Granularity analysis for mathematical proofs.

Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size.

Imaging and elemental mapping of biological specimens with a dual-EDS dedicated scanning transmission electron microscope.

A dedicated analytical scanning transmission electron microscope (STEM) with dual energy dispersive spectroscopy (EDS) detectors has been designed for complementary high performance imaging as well as high sensitivity elemental analysis and mapping of biological structures. The performance of this new design, based on a Hitachi HD-2300A model, was evaluated using a variety of biological specimens. With three imaging detectors, both the surface and internal structure of cells can be examined simultaneously. The whole-cell elemental mapping, especially of heavier metal species that have low cross-section for electron energy loss spectroscopy (EELS), can be faithfully obtained. Optimization of STEM imaging conditions is applied to thick sections as well as thin sections of biological cells under low-dose conditions at room and cryogenic temperatures. Such multimodal capabilities applied to soft/biological structures usher a new era for analytical studies in biological systems.

Nitroprusside in resuscitation of major torso trauma.

OBJECTIVE: Patients with thoracic aortic injury (TAI) usually have sustained other major trauma, and may require aggressive shock resuscitation. In the 24 hours after aortic repair and during resuscitation, our cardiothoracic surgeons request intravenous nitroprusside to maintain mean arterial pressure (MAP) less than 90 mm Hg to minimize bleeding at the repair. We compared the resuscitation response of patients who sustained major torso trauma (MTT) and TAI with that of patients who had MTT with no TAI to determine whether nitroprusside can effectively control MAP during resuscitation and whether use of nitroprusside, because of its peripheral vasodilatory effects, is associated with a favorable resuscitation response. METHODS: During the 9-month study period, 11 patients who sustained TAI and 38 patients who sustained MTT with no TAI met multiple organ failure risk/shock criteria and were resuscitated by a standardized protocol emphasizing volume loading and hemoglobin replacement to maintain systemic oxygen delivery index (DO2I) > or = 600 mL O2/min-m2 for the first 24 intensive care unit hours. For TAI patients, postoperative management included intravenous nitroprusside infusion titrated by the bedside nurse to maintain mean arterial pressure (MAP) less than 90 mm Hg during the same 24 hours. Data were obtained prospectively during resuscitation. Retrospectively, the resuscitation response of TAI and non-TAI patients was compared. RESULTS: For the TAI group, nitroprusside effectively controlled MAP (range, 77-87 mm Hg); for the non-TAI group, mean MAP exceeded 95 mm Hg within 5 hours. During the first 8 hours, MAP, pulmonary capillary wedge pressure, and systemic vascular resistance index were less, and DO2I was greater for the TAI than for the non-TAI group. The resuscitation goal of DO2I > or = 600 mL O2/ min-m2 was attained at 4 hours for the TAI group, and was attained at 12 hours for the non-TAI group. No revisions of aortic repairs were required during or as a result of resuscitation. CONCLUSION: During aggressive shock resuscitation, control of MAP using nitroprusside is feasible and is associated with a favorable resuscitation response. Nitroprusside may be a useful adjunct during shock resuscitation of MTT as a vasoactive agent that promotes peripheral tissue perfusion.

Blunt trauma resuscitation: the old can respond.

HYPOTHESIS: Old and young trauma patients are capable of hyperdynamic response during standardized shock resuscitation. DESIGN: The responses of old and young trauma patients resuscitated using a standardized protocol are compared in an inception cohort study. A standardized resuscitation protocol was used to attain and maintain an oxygen delivery index of 600 mL/min x m2 or greater (DO2I > or = 600) for the first 24 hours in the intensive care unit. Interventions, responses, and outcomes for old (> or = 65 years) and young (<65 years) patients are described. Data were analyzed using analysis of variance, the chi2 test, and the t test; P<.05 was considered significant. SETTING: A 20-bed shock trauma intensive care unit in a regional level I trauma center. PATIENTS: Patients at high risk of postinjury multiple organ failure, ie, major organ or vascular injury and/or skeletal fractures, initial base deficit of 6 mEq/L or greater, need for 6 units or more of packed red blood cells in the first 12 hours, or age of 65 years or older with any 2 previous criteria. INTERVENTIONS: Pulmonary artery catheter, crystalloid fluid infusion, packed red blood cell transfusion, and moderate inotrope support, as needed in that sequence, to attain DO2I > or = 600. MAIN OUTCOME MEASURES: Intensive care unit length of stay and survival. RESULTS: During 19 months ending June 1999, 12 old patients (58% male; age, 76 +/- 2 years [mean +/- SEM] [P<.0011; Injury Severity Score, 20 +/- 2 [P=.02]) and 54 young patients (61% male; age, 37 +/- 2 years; Injury Severity Score, 32 +/- 2) were resuscitated. Initially, for old patients (cardiac index, 2.0 +/- 0.2 L/min x m2) and for young patients (cardiac index, 3.0 +/- 0.2 L/min x m2; P=.01), 24-hour volumes were as follows: 16 +/- 3 L of crystalloid and 12 +/- 3 units of packed red blood cells for the old patients and 21 +/- 2 L of crystalloid and 19 +/- 2 units of packed red blood cells for the young patients. For old patients, 9 (75%) attained DO2I > or = 600, and 11 (92%) survived 7 or more days and 5 (42%) 30 or more days. For young patients, 45 (83%) attained the DO2I goal, and 48 (89%) survived 30 or more days. Intensive care unit length of stay was 25 +/- 9 days for the old patients and 23 +/- 2 days for the young patients. CONCLUSIONS: Elderly patients have initially depressed cardiac index but generate hyperdynamic response. Although ultimate outcome is poorer than in the younger cohort, resuscitation is not futile.

Age should not be a consideration for nonoperative management of blunt splenic injury.

BACKGROUND: Operative management of blunt splenic injury is recommended for adults > or = 55 years. Because this is not our practice, we did a retrospective review to compare outcomes of patients > or = 55 years old versus patients < 55 years old. METHODS: During a 5-year period ending in July of 1998, 461 patients (3%) admitted to our Level I trauma center had a blunt splenic injury. Eighty-six patients (19%) died within 24 hours of massive injuries, leaving 375 patients for evaluation. Data were obtained from our trauma registry and medical records. RESULTS: A total of 29 patients (8%) were > or = 55 years old (mean age, 67 +/- 2 years; mean injury severity score [ISS] 25 +/- 2). Of these, 18 patients (62%) underwent nonoperative management (NOM). A total of 346 patients (92%) were < 55 years old (mean age, 28 +/- 0.6; mean ISS, 20 +/- 1). Of these, 198 patients (57%) underwent NOM. The failure rate was not different between the two age groups (17% vs. 14%). However, the ISS and mortality rate were significantly higher in the older age group that failed (ISS, 29.3 +/- 2.6 vs. 19.5 +/- 2.1; mortality: 67% vs. 4%). None of the deaths could be attributed to splenic injury. CONCLUSION: Adults > or = 55 years old with blunt splenic injury are successfully treated by NOM. Although older adults had significantly greater injuries, they had similar failure rates of NOM when compared with younger adults. Older adults had significantly higher mortality, but this was not a result of their splenic injury. Therefore, age should not be a criteria for NOM of blunt splenic injury.

Tissue hemoglobin O2 saturation during resuscitation of traumatic shock monitored using near infrared spectrometry.

BACKGROUND: Near infrared (NIR) spectrometry offers a noninvasive monitor of tissue hemoglobin O2 saturation and has been developed to report a quantitative clinical variable, StO2 [= HbO2/(HbO2 + Hb)]. In this study, a prototype NIR oximeter was used to investigate the hypothesis that changes in systemic O2 delivery index (D(O2)I) would be reflected by changes in StO2 in skeletal muscle, subcutaneous tissue, or both, as reperfusion occurs during shock resuscitation. StO2 was also compared with other indices of severity of shock or adequacy of resuscitation, including arterial base deficit, lactate, gastric mucosal P(CO2) (PgCO2), and mixed venous hemoglobin O2 saturation (S(VO2)). METHODS: Skeletal muscle and subcutaneous tissue StO2 were monitored simultaneously in eight severely injured trauma patients (88% blunt mechanism; age, 42 +/- 6 years; Injury Severity Score, 27 +/- 3) during standardized shock resuscitation in the intensive care unit with the primary goal of D(O2)I > or = 600 mL O2/min/m2 for 24 hours, and for an additional 12 hours during transition from resuscitation to standard intensive care unit care. RESULTS: Skeletal muscle StO2 increased significantly from 15 +/- 2% (mean +/- SEM) at the start of resuscitation to 49 +/- 14% at 24 hours, and to approximately 55% from 25 to 36 hours. Subcutaneous tissue StO2 approximately 82% and was significantly greater than skeletal muscle StO2 throughout. D(O2)I increased significantly from 372 +/- 54 to 718 +/- 47 mL O2/min/m2 during resuscitation. Over 36 hours, mean D(O2)I and skeletal muscle StO2 were highly correlated (r = 0.95). Neither D(O2)I-PgCO2 nor D(O2)I-S(VO2) were significantly correlated; neither S(VO2) nor subcutaneous tissue StO2 changed significantly. CONCLUSION: Hemoglobin O2 saturation was monitored noninvasively and simultaneously in skeletal muscle and subcutaneous tissues as StO2 (%) by using a prototype NIR oximeter. Skeletal muscle StO2 tracked systemic O2 delivery during and after resuscitation. As a rapidly deployable, noninvasive monitor of peripheral tissue oxygenation and O2 delivery, skeletal muscle StO2 obtained using NIR spectrometry would be useful to guide resuscitation in the intensive care unit, to monitor resuscitation status in the operating room, and, potentially, in combination with indicators such as base deficit and lactate, to detect shock during initial assessment of the severe trauma patient in the emergency department.

Nonocclusive bowel necrosis occurring in critically ill trauma patients receiving enteral nutrition manifests no reliable clinical signs for early detection.

BACKGROUND: Nonocclusive bowel necrosis (NOBN) has been associated with early enteral nutrition (EN). The purpose of this study was to determine the incidence of this complication in our trauma intensive care unit population and to define a typical patient profile vulnerable to NOBN. METHODS: Thirteen cases of NOBN were identified among 4,311 patients (0.3%) over a 64-month period ending October 1998. Their charts were analyzed for a variety of clinical data, including prospective EN tolerance data in 4. RESULTS: Twelve (92%) patients were enterally fed prior to diagnosis for 10 +/- 8 days (range 3 to 21). Tachycardia (n = 12, 92%); fever/hypothermia, (n = 12, 92%), and an abnormal white blood cell count (n = 11, 85%) were consistently present. Abdominal distention was common but tended to be a late sign (n = 12). Seven (56%) survived. In 4 patients with tolerance data, 3 reached the goal rate of feeds prior to diagnosis. Two became distended at >12 hours from diagnosis. Gastric tonometry demonstrated a decreased NgpHi (<7.30) after starting EN in all 3 in whom it was monitored. CONCLUSIONS: NOBN developed in 0.3% of our trauma patients. Onset occurs in the second week in high-acuity patients who have had a period of EN tolerance. Clinical findings resemble bacterial sepsis with tachycardia, fever, and leukocytosis. Gastrointestinal specific signs are not consistent or occur late. Thus, we could not identify an early, useful clinical indicator. Gastric carbon dioxide tonometry may detect a vulnerable subgroup of patients.

Delayed complications of nonoperative management of blunt adult splenic trauma.

OBJECTIVE: To determine the incidence and type of delayed complications from nonoperative management of adult splenic injury. DESIGN: Retrospective medical record review. SETTING: University teaching hospital, level I trauma center. PATIENTS: Two hundred eighty patients were admitted to the adult trauma service with blunt splenic injury during a 4-year period. Men constituted 66% of the population. The mean (+/-SEM) age was 32.2+/-1.0 years and the mean (+/-SEM) Injury Severity Score was 22.8+/-0.9. Fifty-nine patients (21%) died of multiple injuries within 48 hours and were eliminated from the study. One hundred thirty-four patients (48%) were treated operatively within the first 48 hours after injury and 87 patients (31%) were managed nonoperatively. MAIN OUTCOME MEASURES: We reviewed the number of units of blood transfused, intensive care unit length of stay, overall length of stay, outcome, and complications occurring more than 48 hours after injury directly attributable to the splenic injury. RESULTS: Patients managed nonoperatively had a significantly lower Injury Severity Score (P<.05) than patients treated operatively. Length of stay was significantly decreased in both the number of intensive care unit days as well as total length of stay (P<.05). The number of units of blood transfused was also significantly decreased in patients managed nonoperatively (P<.05). Seven patients (8%) managed nonoperatively developed delayed complications requiring intervention. Five patients had overt bleeding that occurred at 4 days (3 patients), 6 days (1 patient), and 8 days (1 patient) after injury. Three patients underwent splenectomy, 1 had a splenic artery pseudoaneurysm embolization, and 1 had 2 areas of bleeding embolization. Two patients developed splenic abscesses at approximately 1 month after injury; both were treated by splenectomy. CONCLUSION: Significant numbers of delayed splenic complications do occur with nonoperative management of splenic injuries and are potentially life-threatening.

Renal allograft torsion associated with prune-belly syndrome.

We report a 26-month-old child diagnosed with prune-belly syndrome and end-stage renal disease who received intraperitoneal implantation of an adult cadaveric renal graft which functioned very well for approximately 6 weeks. The patient then presented with acute renal failure which was proved to be secondary to torsion of the graft, twisting the artery and vein. The ureter was wrapped 360 degrees around the graft. These conditions resulted in loss of the graft and nephrectomy. Ours is the second report of such an occurrence; the first was from a living-related kidney donor. We believe the lack of abdominal wall tone contributes to graft mobility and risk of torsion of the kidney. We recommend that nephropexy be considered in these patients. In addition, the risk of torsion must be at the forefront of the differential diagnosis in a prune-belly renal transplant patient with acute onset of oliguria. Renal sonography with Doppler should be employed as soon as possible so that the graft can be saved.