Recurrent Radiculopathy Following Transforaminal Lumbar Interbody Fusion: Successful Management with Endoscopic Sacroiliac Joint Ablation.

Introduction: Low back pain persisting after spine surgery presents diagnostic and treatment complexities for spine surgeons. Failed back syndrome is a term usually used to characterize chronic back or leg pain following spine surgery. Research has indicated a range of persistent pain occurrences after spine surgery. The sacroiliac joint (SIJ) has been recognized as a potential source of pain for a long time but has not received sufficient attention in subsequent years. Dysfunctions in the SIJ can result in a spectrum of clinical conditions, such as low back pain and lower limb radiculopathy. Traditional treatment approaches for SIJ disorders often involve conservative measures such as physical therapy, medications, intra-articular injections, and surgical options. In the past decade, endoscopic SIJ ablation has emerged as a minimally invasive alternative for managing SIJ pain and dysfunction. This approach combines minimal invasiveness with precise targeting, potentially reducing morbidity and enabling quicker recovery compared to open surgical procedures. Case Report: A 60-year-old female patient with grade 2 L5-S1 lytic listhesis initially underwent lumbar interbody fusion to address chronic low back pain and radiculopathy, resulting in significant symptom resolution for a brief period. The patient experienced a resurgence of symptoms within a short duration that proved refractory to conventional medical management and interventional pain management procedures. Ultimately, the patient achieved sustained relief after undergoing endoscopic SIJ ablation. Conclusion: This case report highlights the importance of endoscopic SIJ ablation as an innovative treatment for recurrent lower limb radiculopathy. Focusing on the SIJ, often neglected in lumbar spine surgery, this minimally invasive procedure shows promise in alleviating symptoms and enhancing patient outcomes.

Postoperative discal pseudocyst: Report of A case with an unusual complication after microlumbar discectomy and successful treatment by transforaminal endoscopic lumbar decompression.

Background: Lumbar discal pseudocysts are uncommon complications that can arise following lumbar spine surgery. It manifests as a fluid-filled sac near the intervertebral disc, causing pain and discomfort. Understanding its causes, symptoms, and management is crucial for patients and healthcare professionals involved in postoperative spinal care. Case Description A: 35-year-old female developed a discal pseudocyst after undergoing laminectomy and discectomy for lumbar disc herniation. The patient presented with recurrent lower back pain, radiculopathy, and neurological deficit two months post-surgery. Imaging revealed a discal pseudo cyst causing compression of the traversing right L5 nerve root. Given the refractory nature of her symptoms, an endoscopic procedure was offered. Using the transforaminal endoscopic technique, the pseudo cyst was identified and removed, leading to immediate symptomatic relief. Conclusion: This article reports the rare occurrence of discal pseudocyst and highlights the use of endoscopic techniques in its surgical management. Surgeons should be aware of the minimally invasive techniques, as they can offer less morbidity, shorter recovery times, and reduced healthcare costs compared to traditional open surgery.

Phosphaturic Mesenchymal Tumor in the Proximal Femur Presenting as Tumor-induced Osteomalacia: A Case Report and Literature Review.

Introduction: An uncommon medical disorder known as tumor-induced osteomalacia (TIO) is characterized by severe hypophosphatemia, renal phosphate wasting, and osteomalacia due to a tumor. TIO has recently been linked to a particular kind of tumor known as phosphaturic mesenchymal tumor (PMT). PMTs release phosphatonins, such as fibroblast growth factor-23 (FGF23), which elevates serum levels of FGF23, leading to phosphate wasting and osteomalacia. However, due to their infrequent occurrence and vague symptoms, such as bone pain, myopathies, arthralgias, fractures, and weakness, the diagnosis of PMTs is often delayed or misdiagnosed. In this case report, a rare case of PMT in the proximal femur resulted in TIO, and it highlights the long and difficult journey from symptom onset to correct diagnosis and successful surgical management. Case Report: A 51-year-old woman endured persistent joint pain, muscle weakness, and fatigue for 2 years. Despite having no known health issues, she suffered from hip pain that spreads to her knees and ankles, and tingling and paresthesia in her legs, making it difficult to bear weight. She underwent surgery to remove a parathyroid adenoma, but unfortunately, her symptoms returned. Her magnetic resonance imaging revealed a lesion in her proximal femur, which was promptly removed. The tissue examination results verified the identity of the tumor as a PMT. The patient's phosphorus levels returned to normal and after a year of follow-up, she was able to resume normal daily activities, bear weight on the affected limb and showed no signs of the tumor recurrence. Conclusion: Adult patients experiencing bone pain, progressive weakness, and multiple fractures with no family history of similar conditions should consider TIO as a potential cause. It is rare and often misdiagnosed and complete surgical removal of the tumor is the optimal treatment for TIO, resulting in the resolution of long-standing symptoms and biochemical abnormalities. Timely recognition, localization, and surgical removal of the tumor are crucial for symptom resolution and the restoration of normal bone mineralization.

Multilevel Pre-extensively Drug-resistant Tubercular Spondylodiscitis: Underdiagnosed or Overlooked? A Case Report.

Introduction: Pre-extensively drug-resistant tuberculosis (TB) is characterized by resistance to either a fluoroquinolone (FQ) or a second-line injectable but not both. The urgent need for prompt diagnosis and targeted treatment is emphasized. This report aims to spotlight a case of spinal TB with insufficient assessment, resulting in delayed definitive treatment and an oversight contributing to heightened morbidity. Case Report: An 18-year-old female who was initially diagnosed to have multidrug-resistant TB leading to a 2-year treatment which eventually resulted in multifocal involvement of the spine revealing TB relapse with FQ resistance, categorized as pre-extensively drug-resistant TB. Treatment was shifted to newer drugs, addressing challenges like bilateral psoas abscess, which lead to clinical improvement, allowing the patient to make a good recovery. Conclusion: This case report emphasizes the significance of conducting culture and drug sensitivity testing in patients with tubercular spondylodiscitis. The aim is to prevent misdiagnosis and ensure informed decisions regarding definitive medical treatment or surgical management when necessary.

Anti-retroviral Therapy-Induced Multiple Pathological Fractures in a HIV-Positive Young Female: A Case Report and Review of Literature.

Introduction: A higher prevalence of osteoporosis and osteopenia, as well as an increased risk of fracture is seen in patients with HIV infection. Anti-retroviral therapy (ART) is the one of the factors associated with pathological fractures in those patients. We present one case with multiple pathological fractures secondary to severe osteoporosis in a known case of HIV on Tenofovir-based ART. The patient was managed with a combined surgical and conservative approach with a satisfactory outcome at 1-year follow-up. Case Report: We analyzed a 35-year-old female patient with HIV infection on ART for 5 years. She was diagnosed with right-sided subtrochanteric femur and bilateral forearm fracture and stress fracture in the left lower limb. Tenofovir was substituted with Zidovudine before surgery. Subtrochanteric femur fracture and right forearm fracture were managed surgically, whereas the other fractures were managed conservatively. The patient was followed up till 1 year and assessed with serial X-rays, blood investigations, Harris Hip Score, and Upper Extremity Functional Index. Functional outcome in all four limbs was found to be satisfactory. Conclusion: The patient taking ART based on Tenofovir should be monitored for pathological fractures. ART-induced fractures can be managed surgically and conservatively like any other pathological fracture. Tenofovir-containing regimens may be gradually replaced with alternative regimens for the treatment of HIV infection, especially in those at a higher risk for fragility fractures.

Butyl Acetate Pyrolysis and Combustion Chemistry: Mechanism Generation and Shock Tube Experiments.

The combustion and pyrolysis behaviors of light esters and fatty acid methyl esters have been widely studied due to their relevance as biofuel and fuel additives. However, a knowledge gap exists for midsize alkyl acetates, especially ones with long alkoxyl groups. Butyl acetate, in particular, is a promising biofuel with its economic and robust production possibilities and ability to enhance blendstock performance and reduce soot formation. However, it is little studied from both experimental and modeling aspects. This work created detailed oxidation mechanisms for the four butyl acetate isomers (normal-, sec-, tert-, and iso-butyl acetate) at temperatures varying from 650 to 2000 K and pressures up to 100 atm using the Reaction Mechanism Generator. About 60% of species in each model have thermochemical parameters from published data or in-house quantum calculations, including fuel molecules and intermediate combustion products. Kinetics of essential primary reactions, retro-ene and hydrogen atom abstraction by OH or HO2, governing the fuel oxidation pathways, were also calculated quantum-mechanically. Simulation of the developed mechanisms indicates that the majority of the fuel will decompose into acetic acid and relevant butenes at elevated temperatures, making their ignition behaviors similar to butenes. The adaptability of the developed models to high-temperature pyrolysis systems was tested against newly collected high-pressure shock experiments; the simulated CO mole fraction time histories have a reasonable agreement with the laser measurement in the shock tube. This work reveals the high-temperature oxidation chemistry of butyl acetates and demonstrates the validity of predictive models for biofuel chemistry established on accurate thermochemical and kinetic parameters.

Characterization of a new ultra-high pressure shock tube facility for combustion and propulsion studies.

A new shock tube facility has been designed, constructed, and characterized at the University of Central Florida. This facility is capable of withstanding pressures of up to 1000 atm, allowing for combustion diagnostics of extreme conditions, such as in rocket combustion chambers or in novel power conversion cycles. For studies with toxic gas impurities, the high initial pressures required the development of a gas delivery system to ensure the longevity of the facility and the safety of the personnel. Data acquisition and experimental propagation were implemented with remote access to ensure safety, paired with a LabVIEW- and Python-based user interface. Thus far, test pressures of 270 atm, blast pressures of 730 atm, and temperatures approaching 10 000 K have been achieved. The extreme limitations of this facility allow for emission spectroscopy to be performed during the oxidation of fuel mixtures, e.g., alkanes diluted in argon and carbon dioxide. Ignition delay times were determined and compared to simulations using chemical kinetic mechanisms. The design, experimental procedures, processes of analysis, and uncertainty determination are outlined, and typical pressure profiles are compared with a new gas dynamics solver and empirical correlations developed across multiple shock tube facilities. Preliminary reactive mixture analyses are included with further investigation of the mixtures outlined.

Selective terahertz absorber for angle and polarization-independent spectral sensing.

Polarization- and incident-angle-independent narrow-band terahertz (THz) absorbers were developed to enable THz imaging, radar, and spectroscopy applications. The design comprises a transparent fused silica (SiOx) substrate backed by an optically thick metal layer and topped by a periodic array of metal cross patterns. Finite element analysis (FEA) simulations optimized the geometry of devices fabricated by contact photolithography. Resonances were characterized by Fourier-transform reflectance spectroscopy. The design tunable absorption bands appeared in the range 50-200 cm-1 (1.5-6 THz) with full widths at half maximum of 20-56 cm-1 (0.6-1.68 THz). Maximum absorption was -8.5 to -16.8 dB. The absorption bands are independent of incidence angle and polarization in agreement with simulation.

Laser-induced fluorescence thermometry of supercritical CO2 flows inside a micro-channel.

This work demonstrates a thermometric technique using laser-induced fluorescence (LIF) in supercritical carbon dioxide flows in a micro-channel. Rhodamine 6G was used as a temperature-sensitive fluorescent dye. The flow conditions were at a pressure of 7.9 MPa and temperature in the range of 23°-90°C. 2D spatial distributions and time-resolved temperature profiles were obtained at this high pressure. Measured LIF signals showed close relations to the temperatures obtained from resistance temperature detectors.

Accurate prediction of terahertz spectra of molecular crystals of fentanyl and its analogs.

Fentanyl is a potent synthetic opioid pain reliever with a high bioavailability that can be used as prescription anesthetic. Rapid identification via non-contact methods of both known and emerging opioid substances in the fentanyl family help identify the substances and enable rapid medical attention. We apply PBEh-3c method to identify vibrational normal modes from 0.01 to 3 THz in solid fentanyl and its selected analogs. The molecular structure of each fentanyl analog and unique arrangement of H-bonds and dispersion interactions significantly change crystal packing and is subsequently reflected in the THz spectrum. Further, the study of THz spectra of a series of stereoisomers shows that small changes in molecular structure results in distinct crystal packing and significantly alters THz spectra as well. We discuss spectral features of synthetic opioids with higher potency than conventional fentanyl such as ohmefentanyl and sufentanil and discover the pattern of THz spectra of fentanyl analogs.

Elucidating the differences in oxidation of high-performance α- and ß- diisobutylene biofuels via Synchrotron photoionization mass spectrometry.

Biofuels are a promising ecologically viable and renewable alternative to petroleum fuels, with the potential to reduce net greenhouse gas emissions. However, biomass sourced fuels are often produced as blends of hydrocarbons and their oxygenates. Such blending complicates the implementation of these fuels in combustion applications. Variations in a biofuel's composition will dictate combustion properties such as auto ignition temperature, reaction delay time, and reaction pathways. A handful of novel drop-in replacement biofuels for conventional transportation fuels have recently been down selected from a list of over 10,000 potential candidates as part of the U.S. Department of Energy's (DOE) Co-Optimization of Fuels and Engines (Co-Optima) initiative. Diisobutylene (DIB) is one such high-performing hydrocarbon which can readily be produced from the dehydration and dimerization of isobutanol, produced from the fermentation of biomass-derived sugars. The two most common isomers realized, from this process, are 2,4,4-trimethyl-1-pentene (α-DIB) and 2,4,4-trimethyl-2-pentene (ß-DIB). Due to a difference in olefinic bond location, the α- and ß- isomer exhibit dramatically different ignition temperatures at constant pressure and equivalence ratio. This may be attributed to different fragmentation pathways enabled by allylic versus vinylic carbons. For optimal implementation of these biofuel candidates, explicit identification of the intermediates formed during the combustion of each of the isomers is needed. To investigate the combustion pathways of these molecules, tunable vacuum ultraviolet (VUV) light (in the range 8.1-11.0 eV) available at the Lawrence Berkeley National Laboratory's Advanced Light Source (ALS) has been used in conjunction with a jet stirred reactor (JSR) and time-of-flight mass spectrometry to probe intermediates formed. Relative intensity curves for intermediate mass fragments produced during this process were obtained. Several important unique intermediates were identified at the lowest observable combustion temperature with static pressure of 93,325 Pa and for 1.5 s residence time. As this relatively short residence time is just after ignition, this study is targeted at the fuels' ignition events. Ignition characteristics for both isomers were found to be strongly dependent on the kinetics of C4 and C7 fragment production and decomposition, with the tert-butyl radical as a key intermediate species. However, the ignition of α-DIB exhibited larger concentrations of C4 compounds over C7, while the reverse was true for ß-DIB. These identified species will allow for enhanced engineering modeling of fuel blending and engine design.

High accuracy machine learning identification of fentanyl-relevant molecular compound classification via constituent functional group analysis.

Fentanyl is an anesthetic with a high bioavailability and is the leading cause of drug overdose death in the U.S. Fentanyl and its derivatives have a low lethal dose and street drugs which contain such compounds may lead to death of the user and simultaneously pose hazards for first responders. Rapid identification methods of both known and emerging opioid fentanyl substances is crucial. In this effort, machine learning (ML) is applied in a systematic manner to identify fentanyl-related functional groups in such compounds based on their observed spectral properties. In our study, accurate infrared (IR) spectra of common organic molecules which contain functional groups that are constituents of fentanyl is determined by investigating the structure-property relationship. The average accuracy rate of correctly identifying the functional groups of interest is 92.5% on our testing data. All the IR spectra of 632 organic molecules are from National Institute of Standards and Technology (NIST) database as the training set and are assessed. Results from this work will provide Artificial Intelligence (AI) based tools and algorithms increased confidence, which serves as a basis to detect fentanyl and its derivatives.

Measuring the effectiveness of high-performance Co-Optima biofuels on suppressing soot formation at high temperature.

Soot emissions in combustion are unwanted consequences of burning hydrocarbon fuels. The presence of soot during and following combustion processes is an indication of incomplete combustion and has several negative consequences including the emission of harmful particulates and increased operational costs. Efforts have been made to reduce soot production in combustion engines through utilizing oxygenated biofuels in lieu of traditional nonoxygenated feedstocks. The ongoing Co-Optimization of Fuels and Engines (Co-Optima) initiative from the US Department of Energy (DOE) is focused on accelerating the introduction of affordable, scalable, and sustainable biofuels and high-efficiency, low-emission vehicle engines. The Co-Optima program has identified a handful of biofuel compounds from a list of thousands of potential candidates. In this study, a shock tube was used to evaluate the performance of soot reduction of five high-performance biofuels downselected by the Co-Optima program. Current experiments were performed at test conditions between 1,700 and 2,100 K and 4 and 4.7 atm using shock tube and ultrafast, time-resolve laser absorption diagnostic techniques. The combination of shock heating and nonintrusive laser detection provides a state-of-the-art test platform for high-temperature soot formation under engine conditions. Soot reduction was found in ethanol, cyclopentanone, and methyl acetate; conversely, an α-diisobutylene and methyl furan produced more soot compared to the baseline over longer test times. For each biofuel, several reaction pathways that lead towards soot production were identified. The data collected in these experiments are valuable information for the future of renewable biofuel development and their applicability in engines.

Molecular Dynamics of Combustion Reactions in Supercritical Carbon Dioxide. 6. Computational Kinetics of Reactions between Hydrogen Atom and Oxygen Molecule H + O2 ⇌ HO + O and H + O2 ⇌ HO2.

Reactions of the hydrogen atom and the oxygen molecule are among the most important ones in the hydrogen and hydrocarbon oxidation mechanisms, including combustion in a supercritical CO2 (sCO2) environment, known as oxy-combustion or the Allam cycle. Development of these energy technologies requires understanding of chemical kinetics of H + O2 ⇌ HO + O and H + O2 ⇌ HO2 in high pressures and concentrations of CO2. Here, we combine quantum treatment of the reaction system by the transition state theory with classical molecular dynamics simulation and the multistate empirical valence bonding method to treat environmental effects. Potential of mean force in the sCO2 solvent at various temperatures 1000-2000 K and pressures 100-400 atm was obtained. The reaction rate for H + O2 ⇌ HO + O was found to be pressure-independent and described by the extended Arrhenius equation 4.23 × 10-7 T-0.73 exp(-21 855.2 cal/mol/RT) cm3/molecule/s, while the reaction rate H + O2 ⇌ HO2 is pressure-dependent and can be expressed as 5.22 × 10-2 T-2.86 exp(-7247.4 cal/mol/RT) cm3/molecule/s at 300 atm.

Molecular Dynamics of Combustion Reactions in Supercritical Carbon Dioxide. Part 5: Computational Study of Ethane Dissociation and Recombination Reactions C2H6 ⇌ CH3 + CH3.

Fossil fuel oxy-combustion is an emerging technology where the habitual nitrogen diluent is replaced by high-pressure supercritical CO2 (sCO2), which increases the efficiency of energy conversion. In this study, the chemical kinetics of the combustion reaction C2H6 ⇌ CH3 + CH3 in the sCO2 environment is predicted at 30-1000 atm and 1000-2000 K. We adopt a multiscale approach, where the reactive complex is treated quantum mechanically in rigid rotor/harmonic oscillator approximation, while environment effects at different densities are taken into account by the potential of mean force, produced with classical molecular dynamics (MD). Here, we used boxed MD, where enhanced sampling of infrequent events of barrier crossing is accomplished without application of the bias potential. The multistate empirical valence bond model is applied to describe free radical formation accurately at the cost of the classical force field. Predicted rates at low densities agree well with the literature data. Rate constants at 300 atm are 2.41 × 1014 T-0.20 exp(-77.03 kcal/mol/ RT) 1/s for ethane dissociation and 8.44 × 10-19 T1.42 exp(19.89 kcal/mol/ RT) cm3/molecule/s for methyl-methyl recombination.

Theoretical Calculation of Reaction Rates and Combustion Kinetic Modeling Study of Triethyl Phosphate (TEP).

Triethyl phosphate (TEP) is an organophosphorus compound used as a simulant for highly toxic nerve agents such as sarin GB. A high temperature decomposition pathway during TEP pyrolysis has been proposed previously and takes place via seven concerted elimination reactions. A computational study to investigate the kinetics of these seven reactions was carried out at the CBS-QB3 level of theory. The transition state optimization was done at the B3LYP/6-311G(2d,d,p) theory level, and CanTherm was used to derive the Arrhenius coefficients. The pre-exponential factors of the rate constant of these reactions were found to be up to 50 times lower than the estimated values from the literature. In addition, kinetics of reaction of the trioxidophosphorus radical (PO3) with H2 (H2 + PO3 → HOPO2 + H), which is one of the important reactions in predicting CO formation during TEP decomposition, was also investigated computationally at the same theory level. The new kinetic parameters derived from the computational study were used with the TEP kinetic model proposed recently by our group. In addition, an alternative decomposition pathway for TEP decomposition via H-abstraction, radical decomposition, and recombination reactions was added. The proposed mechanism was validated with the literature's experimental data, that is, intermediate CO time-history data from pyrolysis and oxidation experiments and ignition delay times. Fairly good agreement with experiments was obtained for pyrolysis and oxidation CO yield within 1200-1700 K. The model was able to predict the ignition times of the rich TEP mixture (φ = 2) within 25% of the experimental results, while the discrepancies for stoichiometric and rich mixtures were larger. Discussions on results of sensitivity and reaction pathway analysis are presented to identify the important phosphorus reactions and to understand the effect of addition of the alternative TEP decomposition pathway.

Acousto-optically modulated quantum cascade laser for high-temperature reacting systems thermometry.

We demonstrate time-resolved temperature measurements in shock-heated mixtures of carbon monoxide over a temperature range of 1000-1800 K for two pressure ranges, 2.0-2.9 atm and 7.6-10.7 atm, at rates up to 250 kHz using a single acousto-optically modulated quantum cascade laser with mid-infrared output spanning from 1975 to 2260 cm-1. Measured temperatures were in excellent agreement with values determined by ideal shock relations, and the temperature profile after the passage of the reflected shock wave was found to be well-modeled by an isentropic compression assumption. Temperature measurements made with this setup are largely immune to effects of emissions and beam steering, making the diagnostic system well-suited for studying high-temperature gas-phase reactions of energetic materials such as octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine and hexahydro-1,3,5-trinitro-1,3,5-triazine.

Molecular dynamics of combustion reactions in supercritical carbon dioxide. Part 4: boxed MD study of formyl radical dissociation and recombination.

Fossil fuel oxy-combustion is an emergent technology where habitual nitrogen diluent is replaced by high pressure (supercritical) carbon dioxide. The supercritical state of CO2 increases the efficiency of the energy conversion and the absence of nitrogen from the reaction mixture reduces pollution by NOx. However, the effects of a supercritical environment on elementary reactions kinetics are not well understood at present. We used boxed molecular dynamics simulations at the QM/MM theory level to predict the kinetics of dissociation/recombination reaction HCO• + [M] ↔ H• + CO + [M], an important elementary step in many combustion processes. A wide range of temperatures (400-1600 K) and pressures (0.3-1000 atm) were studied. Potentials of mean force were plotted and used to predict activation free energies and rate constants. Based on the data obtained, extended Arrhenius equation parameters were fitted and tabulated. The apparent activation energy for the recombination reaction becomes negative above 30 atm. As the temperature increased, the pressure effect on the rate constant decreased. While at 400 K the pressure increase from 0.3 atm to 300 atm accelerated the dissociation reaction by a factor of 250, at 1600 K the same pressure increase accelerated this reaction by a factor of 100. Graphical abstract Formyl radical surrounded by carbon dioxide molecules.

Catalytic Effect of Carbon Dioxide on Reaction OH + CO → H + CO2 in Supercritical Environment: Master Equation Study.

We investigated the reaction rates of OH + CO → H + CO2 in supercritical CO2 environment with and without additional CO2 molecule included in reactive complex. Ab initio potential energy surfaces previously reported a lower activation barrier and hence a catalytic effect of additional CO2 molecule. Here we solve the steady-state unimolecular master equations based on the Rice-Ramsperger-Kassel-Marcus theory (RRKM) and compare the rates for the two mechanisms. We found that the alternative reaction mechanism becomes faster at high pressure and low temperature, when the concentration of prereactive complex with additional CO2 molecule becomes appreciable. Therefore, this catalytic effect may be important for the chemical processes in CO2 solvent but is unlikely to play a role during combustion.

Molecular Dynamics Study of Combustion Reactions in Supercritical Environment. Part 3: Boxed MD Study of CH3 + HO2 → CH3O + OH Reaction Kinetics.

The kinetics of reaction CH3 + HO2 → CH3O + OH in supercritical carbon dioxide media at pressures from 0.3 to 1000 atm in the temperature range (600-1600) K was studied using boxed molecular dynamics simulations at QM/MM theory level with periodical boundary conditions. The mechanism of this process includes two consecutive steps: formation and decomposition of CH3OOH intermediate. We calculated the activation free energies and rate constants of each step, then used Bodenstein's quasistationary concentrations approximation to estimate the rate constants of the reaction. On the basis of the temperature dependence of the rate constants, parameters in the extended Arrhenius equation were determined. We found that reaction rate of each step, as well as overall reaction, increases with increasing CO2 pressure in the system. The most effective zone for the process is T = 1000-1200 K, and the CO2 pressure is about 100 atm.