Intravascular US-guided direct intrahepatic portocaval shunt with an expanded polytetrafluoroethylene-covered stent-graft

PURPOSE: To retrospectively evaluate the midterm patency rate of the nitinol (Viatorr, W.L. Gore and Associates, Flagstaff, Ariz) stent-graft for direct intrahepatic portacaval shunt (DIPS) creation. MATERIALS AND METHODS: Institutional Review Board approval for this retrospective HIPAA-compliant study was obtained with waiver of informed consent. DIPS was created in 18 men and one woman (median age, 54 years; range, 45-65 years) by using nitinol polytetrafluoroethylene (PTFE)-covered stent-grafts. The primary indications were intractable ascites (n = 14), acute variceal bleeding (n = 3), and hydrothorax (n = 2). Follow-up included Doppler ultrasonography at 1, 6, and 12 months and venography with manometry at 6-month intervals after the procedure. Shunt patency and cumulative survival were evaluated by using the Kaplan-Meier method and survival curves were plotted. Differences in mean portosystemic gradients (PSGs) were evaluated by using the Student t test. Multiple regression analysis for survival and DIPS patency were performed for the following parameters: Child-Pugh class, model of end-stage liver disease score, pre- and post-DIPS PSGs, pre-DIPS liver function tests, and pre-DIPS creatinine levels. RESULTS: DIPS creation was successful in all patients. Effective portal decompression and free antegrade shunt flow was achieved in all patients. Intraperitoneal bleeding occurred in one patient during the procedure and was controlled during the same procedure by placing a second nitinol stent-graft. The primary patency rate was 100% at all times during the follow-up period (range, 2 days to 30 months; mean, 256 days; median, 160 days). Flow restrictors were deployed in two (11%) of 19 patients. The 1-year mortality rate was 37% (seven of 19). CONCLUSION: Patency after DIPS creation with the nitinol PTFE-covered stent-graft was superior to that after TIPS with the nitinol stent-graft.

Effect of echo time pair selection on quantitative analysis for adrenal tumor characterization with in-phase and opposed-phase MR imaging: initial experience

PURPOSE: To determine the effect of two pairs of echo times (TEs) for in-phase (IP) and opposed-phase (OP) 3.0-T magnetic resonance (MR) imaging on (a) quantitative analysis prospectively in a phantom study and (b) diagnostic accuracy retrospectively in a clinical study of adrenal tumors, with use of various reference standards in the clinical study. MATERIALS AND METHODS: A fat-saline phantom was used to perform IP and OP 3.0-T MR imaging for various fat fractions. The institutional review board approved this HIPAA-compliant study, with waiver of informed consent. Single-breath-hold IP and OP 3.0-T MR images in 21 patients (14 women, seven men; mean age, 63 years) with 23 adrenal tumors (16 adenomas, six metastases, one adrenocortical carcinoma) were reviewed. The MR protocol involved two acquisition schemes: In scheme A, the first OP echo (approximately 1.5-msec TE) and the second IP echo (approximately 4.9-msec TE) were acquired. In scheme B, the first IP echo (approximately 2.4-msec TE) and the third OP echo (approximately 5.8-msec TE) were acquired. Quantitative analysis was performed, and analysis of variance was used to test for differences between adenomas and nonadenomas. RESULTS: In the phantom study, scheme B did not enable discrimination among voxels that had small amounts of fat. In the clinical study, no overlap in signal intensity (SI) index values between adenomas and nonadenomas was seen (P < .05) with scheme A. However, with scheme B, no overlap in the adrenal gland SI-to-liver SI ratio between adenomas and nonadenomas was seen (P < .05). With scheme B, no overlap in adrenal gland SI index-to-liver SI index ratio between adenomas and nonadenomas was seen (P < .05). CONCLUSION: This initial experience indicates SI index is the most reliable parameter for characterization of adrenal tumors with 3.0-T MR imaging when obtaining OP echo before IP echo. When acquiring IP echo before OP echo, however, nonadenomas can be mistaken as adenomas with use of the SI index value.

Hypervascular liver tumors: low tube voltage, high tube current multi-detector row CT for enhanced detection--phantom study

PURPOSE: To prospectively evaluate, for the depiction of simulated hypervascular liver lesions in a phantom, the effect of a low tube voltage, high tube current computed tomographic (CT) technique on image noise, contrast-to-noise ratio (CNR), lesion conspicuity, and radiation dose. MATERIALS AND METHODS: A custom liver phantom containing 16 cylindric cavities (four cavities each of 3, 5, 8, and 15 mm in diameter) filled with various iodinated solutions to simulate hypervascular liver lesions was scanned with a 64-section multi-detector row CT scanner at 140, 120, 100, and 80 kVp, with corresponding tube current-time product settings at 225, 275, 420, and 675 mAs, respectively. The CNRs for six simulated lesions filled with different iodinated solutions were calculated. A figure of merit (FOM) for each lesion was computed as the ratio of CNR2 to effective dose (ED). Three radiologists independently graded the conspicuity of 16 simulated lesions. An anthropomorphic phantom was scanned to evaluate the ED. Statistical analysis included one-way analysis of variance. RESULTS: Image noise increased by 45% with the 80-kVp protocol compared with the 140-kVp protocol (P < .001). However, the lowest ED and the highest CNR were achieved with the 80-kVp protocol. The FOM results indicated that at a constant ED, a reduction of tube voltage from 140 to 120, 100, and 80 kVp increased the CNR by factors of at least 1.6, 2.4, and 3.6, respectively (P < .001). At a constant CNR, corresponding reductions in ED were by a factor of 2.5, 5.5, and 12.7, respectively (P < .001). The highest lesion conspicuity was achieved with the 80-kVp protocol. CONCLUSION: The CNR of simulated hypervascular liver lesions can be substantially increased and the radiation dose reduced by using an 80-kVp, high tube current CT technique.

Renal oxygenation changes during acute unilateral ureteral obstruction: assessment with blood oxygen level-dependent mr imaging--initial experience

PURPOSE: To prospectively determine if changes in intrarenal oxygenation during acute unilateral ureteral obstruction can be depicted with blood oxygen level-dependent (BOLD) magnetic resonance (MR) imaging. MATERIALS AND METHODS: The study was approved by the local ethics committee, and written informed consent was obtained from all patients. BOLD MR imaging was performed in 10 male patients (mean age, 45 years +/- 17 [standard deviation]; range, 20-73 years) with a distal unilateral ureteral calculus and in 10 healthy age-matched male volunteers to estimate R2*, which is inversely related to tissue Po(2). R2* values were determined in the cortex and medulla of the obstructed and the contralateral nonobstructed kidneys. To reduce external effects on R2*, the R2* ratio between the medulla and cortex was also analyzed. Statistical analysis was performed with nonparametric rank tests. P < .05 was considered to indicate a significant difference. RESULTS: All patients had significantly lower medullary and cortical R2* values in the obstructed kidney (median R2* in medulla, 10.9 sec(-1) [range, 9.1-14.3 sec(-1)]; median R2* in cortex, 10.4 sec(-1) [range, 9.7-11.3 sec(-1)]) than in the nonobstructed kidney (median R2* in medulla, 17.2 sec(-1) [range, 14.6-23.2 sec(-1)], P = .005; median R2* in cortex, 11.7 sec(-1) [range, 11.0-14.0 sec(-1)], P = .005); values in the obstructed kidneys were also significantly lower than values in the kidneys of healthy control subjects (median R2* in medulla, 16.1 sec(-1) [range, 13.9-18.1 sec(-1)], P < .001; median R2* in cortex, 11.6 sec(-1) [range, 10.5-12.9 sec(-1)], P < .001). R2* ratios in the obstructed kidneys (median, 1.06; range, 0.85-1.27) were significantly lower than those in the nonobstructed kidneys (median, 1.49; range, 1.26-1.71; P = .005) and those in the kidneys of healthy control subjects (median, 1.38; range, 1.23-1.47; P < .001). In contrast, R2* ratios in the nonobstructed kidneys of patients were significantly higher than those in kidneys of healthy control subjects (P = .01). CONCLUSION: Increased oxygen content in the renal cortex and medulla occurs with acute unilateral ureteral obstruction, suggesting reduced function of the affected kidney.

Effective doses from scan projection radiographs of the head: impact of different scanning practices and comparison with conventional radiography

For CT scan planning, scan projection radiographs (SPR) are used. Tube tension and current for head SPR can be reduced to a minimum because of the small head diameter and because only high-contrast structures need to be visualized for planning. The goal of this study was to investigate SPR of the head in respect to effective doses, the influence of dose-reduction measures, and comparison with conventional x-ray.

CT radiation dose for computer-assisted endoscopic sinus surgery: dose survey and determination of dose-reduction limits

BACKGROUND AND PURPOSE: Computer-assisted navigation is increasingly used in functional endoscopic sinus surgery (FESS) to prevent injury to vital structures, necessitating preparative CT and, thus, radiation exposure. The purpose of our study was to investigate currently used radiation doses for CT in computer-assisted navigation in sinus surgery (CAS-CT) and to assess minimal doses required. MATERIALS AND METHODS: A questionnaire inquiring about dose parameters used for CAS-CT was sent to 30 radiologic institutions. The feasibility of low-dose registration was tested with a phantom. The influence of CAS-CT dose on technical accuracy and on the practical performance of 5 ear, nose, and throat (ENT) surgeons was evaluated with cadaver heads. RESULTS: The questionnaire response rate was 63%. Variation between minimal and maximal dose used for CAS-CT was 18-fold. Phantom registration was possible with doses as low as 1.1 mGy. No dose dependence on technical accuracy was found. ENT surgeons were able to identify anatomic landmarks on scans with a dose as low as 3.1 mGy. CONCLUSIONS: The vast dose difference between institutions mirrors different attitudes toward image quality and radiation-protection issues rather than being technically founded, and many patients undergo CAS-CT at higher doses than necessary. The only limit for dose reduction in CT for computer-assisted endoscopic sinus surgery is the ENT surgeon's ability to cope with impaired image quality, whereas there is no technically justified lower dose limit. We recommend, generally, doses used for the typical diagnostic low-dose sinus CT (120 kV/20-50 mAs). When no diagnostic image quality is needed, even a reduction down to a third is possible.

Functionally relevant coronary artery disease: comparison of 64-section CT angiography with myocardial perfusion SPECT

PURPOSE: To prospectively determine the accuracy of 64-section computed tomographic (CT) angiography for the depiction of coronary artery disease (CAD) that induces perfusion defects at myocardial perfusion imaging with single photon emission computed tomography (SPECT), by using myocardial perfusion imaging as the reference standard. MATERIALS AND METHODS: All patients gave written informed consent after the study details, including radiation exposure, were explained. The study protocol was approved by the local institutional review board. In patients referred for elective conventional coronary angiography, an additional 64-section CT angiography study and a myocardial perfusion imaging study (1-day adenosine stress-rest protocol) with technetium 99m-tetrofosmin SPECT were performed before conventional angiography. Coronary artery diameter narrowing of 50% or greater at CT angiography was defined as stenosis and was compared with the myocardial perfusion imaging findings. Quantitative coronary angiography served as a reference standard for CT angiography. RESULTS: A total of 1093 coronary segments in 310 coronary arteries in 78 patients (mean age, 65 years +/- 9 [standard deviation]; 35 women) were analyzed. CT angiography revealed stenoses in 137 segments (13%) corresponding to 91 arteries (29%) in 46 patients (59%). SPECT revealed 14 reversible, 13 fixed, and six partially reversible defects in 31 patients (40%). Sensitivity, specificity, and negative and positive predictive values, respectively, of CT angiography in the detection of reversible myocardial perfusion imaging defects were 95%, 53%, 94%, and 58% on a per-patient basis and 95%, 75%, 96%, and 72% on a per-artery basis. Agreement between CT and conventional angiography was very good (96% and kappa = 0.92 for patient-based analysis, 93% and kappa = 0.84 for vessel-based analysis). CONCLUSION: Sixty-four-section CT angiography can help rule out hemodynamically relevant CAD in patients with intermediate to high pretest likelihood, although an abnormal CT angiography study is a poor predictor of ischemia.

Myocardial bridging: depiction rate and morphology at CT coronary angiography--comparison with conventional coronary angiography

PURPOSE: To prospectively assess the depiction rate and morphologic features of myocardial bridging (MB) of coronary arteries with 64-section computed tomographic (CT) coronary angiography in comparison to conventional coronary angiography. MATERIALS AND METHODS: Patients were simultaneously enrolled in a prospective study comparing CT and conventional coronary angiography, for which ethics committee approval and informed consent were obtained. One hundred patients (38 women, 62 men; mean age, 63.8 years +/- 11.6 [standard deviation]) underwent 64-section CT and conventional coronary angiography. Fifty additional patients (19 women, 31 men; mean age, 59.2 years +/- 13.2) who underwent CT only were also included. CT images were analyzed for the direct signs length, depth, and degree of systolic compression, while conventional angiograms were analyzed for the indirect signs step down-step up phenomenon, milking effect, and systolic compression of the tunneled segment. Statistical analysis was performed with Pearson correlation analysis, the Wilcoxon two-sample test, and Fisher exact tests. RESULTS: MB was detected with CT in 26 (26%) of 100 patients and with conventional angiography in 12 patients (12%). Mean tunneled segment length and depth at CT (n = 150) were 24.3 mm +/- 10.0 and 2.6 mm +/- 0.8, respectively. Systolic compression in the 12 patients was 31.3% +/- 11.0 at CT and 28.2% +/- 10.5 at conventional angiography (r = 0.72, P < .001). With CT, a significant correlation was not found between systolic compression and length (r = 0.16, P = .25, n = 150) but was found with depth (r = 0.65, P < .01, n = 150) of the tunneled segment. In 14 patients in whom MB was found at CT but not at conventional angiography, length, depth, and systolic compression were significantly lower than in patients in whom both modalities depicted the anomaly (P < .001, P < .01, and P < .001, respectively). CONCLUSION: The depiction rate of MB is greater with 64-section CT coronary angiography than with conventional coronary angiography. The degree of systolic compression of MB significantly correlates with tunneled segment depth but not length.

Retention of canopy trees as biological legacies for balancing woody biomass production and biodiversity in managed aspen forests of the Great Lakes Region

Green-tree retention under the conceptual framework of ecological forestry has the potential to provide both biomass feedstock for industry and maintain quality wildlife habitat. I examined the effects of retained canopy trees as biological legacies (“legacy trees”) in aspen (Populus spp.) forests on above-ground live woody biomass, understory plant floristic quality, and bird diversity. Additionally, I evaluated habitat quality for a high conservation priority species, the Golden-winged Warbler (Vermivora chrysoptera). I selected 27 aspen-dominated forest stands in northern Wisconsin with nine stands in each of three legacy tree retention treatments (conifer retention, hardwood retention, and clearcuts or no retention) across a chronosequence (4-36 years post-harvest). Conifer retention stands had greater legacy tree and all tree species biomass but lower regenerating tree biomass than clearcuts. Coniferous but not hardwood legacy trees appeared to suppress regenerating tree biomass. I evaluated the floristic quality of the understory plant assemblage by estimating the mean coefficient of conservatism (C). Mean C was lower in young stands than in middle-age or old stands; there was a marginally significant (p=0.058) interaction effect between legacy tree retention treatment and stand age. Late-seral plant species were positively associated with stand age and legacy tree diameter or age revealing an important relationship between legacy tree retention and stand development. Bird species richness was greatest in stands with hardwood retention particularly early in stand development. Six conservation priority bird species were indicators of legacy tree retention or clearcuts. Retention of legacy trees in aspen stands provided higher quality nest habitat for the Golden-winged Warbler than clearcuts based on high pairing success and nesting activity. Retention of hardwoods, particularly northern red oak (Quercus rubra), yielded the most consistent positive effects in this study with the highest bird species richness and the highest quality habitat for the Golden-winged Warbler. This treatment maintained stand biomass comparable to clearcuts and did not suppress regenerating tree biomass. In conclusion, legacy tree retention can enhance even-aged management techniques to produce a win-win scenario for the conservation of declining bird species and late-seral understory plants and for production of woody biomass feedstock from naturally regenerating aspen forests.

Cartilage T2 assessment at 3-T MR imaging: in vivo differentiation of normal hyaline cartilage from reparative tissue after two cartilage repair procedures--initial experience

PURPOSE: To prospectively compare cartilage T2 values after microfracture therapy (MFX) and matrix-associated autologous chondrocyte transplantation (MACT) repair procedures. MATERIALS AND METHODS: The study had institutional review board approval by the ethics committee of the Medical University of Vienna; informed consent was obtained. Twenty patients who underwent MFX or MACT (10 in each group) were enrolled. For comparability, patients of each group were matched by mean age (MFX, 40.0 years +/- 15.4 [standard deviation]; MACT, 41.0 years +/- 8.9) and postoperative interval (MFX, 28.6 months +/- 5.2; MACT, 27.4 months +/- 13.1). Magnetic resonance (MR) imaging was performed with a 3-T MR imager, and T2 maps were calculated from a multiecho spin-echo measurement. Global, as well as zonal, quantitative T2 values were calculated within the cartilage repair area and within cartilage sites determined to be morphologically normal articular cartilage. Additionally, with consideration of the zonal organization, global regions of interest were subdivided into deep and superficial areas. Differences between cartilage sites and groups were calculated by using a three-way analysis of variance. RESULTS: Quantitative T2 assessment of normal native hyaline cartilage showed similar results for all patients and a significant trend of increasing T2 values from deep to superficial zones (P < .05). In cartilage repair areas after MFX, global mean T2 was significantly reduced (P < .05), whereas after MACT, mean T2 was not reduced (P > or = .05). For zonal variation, repair tissue after MFX showed no significant trend between different depths (P > or = .05), in contrast to repair tissue after MACT, in which a significant increase from deep to superficial zones (P < .05) could be observed. CONCLUSION: Quantitative T2 mapping seems to reflect differences in repair tissues formed after two surgical cartilage repair procedures. (c) RSNA, 2008.

Neoplastic invasion of laryngeal cartilage: reassessment of criteria for diagnosis at MR imaging

PURPOSE: To evaluate whether proposed diagnostic criteria applied to magnetic resonance (MR) images of patients with laryngeal and hypopharyngeal carcinoma may be used to distinguish neoplastic from inflammatory involvement of the laryngeal cartilages. MATERIALS AND METHODS: The radiologic and histopathologic data in 121 consecutive patients with primary squamous cell carcinoma of the larynx (n = 63) or hypopharynx (n = 58) who underwent MR imaging before laryngectomy formed the basis of this retrospective study. Patient consent for retrospective chart review was waived by the institutional review board. All laryngectomy specimens were processed with a dedicated histopathologic whole-organ slice technique. MR images were evaluated by two readers according to established ("old") and proposed ("new") diagnostic criteria on the basis of the signal intensity behavior of cartilage on T2-weighted images and contrast material-enhanced T1-weighted images compared with that of the adjacent tumor. Specifically, with the new criteria, T2-weighted or postcontrast T1-weighted cartilage signal intensity greater than that of the adjacent tumor was considered to indicate inflammation, and signal intensity similar to that of the adjacent tumor was considered to indicate neoplastic invasion. The results of the MR image interpretation were compared with the histologic reference standard. RESULTS: The area under the receiver operating characteristic curve for the new criteria (0.94) was nominally but significantly larger than that for the old criteria (0.92) (P = .01). Overall specificity was significantly improved (82% for new vs 74% for old criteria, P < .001) and was greatest for the thyroid cartilage (75% for new vs 54% for old criteria, P < .001) with the new criteria. The sensitivities of the established and the proposed criteria were identical. CONCLUSION: The proposed MR imaging criteria enable improved differentiation of neoplastic cartilage invasion from peritumoral inflammation.

Habitat Associations of the Golden-Winged Warbler in Honduras

The global population of the Neotropical migrant Golden-winged Warbler (Vermivora chrysoptera) has declined steadily over the past fifty years. While factors influencing this decline have been well researched on the breeding grounds, little is known about the distribution and habitat requirements of this warbler on its stationary non-breeding range. Recent efforts to quantify the non-breeding habitat requirements of this warbler have focused on Colombia and Costa Rica, though the species ranges as far north as the Yucatan Peninsula, Mexico. To address the gap in knowledge from the northern portion of the non-breeding range, I conducted 80 serial point-count surveys targeting Goldenwinged Warblers at eight field sites in Honduras, Central America. I found that Goldenwinged Warblers occupy a greater variety of habitats than previously recognized, including pine-oak forest and semi-deciduous broadleaf forest. I also documented habitat associations that have not been observed in other parts of the non-breeding range with respect to elevation, rainfall, and spatial segregation by sex. These results demonstrate the need to consider the entire non-breeding range in conservation planning, as Goldenwinged Warbler habitat associations appear to vary regionally.

Speciation with gene-flow in eastern North American red oaks (Quercus section Lobatae)

As foundational species, oaks (Quercus : Fagaceae) support the activities of both humans and wildlife. However, many oaks in North America are declining, a crisis exacerbated by the previous disappearance of other hard mast-producing trees. In addition, the economic demands placed on this drought-tolerant group may intensify if climate change extirpates other, relatively mesophytic species. Genetic tools can help address these management challenges. To this end, we developed a suite of 27 microsatellite markers, of which 22 are derived from expressed sequence tags (ESTs). Many of these markers bear significant homology to known genes and may be able to directly assay functional genetic variation. Markers obtained from enriched microsatellite libraries, on the other hand, are typically located in heterochromatic regions and should reflect demographic processes. Considered jointly, genic and genomic microsatellites can elucidate patterns of gene-flow and natural selection, which are fundamental to both an organism's evolutionary ecology and conservation biology. To this end, we employed the developed markers in an FST-based genome scan to detect the signature of divergent selection among the red oaks (Quercus section Lobatae). Three candidate genes with putative roles in stress responses demonstrated patterns of diversity consistent with adaptation to heterogeneous selective pressures. These genes may be important in both local genetic adaptation within species and divergence among them. Next, we used an isolation-with-migration model to quantify levels of gene-flow among four red oaks species during speciation. Both speciation in allopatry and speciation with gene-flow were found to be major drivers of red oak biodiversity. Loci playing a key role in speciation are also likely to be ecologically important within species

Spatial and temporal analysis of land cover and landscape structure change in Zagros Forests

The Zagros oak forests in Western Iran are critically important to the sustainability of the region. These forests have undergone dramatic declines in recent decades. We evaluated the utility of the non-parametric Random Forest classification algorithm for land cover classification of Zagros landscapes, and selected the best spatial and spectral predictive variables. The algorithm resulted in high overall classification accuracies (>85%) and also equivalent classification accuracies for the datasets from the three different sensors. We evaluated the associations between trends in forest area and structure with trends in socioeconomic and climatic conditions, to identify the most likely driving forces creating deforestation and landscape structure change. We used available socioeconomic (urban and rural population, and rural income), and climatic (mean annual rainfall and mean annual temperature) data for two provinces in northern Zagros. The most correlated driving force of forest area loss was urban population, and climatic variables to a lesser extent. Landscape structure changes were more closely associated with rural population. We examined the effects of scale changes on the results from spatial pattern analysis. We assessed the impacts of eight years of protection in a protected area in northern Zagros at two different scales (both grain and extent). The effects of protection on the amount and structure of forests was scale dependent. We evaluated the nature and magnitude of changes in forest area and structure over the entire Zagros region from 1972 to 2009. We divided the Zagros region in 167 Landscape Units and developed two measures— Deforestation Sensitivity (DS) and Connectivity Sensitivity (CS) — for each landscape unit as the percent of the time steps that forest area and ECA experienced a decrease of greater than 10% in either measure. A considerable loss in forest area and connectivity was detected, but no sudden (nonlinear) changes were detected at the spatial and temporal scale of the study. Connectivity loss occurred more rapidly than forest loss due to the loss of connecting patches. More connectivity was lost in southern Zagros due to climatic differences and different forms of traditional land use.

Parameter identification of a copper-zeolite SCR catalyst model using reactor data

The selective catalytic reduction system is a well established technology for NOx emissions control in diesel engines. A one dimensional, single channel selective catalytic reduction (SCR) model was previously developed using Oak Ridge National Laboratory (ORNL) generated reactor data for an iron-zeolite catalyst system. Calibration of this model to fit the experimental reactor data collected at ORNL for a copper-zeolite SCR catalyst is presented. Initially a test protocol was developed in order to investigate the different phenomena responsible for the SCR system response. A SCR model with two distinct types of storage sites was used. The calibration process was started with storage capacity calculations for the catalyst sample. Then the chemical kinetics occurring at each segment of the protocol was investigated. The reactions included in this model were adsorption, desorption, standard SCR, fast SCR, slow SCR, NH3 Oxidation, NO oxidation and N2O formation. The reaction rates were identified for each temperature using a time domain optimization approach. Assuming an Arrhenius form of the reaction rates, activation energies and pre-exponential parameters were fit to the reaction rates. The results indicate that the Arrhenius form is appropriate and the reaction scheme used allows the model to fit to the experimental data and also for use in real world engine studies.