This study examines the role of self-reported pain, pain diagnosis, age, gender, depression, and the personality trait of self-criticism (defined as individuals' tendency to set unrealistically high self-standards and to adopt a punitive stance toward one's self), in determining physicians' view of expected prognosis in response to chronic pain management. Before the first visit to a tertiary chronic pain clinic, patients provided information regarding their perceived pain, depression, and self-criticism. Immediately subsequent to the visit, physicians' evaluated expected prognosis. Participating physicians were blinded to the patient's psychosocial variables collected. Sixty-four patients with chronic pain (34 women and 30 men) with various diagnoses were included. Patients' age, gender, pain diagnosis, self-reported pain, and depression did not significantly correlate with physician's estimation of expected prognosis. In contrast, patients' self-criticism emerged as an independent predictor of physicians' pessimism regarding outcome. Thus, in the chronic pain clinic setting, patients' personality, rather than self-reported pain experience, determines doctor's clinical judgment of expected prognosis. PERSPECTIVE: Chronic pain is a multimodal negative experience that is determined by physiological, cognitive, personological, and interpersonal factors. In line with this observation, we found patients' personality, specifically, their self-criticism, determines physicians' clinical judgment of expected prognosis.

Anesthetic considerations during percutaneous nephrolithotomy.

STUDY OBJECTIVE: To assess anesthesia-related complications during and following percutaneous nephrolithotomy (PCNL) for staghorn stones. DESIGN: Prospective study and a detailed case report. SETTING: Medical center in southern Israel. PATIENTS: 20 consecutive patients undergoing PCNL for staghorn stones. INTERVENTIONS: All patients underwent PCNL during general anesthesia. MEASUREMENTS: Duration of surgery, esophageal temperature, hemoglobin (Hb) concentration, and requirements for blood transfusion, mean volume of irrigation fluid, and serum sodium and potassium concentration were recorded. MAIN RESULTS: Mean age was 50.7 +/- 14.9 y (range, 26-76 y). Mean duration of the procedure was 120.0 +/- 42.5 min (range, 75-240 min). Mean volume of irrigation fluid was 34.1 +/- 15.3 L (range, 18-80 L). There was a significant decrease in Hb concentration from 13.7 +/- 1.71 to 12.2 +/- 1.4 g/dL, but no patient required blood transfusion. There was a statistically significant reduction in esophageal temperature from 36.4 degrees C +/- 0.32 degrees C to 35.2 degrees C +/- 0.5 degrees C. There were no significant changes in sodium or potassium concentration before or after PCNL. CONCLUSIONS: Anesthesia during PCNL for staghorn stones is a challenge because of the possibility of fluid absorption, dilutional anemia, hypothermia, or significant blood loss.

Brain neuroprotection by scavenging blood glutamate.

Excess glutamate in brain fluids characterizes acute brain insults such as traumatic brain injury and stroke. Its removal could prevent the glutamate excitotoxicity that causes long-lasting neurological deficits. As blood glutamate scavenging has been demonstrated to increase the efflux of excess glutamate from brain into blood, we tested the prediction that oxaloacetate-mediated blood glutamate scavenging causes neuroprotection in a pathological situation such as closed head injury (CHI), in which there is a well established deleterious increase of glutamate in brain fluids. We observed highly significant improvements of the neurological status of rats submitted to CHI following an intravenous treatment with 1 mmol oxaloacetate/100 g rat weight which decreases blood glutamate levels by 40%. No detectable therapeutic effect was obtained when rats were treated IV with 1 mmol oxaloacetate together with 1 mmol glutamate/100 g rat. The treatment with 0.005 mmol/100 g rat oxaloacetate was no more effective than saline but when it was combined with the intravenous administration of 0.14 nmol/100 g of recombinant glutamate-oxaloacetate transaminase, recovery was almost complete. Oxaloacetate provided neuroprotection when administered before CHI or at 60 min post CHI but not at 120 min post CHI. Since neurological recovery from CHI was highly correlated with the decrease of blood glutamate levels (r=0.89, P=0.001), we conclude that blood glutamate scavenging affords brain neuroprotection Blood glutamate scavenging may open now new therapeutic options.

The effect of hypertonic (3%) saline with and without furosemide on plasma osmolality, sodium concentration, and brain water content after closed head trauma in rats.

Adding furosemide (F) to mannitol causes a greater decrease of brain volume, intracranial pressure, and brain water content (BW) as compared with mannitol alone. We examined whether adding F to hypertonic saline (HS) causes less increase of BW early after closed head trauma (CHT) as compared with HS alone. With institutional approval, 125 rats underwent sham surgery or CHT and then immediately received no treatment, HS (1.2 g/kg, 3% solution), or HS + F (2 mg/kg). In groups 1-10 (n = 8/group), the percent BW content was determined at 30, 60, or 120 minutes. In groups 11-14 (n = 8/group), physiologic values were determined at 0, 30, 60, and 120 minutes. At 120 minutes, the increase of BW caused by CHT (sham = 78.9 +/- 0.6% and CHT = 81.5 +/- 2.2%, mean +/- SD) was prevented by HS + F (78.0 +/- 0.8%) but not by HS (80.7 +/- 2.2%). Both HS and HS + F similarly increased plasma osmolality and sodium concentration. Post-CHT hypotension and acidosis (30 and 60 minutes) and decrease of hemoglobin concentration (120 minutes) were less with HS + F than with HS. We conclude that adding F to HS decreases BW without causing more increase of osmolality and Na than that caused by HS alone.

Controlled-release oxycodone-induced seizures.

BACKGROUND: The use of the opioid oxycodone hydrochloride in the management of chronic pain is gaining popularity principally because of its tolerability. However, opioid-related seizure in patients with epilepsy or other conditions that may decrease seizure threshold has been described in the literature; in particular, oxycodone has been associated with seizure in a patient with acute renal failure. OBJECTIVE: The aim of this article was to report a patient with a history of seizures but normal renal and hepatic function who developed seizure on 2 occasions after oxycodone ingestion. METHODS: A 54-year-old male patient presented with a history of tonic-clonic seizures that developed immediately after intracranial surgery. Long-term treatment with carbamazepine 400 mg QD was started, and the patient was free of convulsions for approximately 7 years. The patient presented to us with severe headache that was nonresponsive to an NSAID and the opiate agonist tramadol. Treatment with controlled-release (CR) oxycodone and tramadol drops (50 mg QID if necessary) was started, and tonic-clonic seizures developed 3 days later. RESULTS: Based on laboratory analysis, the patient had normal renal and hepatic function. On discontinuation of oxycodone treatment, the seizures resolved. However, due to effective pain relief with oxycodone, the patient decided to continue treatment, and seizures recurred. Carbamazepine was then administered 4 hours before oxycodone dosing, which allowed continuation of treatment without seizure. CONCLUSIONS: A patient with a history of seizures controlled with long-term carbamazepine therapy developed seizures when he started treatment with oxycodone CR at recommended doses. Oxycodone CR should be used with extreme caution in patients with epilepsy or other conditions that may decrease seizure threshold.

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves.

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.

A first-order statistical smoothing approximation for the coherent wave field in random porous random media.

An important dissipation mechanism for waves in randomly inhomogeneous poroelastic media is the effect of wave-induced fluid flow. In the framework of Biot's theory of poroelasticity, this mechanism can be understood as scattering from fast into slow compressional waves. To describe this conversion scattering effect in poroelastic random media, the dynamic characteristics of the coherent wavefield using the theory of statistical wave propagation are analyzed. In particular, the method of statistical smoothing is applied to Biot's equations of poroelasticity. Within the accuracy of the first-order statistical smoothing an effective wave number of the coherent field, which accounts for the effect of wave-induced flow, is derived. This wave number is complex and involves an integral over the correlation function of the medium's fluctuations. It is shown that the known one-dimensional (1-D) result can be obtained as a special case of the present 3-D theory. The expression for the effective wave number allows to derive a model for elastic attenuation and dispersion due to wave-induced fluid flow. These wavefield attributes are analyzed in a companion paper.

Determining minimum alveolar anesthetic concentration of halothane in rats: the effect of incremental change in halothane concentration and number of crossovers.

Computer simulations for the technique of estimating minimum alveolar anesthetic concentration (MAC) in patients (quantal design) suggest that incremental concentration changes and the number of crossovers affect MAC. We hypothesized that these variables may also apply to estimating MAC in rats (bracketing design). This study tested that hypothesis and also examined whether these variables might mask differences in MAC between groups in which MAC might be expected to differ (pregnant [P] versus nonpregnant [NP]). There were 2 cohorts (n = 27 and n = 30 rats). Each cohort included NP females, females in early P, and females in late P. MAC was tested by using an incremental concentration change of 0.20% and one within-subject crossover in the first cohort and by using an increment size of 0.10% and four crossovers in the second cohort. MAC was statistically significantly increased in the three groups in the second cohort (NP, 1.16 +/- 0.12; early P, 1.14 +/- 0.10; late P, 1.07 +/- 0.10; mean +/- sd) compared with values in the three comparable groups in the first cohort (NP, 0.95 +/- 0.06; early P, 1.01 +/- 0.09; late P, 0.93 +/- 0.13). Values did not differ among groups within each cohort. Post hoc simulations indicated that up to 36% of the difference between cohorts was due to increment size, with the balance due to experimental factors. Our findings confirmed the hypothesis that increment size affects estimates of MAC when a bracketing design is used.