Multimodal Pain Management of Femoral Neck Fractures Treated With Hemiarthroplasty.

The purpose of this study was to evaluate a multimodal pain management program incorporating periarticular injections of liposomal bupivacaine after hemiarthroplasty treatment of femoral neck fractures. This retrospective study selected patients treated with periarticular injections of liposomal bupivacaine within the multimodal pain management program (LBUP) (n = 100) and a control group of patients treated without local infiltration (n = 78). Similar pain control was achieved between both groups from day 1 to day 4 postsurgery (min p = .392). Length of stay was significantly lower for LBUP patients (4.8 days vs. 5.7 days, p = .013), and LBUP patients were significantly more likely to be ambulatory at discharge (82% vs. 69%, p = .013). LBUP patients were also less likely to need the intensive care unit (4% vs. 14%, p = .027). The percentage of patients with at least one opioid-related adverse event was lower in the LBUP group (3% vs. 8%, p = .156) as was the 90-day mortality rate (2% vs. 8%, p = .069), but the differences were not statistically significant. (Journal of Surgical Orthopaedic Advances 28(1):58-62, 2019).

Risk of Opioid-Related Adverse Events After Primary and Revision Total Knee Arthroplasty.

Postoperative analgesia after primary total knee arthroplasty (TKA) and revision knee arthroplasty (RKA) can be reliant on the use of opioids and may lead to opioid-related adverse events (ORAEs). This study evaluated the risk of ORAEs following TKA and RKA using the 5% Medicare claims (2010-2013) database. There were 41,702 TKA and 3817 RKA patients who met the inclusion criteria. At 90 days, respiratory complications were the most common complication (TKA: 6.12%; RKA: 8.01%), followed by postoperative nausea and vomiting (TKA: 2.86%; RKA: 3.95%), and urinary retention complications (TKA: 2.79%; RKA: 3.20%). For TKA, risk factors for respiratory complications included older age, lower socioeconomic status, more comorbidities, obesity, chronic obstructive pulmonary disease, white race, and patients in the Midwest and West (vs. South) (p 002). The average Medicare payment for treating complications within 90 days of a TKA was $6206 and $6222 following RKA. Awareness risks for ORAEs in select patients can assist in developing a multimodal postoperative pain control and patient education protocols. (Journal of Surgical Orthopaedic Advances 27(2):148-154, 2018).

No Difference in Early Analgesia Between Liposomal Bupivacaine Injection and Intrathecal Morphine After TKA.

BACKGROUND: Opioid analgesics have been a standard modality for postoperative pain management after total knee arthroplasty (TKA) but are also associated with increased risk of nausea, pruritus, vomiting, respiratory depression, prolonged ileus, and cognitive dysfunction. There is still a need for a method of anesthesia that can deliver effective long-term postoperative pain relief without incurring the high cost and health burden of opioids and nerve blocks. QUESTIONS/PURPOSES: (1) Is liposomal bupivacaine-based periarticular injection (PAI) more effective than morphine-based spinal anesthesia or ropivacaine-based PAI in controlling postoperative pain after TKA? (2) Do patients treated with liposomal bupivacaine-based PAI experience fewer opioid-related adverse events compared with patients treated with morphine-based spinal anesthesia or ropivacaine-based PAI in controlling postoperative pain after TKA? METHODS: This multicenter, blind trial randomized 119 patients undergoing TKA with spinal anesthesia to receive spinal anesthesia plus periarticular injection with liposomal bupivacaine (40 patients), spinal anesthesia with bupivacaine plus intrathecal morphine (41 patients) but no liposomal bupivacaine injection, or spinal anesthesia with bupivacaine (38 patients) and no liposomal bupivacaine injection. The two groups that did not receive periarticular liposomal bupivacaine did receive periarticular injection with ropivacaine, and all three groups had ketorolac (30 mg) plus epinephrine (1:1000) in the periarticular injections. Patients in all three groups received identical perioperative multimodal analgesic and antiemetic drugs. All patients were analyzed in the group to which they were randomized and no patients were lost to followup. The primary study endpoints were visual analog score (VAS) for pain and narcotic use during postoperative day 1. Secondary endpoints included side effects associated with narcotic administration during the hospital stay. RESULTS: Mean VAS pain in the liposomal bupivacaine PAI group was lower than that for the ropivacaine PAI group at 6 hours (1.8 ± 2.1 versus 3.3 ± 2.3, p = 0.005, mean difference: 1.5, 95% confidence interval [CI], 0.5-2.5) and 12 hours (1.5 ± 2.0 versus 3.3 ± 2.4, p < 0.001, mean difference: 1.8, 95% CI, 0.8-2.8) after surgery. The morphine spinal group had lower pain compared with the liposomal bupivacaine PAI group at 6 hours (0.9 ± 1.8 versus 1.8 ± 2.1, p = 0.035, mean difference: 1.0, 95% CI, 0.1-1.8), but there was no difference at 12 hours (0.8 ± 1.5 versus 1.5 ± 2.0, p = 0.086, mean difference: 0.7, 95% CI, -0.1 to 1.5). The magnitude of the differences at 6 and 12 hours are near the lower end of minimal clinically important differences reported in the literature, and thus the improvement shown in this study may only represent a small clinical improvement. Both the liposomal bupivacaine group (13% [five of 40]) and the ropivacaine group (5% [two of 38]) had fewer incidents of itching (pruritus) than the spinal morphine group (38% [15 of 41]) (p = 0.001). CONCLUSIONS: This prospective multicenter three-arm blind randomized controlled trial showed potentially improved pain control at 6 and 12 hours in the liposomal bupivacaine and intrathecal morphine groups compared with the ropivacaine group at the cost of much higher incidences of pruritus (itching) in the intrathecal morphine group. Based on these results, we prefer the use of PAI with liposomal bupivacaine as an alternative to spinal anesthesia with intrathecal morphine as a result of similar postoperative pain control and the potential for reducing adverse events. LEVEL OF EVIDENCE: Level I, therapeutic study.

Postoperative Pain After Primary Total Knee Arthroplasty: Comparison of Local Injection Analgesic Cocktails and the Role of Demographic and Surgical Factors.

BACKGROUND: It has been reported that pain-related outcomes after total knee arthroplasty (TKA) may vary with different analgesic techniques and with patient demographics. The purposes of this study were to compare local infiltration of regular bupivacaine (periarticular infiltration [PAI] group) vs liposomal bupivacaine (LBUP group) and to examine the effect of patient characteristics on postoperative pain after TKA. METHODS: The study sample included 665 consecutive TKA cases performed between December 2011 and August 2013. The primary outcome measures were the average visual analog scale (VAS) pain score and the percent of VAS pain scores that indicated no pain. Multivariable regression analyses investigated the effect of age, race, ethnicity, body mass index, gender, surgeon, and analgesic protocol on outcomes. For the analgesic groups, the "PAI" group received injections of a cocktail including bupivacaine, ketorolac, and morphine, whereas the "LBUP" group received injections of LBUP. RESULTS: The regression analysis demonstrated that postoperative pain was higher in females (P < .001) and younger patients (P < .001). Although overall average VAS pain scores were not significantly different, when specific postoperative days were evaluated, the LBUP group had lower pain scores from day 1 to 5 (P < .014). There were no differences in VAS scores based on patient body mass index (P = .250), race (P = .205), or ethnicity (P = .961) in this sample. CONCLUSION: This multivariate regression analysis study showed that in patients undergoing primary TKA, postoperative pain was lower in males, older patients, and those treated with LBUP. Awareness of these factors may assist in developing patient-specific multimodal postoperative pain and education protocols that reduce opioid reliance and related adverse events.

How Do Demographic, Surgical, Patient, and Cultural Factors Affect Pain Control After Unicompartmental Knee Arthroplasty? A Multivariable Regression Analysis.

BACKGROUND: Controlling pain after unicompartmental knee arthroplasty (UKA) is essential for improving patient satisfaction, minimizing complications, and early rehabilitation. There is little literature available evaluating the effect of both treatment and patient characteristics on in-hospital pain after UKA. The purpose of this study was to examine the effect of patient and treatment characteristics on in-hospital pain after UKA. This study also evaluated the role of analgesic cocktail (traditional periarticular injection cocktail "[PAI]" vs cocktail including liposomal bupivacaine "[LBUP]"). METHODS: The study sample included 442 consecutive UKA cases performed between December 2011 and August 2013. The primary outcome measures were the average Visual Analog Scale pain score and the percent of pain scores during hospitalization that were 0, that is, "no pain." Multivariable regression analyses were implemented to investigate associations between patient demographics and analgesic group with the outcomes. For the analgesic groups, the "PAI" group received injections of a cocktail including Marcaine, ketorolac, and morphine, the "LBUP" group received injections of LBUP. RESULTS: Postoperative pain was higher in females (P < .001) and younger patients (P = .002). The patient group treated with LBUP injection technique had similar overall average Visual Analog Scale pain scores to patients in the PAI group (P = .729); however, there was also a significant improvement in pain scores over time (as the study progressed) for patients in the LBUP group relative to the PAI group (P = .003), potentially indicating better outcomes with more experience with the injection technique. When compared individually by day, the LBUP group had lower pain scores from day 1 to 3 (P < .024). CONCLUSION: The results showed that in patients undergoing UKA, postoperative pain was lower in males, older patients, patients with lower body mass index, and those treated with LBUP over the study period. Understanding these associations is necessary to effectively manage pain and encourage earlier ambulation and physiotherapy after UKA.

Quantifying the Risk of Analgesic-Related Adverse Events After Knee Arthroscopy.

Opioids are frequently used as part of multimodal pain management protocols for knee arthroscopy; however, their use may be associated with opioid-related adverse events. The purpose of this study was to evaluate the risk of potential analgesic-related complications after knee arthroscopy using a nationally representative database. Using 2010\endash 2012 Medicare claims data, patients undergoing knee arthroscopy procedures (including ligament repair, meniscectomy, and chondroplasty) were identified. The risk of complications related to typical modalities of analgesia, including opioids, within 90 days following surgery was assessed using multivariate Cox regression. Based on follow-up of 16,567 cases, respiratory complications (bradypnea, pulmonary insufficiency, asphyxia, and hypoxemia) were the most frequently diagnosed complications (n = 418; 2.52%), followed by postoperative nausea and vomiting (n = 174; 1.05%) and urinary retention complications (n = 166; 1.00%). Risk factors including older age, male gender, lower socioeconomic status, and a high number of comorbidities were associated with development of postsurgical complications.

Readmission and Complications for Catheter and Injection Femoral Nerve Block Administration After Total Knee Arthroplasty in the Medicare Population.

There is general agreement that femoral nerve blocks (FNB) provide adequate immediate postoperative analgesia after total knee arthroplasty (TKA), although the effect of this technique on hospital readmission and other complications has not been quantified in a large sample. The Medicare 5% sample was used to identify TKA patients who were grouped according to postoperative FNB administration: FNB via injection; FNB via pain pump; and no FNB. Multivariate Cox regressions were used to evaluate risk factors for the postoperative outcomes. Both FNB groups were associated with a lower risk of readmission (30, 90 and 365 days, P<0.001). Future clinical studies may help elucidate whether the lower hospital readmissions may be associated with more effective pain control with the use of FNB.

Patient Selection in Short Stay Total Hip Arthroplasty for Medicare Patients.

There is a trend towards shortening inpatient hospital stays following total hip arthroplasty (THA) in an effort to reduce healthcare costs and potentially decrease complications. The purpose of this study was to identify patients who are at risk for readmission, complications, and mortality after short stay THA. The Medicare sample (1997-2011) was used to identify THA patients with 1-2-day (Group A, n=2949) or 3-day (Group B, n=8707) stays. Complication risks were similar between groups, though there was a reduced risk for hospitalization for Group A (adjusted hazard ratio=0.90, P=0.029). These findings suggest that age and comorbidities, particularly diabetes and cardiovascular conditions, have the greatest effect on readmission and event risk after short stay THA.

Mortality, cost, and downstream disease of total hip arthroplasty patients in the medicare population.

The purpose of this study is to compare the differences in downstream cost and health outcomes between Medicare hip OA patients who undergo total hip arthroplasty (THA) and those who do not. All OA patients in the Medicare 5% sample (1998-2009) were separated into non-THA and THA groups. Differences in costs and risk ratios for mortality and new disease diagnoses were adjusted using logistic regression for age, sex, race, socioeconomic status, region, and Charlson score. Mortality, heart failure, depression, and diabetes were all reduced in the THA group, though there was an increased risk for atherosclerosis in the short term. The potential for selection bias was investigated with two separate propensity score analyses. This study demonstrates the potential benefit of THA in reducing mortality and improving aspects of overall health in OA patients.

Complications, mortality, and costs for outpatient and short-stay total knee arthroplasty patients in comparison to standard-stay patients.

The purpose of the present study is to determine the differences in cost, complications, and mortality between knee arthroplasty (TKA) patients who stay the standard 3-4 nights in a hospital compared to patients who undergo an outpatient procedure, a shortened stay or an extended stay. TKA patients were identified in the Medicare 5% sample (1997-2009) and separated into the following groups: outpatient, 1-2 days, 3-4 days, or 5+ days inpatient. At two years, costs associated with the outpatient and the 1-2 day stay groups were $8527 and $1967 lower than the 3-4 day stay group, respectively. Out to 2 years, the outpatient and 1-2 day stay groups reported less pain and stiffness, respectively, though the 1-2 day group also had a higher risk for revision.

Mortality, cost, and health outcomes of total knee arthroplasty in Medicare patients.

There are little data that quantify the long term costs, mortality, and downstream disease after Total Knee Arthroplasty (TKA). The purpose of this study is to compare differences in cost and health outcomes between Medicare patients with OA who undergo TKA and those who avoid the procedure. The Medicare 5% sample was used to identify patients diagnosed with OA during 1997-2009. All OA patients were separated into non-arthroplasty and arthroplasty groups. Differences in costs, mortality, and new disease diagnoses were adjusted using logistic regression for age, sex, race, buy-in status, region, and Charlson score. The 7-year cumulative average Medicare payments for all treatments were $63,940 for the non-TKA group and $83,783 for the TKA group. The risk adjusted mortality hazard ratio (HR) of the TKA group ranged from 0.48 to 0.54 through seven years (all P<0.001). The risk of heart failure in the TKA group was 40.9% at 7years (HR=0.93, P<0.001). The results demonstrate the patients in the TKA cohort as having a lower probability of heart failure and mortality, at a total incremental cost of $19,843.

Developing failure criteria for laceration injury of dermal tissue.

Despite its importance, there is a poor understanding of human injury tolerance to trauma generally, and more specifically understanding of the mechanics of skin penetration or laceration. The objective of this analysis is to determine the failure criteria that will allow the evaluation of the laceration risk of blunt-tipped edges within a computational modeling environment. An axisymmetric tissue finite element model was set up in Abaqus 2021 to match the experimental set-up from a previous study. The model simulated the pressing of penetrometer geometries into dermal tissue, and stress and strain outputs were evaluated at the experimental failure force. Two separate nonlinear hyperelastic material models were calibrated for the dermis to data from the literature (high and low stiffness models). For both the high-stiffness and low-stiffness skin models, the failure force appears to occur near a local maximum in the principal strain. All failures occurred after the maximum strain near or at the top surface is or above 59%, with mid-thickness strain at a similar level. The strain energy density is concentrated near the edge tip for each configuration, indicating highly localized material damage at the point of loading, and increases rapidly prior to the approximate failure force. As the edge is further compressed into the tissue, the stress triaxiality near the edge contacting point decreases towards zero. This study has identified general failure criteria for skin laceration which can be implemented in a computational model. A higher risk for laceration would be indicated with strain energy density larger than 60 mJ/mm3, dermal strain larger than 55%, and stress triaxiality below 0.1. These findings were largely insensitive to the dermal stiffness and broadly applicable across different indenter geometries. It is expected that this framework may be implemented to evaluate hazardous forces for product edges, interactions with robots, and interfaces with medical and drug delivery devices.

Biomechanical optimization of bone plates used in rigid fixation of mandibular fractures.

PURPOSE: To design and optimize a bone plate for fractures of the mandibular body that will provide maximum fracture stability with minimal implanted volume and patient intrusion. The design will be driven by the unique biomechanics specific to this fracture location. MATERIALS AND METHODS: A finite element model of a fractured human mandible was created using tomography scans. Material properties were assigned to the cortical bone, cancellous bone, and dental region. Boundary conditions included simulating a unilateral molar clench and incisal loading. The bone plate design process included a shape optimization routine and design parameter analysis using the model. The optimized bone plate design was finally compared with standard bone plate configurations based on stress and strain measures. RESULTS: For incisal loading, the newly designed InterFlex II plate has 69% of the fracture strain and only 34% of the plate stress of an 8-hole strut plate. For unilateral molar loading, those numbers improve even further to 59% and 27%, respectively. InterFlex II plate stresses are less than or equal to the paired plate configuration, and fracture strain is within 10% of the corresponding paired plate strain under both loading scenarios. In terms of mechanical performance, InterFlex II is in the same class as the commonly used paired plate configuration, despite having only 55% of the implanted volume. CONCLUSION: A design process focused on shape and design variable optimization can produce bone plates that provide maximum fracture stability with minimum implanted volume.

Mechanical design optimization of bioabsorbable fixation devices for bone fractures.

Bioabsorbable bone plates can eliminate the necessity for a permanent implant when used to fixate fractures of the human mandible. They are currently not in widespread use because of the low strength of the materials and the requisite large volume of the resulting bone plate. The aim of the current study was to discover a minimally invasive bioabsorbable bone plate design that can provide the same mechanical stability as a standard titanium bone plate. A finite element model of a mandible with a fracture in the body region is subjected to bite loads that are common to patients postsurgery. The model is used first to determine benchmark stress and strain values for a titanium plate. These values are then set as the limits within which the bioabsorbable bone plate must comply. The model is then modified to consider a bone plate made of the polymer poly-L/DL-lactide 70/30. An optimization routine is run to determine the smallest volume of bioabsorbable bone plate that can perform and a titanium bone plate when fixating fractures of this considered type. Two design parameters are varied for the bone plate design during the optimization analysis. The analysis determined that a strut style poly-L-lactide-co-DL-lactide plate of 690 mm2 can provide as much mechanical stability as a similar titanium design structure of 172 mm2. The model has determined a bioabsorbable bone plate design that is as strong as a titanium plate when fixating fractures of the load-bearing mandible. This is an intriguing outcome, considering that the polymer material has only 6% of the stiffness of titanium.

Postlaparotomy pain management: Comparison of patient-controlled analgesia pump alone, with subcutaneous bupivacaine infusion, or with injection of liposomal bupivacaine suspension.

OBJECTIVE: Efforts to achieve balance between effective pain management and opioid-related adverse events (ORAEs) have led to multimodal analgesia regimens. This study compared opioids delivered via patient-controlled analgesia (PCA) plus liposomal bupivacaine, a long-acting local anesthetic with potential to be an effective component of such regimens, to opioids delivered through PCA alone or PCA plus subcutaneous bupivacaine infusion (ONQ), following laparotomy. DESIGN: Prospective, randomized controlled trial. SETTING: Single, tertiary-care institution. PATIENTS: One hundred patients undergoing nonemergent laparotomy. INTERVENTIONS: Patients were randomly assigned to one of three study treatments: PCA only (PCAO), PCA with ONQ, or PCA with injectable liposomal bupivacaine suspension (EXP). MAIN OUTCOME MEASURES: Cumulative opioid use, daily mean patient-reported pain scores, and ORAEs through 72 hours postoperatively. RESULTS: On average, the EXP (n = 31) group exhibited less than 50 percent of the total opioid consumption of the PCAO (n = 36) group, and less than 60 percent of that for the ONQ (n = 33) group. Postoperative days 1 and 3 pain scores were significantly lower for the EXP group as compared to the ONQ and PCAO groups (p ≤ 0.005). Fewer patients in the EXP group (19.4 percent) experienced ORAEs compared to the PCAO (41.1 percent) and ONQ (45.5 percent) groups (p = 0.002). CONCLUSIONS: Laparotomy patients treated with liposomal bupivacaine as part of a multimodal regimen consumed less opioids, had lower pain scores, and had fewer ORAEs. The role of liposomal bupivacaine in the postoperative care of laparotomy patients merits further study.

The mechanics of corneal deformation and rupture for penetrating injury in the human eye.

Penetrating eye injuries are surgical emergencies with guarded visual prognosis. The purpose of the current study was to determine the force required to rupture the cornea with a penetrating object, and to study how this force is affected by the object geometry. Thirty-six human cadaveric eyes from donors of various ages were characterized for diameter, axial length, and pre-test intraocular pressure. In order to investigate the effects of specimen storage time on the tissue response, half of the specimens were tested within two weeks of donor expiration, and half of the specimens were stored at -4°C for 12-18 months. Indenters of three different diameters (1.0, 1.5, and 2.0mm) were lowered into the apex of the cornea until rupture. Resistance to displacement (stiffness), displacement at failure, and the force at failure were determined. Multi-variable regression analysis was used to determine associations of the input variables (indenter size, test speed, and tissue postmortem time) on the mechanics of the tissue response. Twenty-nine of the 36 specimens failed at the indenter location in the cornea, four failed at the limbus, and three failed in the sclera near sites of muscle attachment. The average force at failure caused by the 1.0mm, 1.5mm, and 2.0mm indenters increased from 30.5±5.5N to 40.5±8.3N to 58.2±14.5N, respectively (p<0.002). The force at failure was associated with the donor age (p<0.001), and globe diameter (p<0.041), but was not associated with pre-test intraocular pressure, tissue postmortem time, axial length, or speed of the indenter. This study has quantified the force-displacement and failure response of a large series of human cadaveric eyes subjected to penetrating indentation loads on the cornea. The results provide useful data for characterizing the relationship between corneal rupture and the geometry of a penetrating object.

Finite element analysis and experimental evaluation of penetrating injury through the cornea.

Penetration injuries of the eye are among the most frequent causes of permanent visual impairment resulting from trauma. The purpose of this study was to determine the peak strain at which rupture occurs in the cornea due to a penetrating object. Probes of varying diameters (1.0, 1.5, and 2.0mm) were pressed into the apex of the cornea of 36 human cadaveric eye specimens until perforation or rupture of the specimen at the cornea, limbus, or sclera occurred. An axisymmetric finite element model of the human globe was created to replicate the experimental set-up. The models were used to map the force-displacement response of the experiments and quantitatively determine a peak strain at which the eye ruptures. For the experiments, the average force at failure increased from the smallest to largest probe (p<0.002). The average forces at failure are as follows: 30.5±5.5N (1.0mm probe); 40.5±8.3N (1.5mm probe); 58.2±14.5N (2.0mm probe). The force-displacement responses of the finite element models of all three probe sizes bounded and tracked the experimental data. In all cases, the peak strain at failure in the cornea was located on the posterior surface of the cornea, directly adjacent to the corneal apex. This strain was in the range of 29% to 33% for all models analyzed. In addition to determining an objective failure strain of corneal tissue, the model developed in this study can provide quantitative information for understanding the risk of penetrating eye injuries.

Biomechanics of the monopedicle skin flap.

OBJECTIVE: The design and implementation of skin flaps remains a puzzle for the reconstructive surgeon. The objective of the present study is to use finite element (FE) analysis to characterize and understand the biomechanics of the monopedicle skin flap design. STUDY DESIGN: The current study uses a nonlinear hyperelastic FE model of the human skin to understand the biomechanics of monopedicle-based flap designs as geometric flap parameters are varied. SETTING: In silico. SUBJECTS AND METHODS: The simulation included the displacement loading, stitching, and relaxation of various forms of the flap design. Stress and strain outcomes, previously correlated with scarring, necrosis, and blood perfusion, are reported for a basic monopedicle design as well as a number of modifications to this design. RESULTS: The results suggest that the length of the monopedicle flap should not exceed 3 times the size of the defect, as the benefit in reducing principal strain (deformation) is diminished beyond this point. Further, to minimize skin strain, the ideal Burrow's triangle size can be described as proportional to flap length and inversely proportional to defect height, according to a linear function. CONCLUSION: The ideal flap design should attempt to minimize not only the stress in the skin, but the size of the incisions and the degree of undermining. The results of our analyses provide guidance to increase the general understanding of monopedicle flap mechanics and provide context for the clinician and insight into designing a better monopedicle flap for individual situations.

Comparison of plate-screw systems used in mandibular fracture reduction: finite element analysis.

A finite element model of the human dentate mandible has been developed to provide a comparison of fixation systems used currently for fracture reduction. Volume domains for cortical bone, cancellous bone, and teeth were created and meshed in ANSYS 8.0 based on IGES curves created from computerized tomography data. A unilateral molar clench was loaded on the model with a fracture gap simulated along the symphysis. Results based on Von Mises stress in cortical and cancellous bone surrounding the screws, and on fracture surface spatial fixation, show some relative differences between different screw-plate systems, yet all were judged to be appropriate in their reduction potential.