Combined radiation injury (CRI) occurs after nuclear disaster, such as reactor accidents or nuclear detonations. Injuries in addition to radiation exposure include trauma, burns, chemical exposures, and infectious complications. Casualty estimates based on previous atomic bomb detonations predict that 65% to 70% of victims of CRI will have traumatic injury in addition to radiation exposure, whereas only 15% to 20% will be affected by radiation alone (1). This has been illustrated by the tragedies of World War II that took place in Hiroshima and Nagasaki, Japan, resulting in greater than 60% of radiation victims also having sustained traumatic injuries (1, 2).
Combined radiation injury results in higher mortality and worse complications than isolated radiation exposure or trauma, with victims sustaining injuries to nearly every organ system (3, 4), and cardiovascular, neurologic, hematopoietic, and gastrointestinal (GI) effects are the most severe (5). Intestinal involvement after CRI is a contributor to early death (6). Therefore, hypotheses accounting for higher morbidity and mortality associated with CRI should focus on the intestine’s function as a barrier to endotoxins and intraluminal bacteria that inhabit the gut.
Both isolated radiation injury and cutaneous burn indirectly results in the breakdown of the GI barrier by remarkably similar mechanisms. Ionizing radiation alters the organization of integral components of tight junctions, such as occludin, ZO-1, and β-catenin, resulting in increased gut permeability (7–9). Radiation exposure generates reactive oxygen species (ROS) causing single- and double-stranded DNA breaks and intracellular alterations resulting in apoptosis, autophagy, and subsequent breakdown of the gut epithelium (10). Increased cell death, specifically affecting mitotically active cells, delays epithelial repair, allowing penetration of antigens, bacterial products, and digestive enzymes. An intense inflammatory response ensues (10, 11).
Cutaneous burn indirectly decreases levels of tight junction proteins in the intestinal epithelium, resulting in a burn-induced gut barrier injury (12). Further disruption is mediated through increased apoptosis of epithelial cells and dysfunctional proliferation (13). Production of gut-derived proinflammatory mediators, which travel through the intestinal lymphatics, has been implicated in a systemic inflammatory response and shock observed after isolated burn (14, 15).
To our knowledge, GI involvement in CRI has not been reexamined since early descriptive studies after World War II (6). Disruption of cell proliferation, increased apoptosis, and the effects of burn and radiation on tight junctions could diminish intestinal barrier function and make victims susceptible to bacterial translocation and subsequent death caused by septic shock. Even in the setting of a smaller burn wound or sublethal dose of radiation exposure, the combination of these disturbances can trigger or elevate gut leakiness, resulting in increased morbidity and mortality. The purpose of this study is to determine if the combined effects of radiation and burn cause GI permeability as a possible explanation for increased mortality not present with isolated injury types.
MATERIALS AND METHODS
Eight- to 10-week-old male C57BL/6 mice (weighing 23–25 g) were obtained from Charles River Laboratories (Wilmington, Mass) and housed in sterile microisolator cages at the Loyola University Medical Center Comparative Medicine Facility. All animal studies described here were approved and performed with accordance to the guidelines established by the Loyola University Institutional Animal Care and Use Committee.
Combined irradiation and burn injury
A model previously described by our group was used to administer isolated burn, isolated radiation, and combined injuries (16) with minor modifications. The radiation dose was adjusted between 5.0 and 5.5 Gy total body irradiation (TBI) to maintain a mortality rate among CRI animals between 40% and 60%. Approximately 1 h after radiation injury, mice were anesthetized with a mixture of ketamine (100 mg/kg) and xylazine (10 mg/kg) intraperitoneally; their dorsal surfaces were then shaved. Mice were placed into a plastic template exposing 15% total body surface area (TBSA), as calculated by previously described methods (17, 18). Scald injury was performed in 90°C to 92°C water bath or sham injury in room temperature water. Animals were dried immediately after burn to prevent further scalding. All animals received 1.0 mL of warmed 0.9% normal saline intraperitoneal resuscitation immediately after the burn injury, and cages were placed on heating pads while the animals recovered from anesthesia. At 24, 48, and 72 h after injury, mice were euthanized by CO2 narcosis followed by exsanguination. Animals that expired before designated study time points were included only in survival data and tissues were not processed for further studies. The sequence of radiation injury then burn was necessary because of the location of the radiation source at another facility and difficulties associated with transporting mice recovering from burn injury.
Bacterial translocation was assessed as previously described with minor modifications (19, 20). At 24 and 72 h after injury, using sterile technique, for each mouse, the mesenteric lymph node (MLN) complex was removed and placed in cold RPMI with 5% fetal bovine serum on ice. Nodes were dissected out from surrounding mesenteric fat, taking note of the total number of lymph nodes isolated, transferred, and homogenized in 500 μL of RPMI. Aliquots of 100 μL were then plated in triplicate (300 μL total) on tryptic soy agar plates and placed in a 37°C incubator overnight, providing a lower limit of detection of less than two colony forming units (CFUs). Colonies were counted the following day. For each animal, the total number of CFUs from the three plates was determined and divided by the total lymph nodes harvested from the MLN complex. Values obtained for each animal were grouped according to injury, and final averages were determined for comparison. In the event that no colonies were recovered, an estimated value of less than 2 CFU/mL was assigned.
Histopathology and apoptosis scoring
Distal ileum was harvested at 24, 48, and 72 h time points after injury. Tissue was suspended in 10% formalin, sectioned, and stained with hematoxylin and eosin (H&E). A pathologist, who was blinded to the experimental groups, evaluated specimens for the presence of apoptotic bodies using a scoring system we developed. All quantification was performed at 40× magnification. The presence of apoptotic bodies was scored 0 to 4, 0 being none, 1 being one per four intestinal crypts, 2 being two per four crypts, 3 being three per four crypts, and 4 being four or more apoptotic bodies per four crypts.
Cell death detection
Total apoptosis was quantified using the Cell Death Detection enzyme-linked immunosorbent assay (ELISA)PLUS (Roche–Applied Science) as previously described (13). Whole ileum was homogenized using Bio-Plex Lysis Buffer (BioRad). Protein concentration of lysate was determined by total protein assay. Reported data are expressed as optical density per 15 μg protein.
Western blot analysis
Western blot was performed as previously described (20) with minor modifications. Thirty micrograms of whole-cell lysate protein was boiled for 5 min, separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis, transferred to polyvinylidene fluoride membranes, and blotted with primary antibodies specific for anti–caspase-3 (Abcam, Cambridge, Mass), anti–caspase-8 (Abcam), and α-tubulin (Abcam). For antibodies that recognized multiple forms of the protein at different molecular weights (caspase-3 and caspase-8), all bands were quantified from the same sample relative to the loading control from that lane using BioRad Image Lab software. Normalized values obtained from densitometry were then expressed as fold change relative to sham. Alternatively, membranes were blotted with rabbit anti-occludin (Life Technologies Corporation, Carlsbad, Calif) and β-actin (Cell Signaling Technology, Danvers, Mass). Quantification of occludin was performed similarly to that of caspase levels, with normalization to β-actin, and presentation of data as fold change relative to sham.
Immunofluorescent staining of occludin
Ileum was sectioned and embedded in OCT at time of euthanasia and frozen for immunofluorescent staining as previously described (20) with minor modifications. Sections were cut 8 μm thick and stained with rabbit anti-occludin antibody (Life Technologies) followed by goat anti-rabbit AlexaFluor 488 antibody (Life Technologies). Sections were counterstained with fluorescent-conjugated phalloidin (actin) and Hoechst nuclear stain (Life Technologies). Using Zeiss software (model LSM 510, version 4.2 SP1), a 20–epithelial cell section (crypt or villus) was outlined. Within this section, the number of colocalized red and green pixels was determined. This number was then divided by the total number of pixels within the section and expressed as a percentage. This process was repeated on four sections per animal, leading to a total of 100 epithelial cells examined for each animal. Averaged results per animal were used to determine treatment group averages.
Statistical analyses (GraphPad Prism) were performed comparing four total groups, including sham, burn, radiation (RAD), and CRI (RAD + BURN). Differences in survival between groups were analyzed using Kaplan-Meier survival analysis with a log-rank significance test. For apoptosis scoring, differences in nonparametric data were noted among injury groups, and analysis was conducted using one-way analysis of variance followed by a Dunn multiple comparison post hoc test if significance was achieved (P < 0.05). For bacterial translocation, Western blot densitometry, histone-associated DNA fragment ELISA, and quantification of percent colocalization between occludin and actin filaments, one-way analysis of variance was performed followed with Tukey-Kramer multiple comparisons post hoc test if significance was achieved (P < 0.05).
Increased mortality at 72 h after CRI
Based on previous studies using a murine model of CRI established in our laboratory (16), we have consistently observed a 40% to 60% mortality rate associated with 15% TBSA scald combined with 5 to 6 Gy TBI by the third day postinjury. A 15% TBSA scald burn alone has been extensively studied, and it is rare that it alone causes mortality in young mice (18, 21). We have also shown that radiation alone does not cause mortality until dosing approaches 11 Gy TBI in mice (16). These findings were comparable to those of the current experiment (Fig. 1). Combined radiation injury demonstrated an expected increase in animal death by 72 h, with only 58.8% surviving (P < 0.05). No deaths occurred in sham animals at any time point. A single mouse exposed to burn alone died before the 24-h time point. There was a 12.5% mortality rate in this group at 72 h, demonstrating the rare, but possible, occurrence of death in this group. Only a single radiation-alone animal died before 24 h; otherwise, there were no casualties.
Evidence of bacterial translocation 72 h after CRI
Mesenteric lymph nodes were harvested after euthanasia at 24 and 72 h postinjury, homogenized, and plated on tryptic soy agar. Bacterial growth was observed in burn-alone animals at 24 h postinjury, with approximately 5.0 × 101 CFU/MLN (P < 0.05 vs. all groups). At 72 h postinjury, only CRI exhibited significant bacterial growth with approximately 1 × 102 CFU/MLN (P < 0.05 vs. all groups) (Fig. 2).
Alterations in quantity and distribution of occludin after CRI correlates with evidence of epithelial barrier dysfunction at 72 h
With the observation of increased bacterial translocation at 72 h, we wanted to determine if alteration in distribution of GI tight junctions preceded gut permeability by staining and quantifying occludin protein colocalization with actin. Immunofluorescence showed less evident staining of occludin along the apical border of the epithelium and diminished colocalization in radiation alone and CRI animals (Fig. 3). Sham animals averaged 10% to 11% colocalization of occludin and actin at all time points. Burn animals had slightly diminished colocalization at 24 and 48 h time points at 9% and 8%, respectively, which returned to sham levels by 72 h. None of these differences reached statistical significance. Radiation-alone animals had approximately half the amount of colocalization of sham at 24 and 48 h (P < 0.05 vs. sham and burn) but returned to 80% at 72 h. Combined radiation injury had the largest decreases in colocalization at all time points, with 3% and 2%, respectively, at 24 and 48 h (P < 0.05 vs. sham and burn) and 4% at 72 h (P < 0.05 vs. all groups) (Fig. 4). Levels after CRI were 50% lower than radiation alone at all time points. To determine if changes were caused by alterations in occludin organization or decreased total protein caused by injury, we performed quantification by Western blot analysis. Occludin (65 kd) measurement by densitometry was decreased relative to sham at 42% and 33% at 24 h in radiation-alone and CRI, respectively (P < 0.05). This trend persisted at 48 h, with levels that were 46% and 27% of sham (P < 0.05). At 72 h postinjury, radiation alone was no longer significantly different from sham, whereas CRI remained lower relative to both sham and burn alone (24%, P < 0.05) (Fig. 5).
Evidence of prolonged apoptosis 48 h after CRI
To determine if greater damage to intestinal lining correlated with tight junction disruption, we sought to characterize and quantify epithelial cell apoptosis after injury. High-power images stained with H&E were used for quantification of apoptosis in distal ileum sections. We developed a scoring system to compare treatment groups. Apoptotic cells were more numerous in animals that underwent radiation. Sham animals had median scores of 0 for apoptotic cells present at all time points. Burn alone animals had median scores of 2, 1, and 0 at 24, 48, and 72 h, respectively, none of which achieved statistical significance. Radiation-alone animals had a median score of 1 and 2 at 24 and 48 h, respectively (P < 0.05 vs. sham). Apoptosis remained elevated at 72 h, with a median score of 2, which was significantly higher than sham and burn alone at the same time point (P < 0.05). Quantification of apoptotic cells in CRI was persistently elevated, with values of 3, 4, and 3 at 24, 48, and 72 h, respectively (P < 0.05 vs. sham at all time points, P < 0.05 vs. burn at 48 and 72 h) (Fig. 6).
After observations of a prolonged increase in epithelial apoptosis in the ileum of CRI-exposed mice, we performed a quantitative analysis of whole-ileum cell death. Histone-associated DNA fragments were measured as an indirect assessment of apoptosis in injury groups at 24, 48, and 72 h after initial injury. Twenty-four hours postinjury, radiation injury alone exhibited a 2-fold increase in histone-associated DNA fragments relative to sham (P < 0.05). At 48 h, there was a 3-fold increase in apoptosis in the CRI group relative to all other injury groups (P < 0.05). Radiation injury alone was comparable to sham and burn alone at this time point. Levels of apoptosis approached sham level values in all injury groups at 72 h postinjury (Fig. 7).
To further characterize apoptosis, caspase-3 and caspase-8 (pro and cleaved forms) protein levels were examined in injury groups at 24-, 48-, and 72-h time points. Procaspase-3 trended toward elevation in burn alone at 24 and 48 h postinjury (2-fold increases at both time points), in CRI at 48 and 72 h (4- and 3-fold increases, respectively), and in radiation injury alone at 72 h (3-fold increase). Similarly, levels of caspase-3 trended toward elevation in CRI at 48 and 72 h (both >2-fold) but did not reach significance at any time point in any injury group (Fig. 8).
The pro form of caspase-8 was elevated approximately 13-fold at 48 h and 5-fold at 72 h relative to sham expression. Burn-alone animals also had increases in procaspase-8 by 4-fold at 48 h and 3-fold at 72 h, although these values were not statistically different. Significant elevation of caspase-8 occurred at 24 h postinjury in burn-alone animals, with 2-fold higher levels relative to sham at the same time point (P < 0.05). Levels in CRI animals at 48 h were found to be approximately three times that of time-matched sham and radiation-alone animals (P < 0.05) (Fig. 9).
Although the potential for nuclear disaster seems remote, it presents an intimidating problem, specifically in the medical management of survivors. Combined radiation injury commonly affects victims in such events, and although knowledge of the nature of these injuries has been present since World War II (3, 4), little is known about the mechanism by which CRI increases morbidity and mortality. Despite concerted research efforts, clear treatment options to improve acute survival remain largely undetermined in humans outside of supportive care (22, 23). Given the systemic nature of total body irradiation, as well as large cutaneous burns, damage to individual organ systems will contribute to a more severe widespread condition. Our murine model of CRI provides a way of better understanding effects of such a rarely occurring, yet devastating, problem to elucidate possible pathways contributing to increased death (16). To our knowledge, we are the first to present GI findings of this nature in any CRI model, with the exception of early studies on CRI in the 1960s (6). Increased knowledge of mechanisms behind elevated mortality in CRI can guide resuscitative efforts, develop therapies for organ-specific damage, and attenuate the resulting systemic inflammatory response. The GI tract is known to be particularly radiosensitive and is an excellent initial target for proposed therapeutics in CRI (5).
Early mortality after a nuclear disaster is often attributed to GI involvement with death secondary to infection, septic shock, dehydration, and severe electrolyte imbalances (6, 22). Our observations of early time points in mouse ileum exposed to CRI confirm the destructive nature of this injury and suggest that a combination of apoptotic activity with suppression of normal cell proliferation are present, much like in isolated burn or radiation exposures. Previous work with isolated burn injury shows organ-specific elevation of caspase-3 after 20% TBSA burn within the first few hours of injury for spleen and thymus (24) and 6 to 12 h after 30% TBSA burn by TUNEL stain and histone-associated DNA fragmentation in the intestine (13, 25). Similarly, ionizing radiation is responsible for ROS, resulting in single- and double-stranded DNA breaks, triggering apoptosis. Both isolated burn and radiation injuries are also with linked to aberrant epithelial cell proliferation (10–13). Given the nature of these injuries, we wanted to determine if the combination would result in evidence of loss of gut barrier integrity not present after isolated injuries.
Bacterial translocation was present with the combined insult, although at a later time point than other studies (15, 19). A modest increase in bacterial translocation was seen in burn-alone animals at 24 h. Although statistically significant, it is low at 5 × 101 and likely would not result in systemic responses large enough to result in animal death. Seventy-two hours postinjury, CRI animals exhibited a significant increase in bacterial accumulation in MLN, which may be caused by the prolonged intestinal damage seen in these animals in conjunction with immunosuppression consistent with radiation exposure (Fig. 1). No other injury group had bacteria in MLN at 72 h postinjury. Given the multiple insults occurring in victims of CRI, it is plausible that opportunistic bacteria could overwhelm the host, leading to septic shock and death.
To examine possible causes for the elevated bacterial translocation seen in the CRI group, we investigated the effects of combined injury on GI epithelial tight junctions relative to isolated burn and radiation injuries. We found that radiation exposure disorganizes tight junctions, as evidenced by decreased relative amounts and altered distribution of occludin protein. These findings are consistent with effects on occludin seen with ionizing radiation as well as decreased amounts of the protein in isolated burn injury (7–9, 15). Changes in gut barrier integrity would explain bacterial translocation seen 72 h after animals were exposed to CRI. Occludin is an important transmembrane protein involved in the maintenance tight junctions. Assembly and disassembly of tight junctions are determined by phosphorylation on either serine and threonine or tyrosine residues of this protein (26). Measurement of the 65-kd protein is not suggestive of states of tight junction assembly but does reflect differences after exposure to CRI. The 65-kd form of occludin was significantly lower in radiation alone and CRI based on Western blot analysis (Fig. 5). Decreases in densitometry were lowest in the combined injury group at all time points, indicating that protein levels were still affected 3 days after initial injury. Alterations in percent colocalization and Western blot findings trended similarly (Figs. 4, 5). Diminished staining for occludin seen by immunofluorescence in radiation-treated animals suggests decreased overall levels (Fig. 3); however, immunoprecipitation of phosphorylated forms may be necessary to assess total quantity of occludin or its role in tight junction maintenance after CRI.
Some discrepancy of image size in Figure 3 is noted at 48 h, specifically in the burn injury (Fig 3F) and combined injury groups (Fig. 3H). Images were selected to be representative of occludin colocalization for an injury group and similar in villus size and shape within a specific time point. Villi seem to be wider despite being taken with the same objective (40×). A slight increase in overall magnification was noted when comparing 48 h to the 24- and 72-h time points, which is evident when looking at the 20-μm scale. Another factor that could affect villus size after burn is the development of interstitial edema caused by increased endothelial permeability (27). This may account for the broader villi seen in the burn-alone and combined injury–treated groups, specifically, at the 48-h time point. Despite the discrepancy in magnification, this had no effect on calculation of percent colocalization of pixels per 100 epithelial cells or on occludin content by Western blot analysis.
Increased apoptosis may contribute to alterations in intestinal epithelial barrier function, including tight junction assembly and maintenance. Combined radiation injury differs from isolated burn or radiation, with histology showing continued apoptosis 72 h after it has subsided in isolated injury groups. Prolongation of apoptosis is occurring simultaneously with increased crypt debris from tissue destruction, disrupted clearance, or both and a delay in recovery of mitosis (data not shown). In contrast, animals given burn or radiation alone have either recovered or are recovering before 48 h postinjury. Further support for prolonged apoptosis at 48 h postinjury in CRI is seen by histone-associated DNA fragmentation (Fig. 7). This measurement was made using whole-ileum homogenate, as opposed to isolated epithelial cells, which may explain inconsistencies seen with histologic scoring in other injury groups, specifically, radiation injury alone at 48 and 72 h. Apoptosis occurring in intestinal tissue other than the epithelium, such as endothelium, may account for these differences. Evidence of apoptotic enzyme activity peaking at 24 to 48 h is seen with Western blot analysis of the extrinsic pathway of apoptosis (Figs. 8, 9). Although caspase-3 was not observed to be elevated, its upstream component in the activation cascade, caspase-8, was elevated at 48 h, suggesting that caspase-3 activation might follow at a later time point (between 48 and 72 h). Caspase-3 is rapidly degraded in vivo; therefore, tissue processing for Western blot analysis may contribute to the lack of significant elevation seen in our analysis. Techniques for stabilization of caspase-3 using caspase inhibitors have been described (28). Despite a lack of significant elevation, trends in CRI point toward increased intestinal caspase-3 activity. Histology, histone-associated DNA fragmentation ELISA, and caspase quantification by Western blot all suggest enhanced apoptotic activity in CRI 48 h after initial injury and beyond when compared with either burn or radiation alone.
Elevated levels of procaspase-8 occurring at 48 and 72 h suggest another explanation for discrepancies in caspase-3 activity and increased mortality. In some cell types, inhibition of caspase-8 has been shown to activate pathways mediated by tumor necrosis factor-α (TNF-α), resulting in necrotic cell death (29). Inactivation of caspases has been implicated in a shift from apoptosis either to cell death morphologies with mixed necrotic and apoptotic features or necrosis termed “necroptosis” (30). Necroptosis is dependent on the serine/threonine kinase activity of receptor-interacting protein kinase 1 and 3 (RIPK-1 and RIPK-3) (30). Active caspase-8 has been implicated in cleaving and inactivating proteins RIPK-1 and RIPK-3, two components of a complex termed “ripoptosome,” which must be enzymatically active for the execution of necroptosis (31). Elevation of procaspase-8 in CRI at 48 and 72 h may indicate a shift from apoptotic activity to necroptosis or concurrent activity. Further elucidation of the role of necroptosis in CRI could explain gut-induced morbidity without significant elevation of caspase-3.
Findings of tight junction alterations and prolonged cell death in CRI correlate with the observed increase in bacterial translocation and mortality of greater than 40% at 72 h postinjury. Mice that did not survive to assigned time points were not included in this study; therefore, it is possible that the findings of this study would be more severe in these animals. Despite the correlation between bacterial translocation and GI morbidity, this may not solely account for increases in mortality. It is likely that other organ systems damaged by CRI, such as cardiovascular, neurologic, hematopoietic, and pulmonary systems are involved in animal death. However, the GI tract remains a major source of early mortality. Therapies directed at attenuating sequelae of CRI such as bacterial translocation would be expected to improve acute survival after injury. From these data, it is not clear whether the combined effects of radiation and burn are additive or if modest burn amplifies the effects of sublethal radiation.
One might suggest that a two-hit phenomenon is occurring in ileum of animals exposed to CRI. The initial insult occurs at the time of injury and consists of ROS and inflammatory responses, with elevations in serum IL-6 and TNF-α, which have been shown at 6- and 48-h time points in CRI using this model (16). Another study corroborates inflammation occurring well after the initial injury using a similar murine model. Three days after exposure to 5 Gy TBI combined with a 20% TBSA burn with a heated rod, serum proinflammatory cytokines were elevated, specifically IL-5, IL-6, IL-10, IL-12, and MCP-1 (32). Disorganization of tight junctions and a prolonged state of apoptosis at 24 to 48 h postexposure contribute to epithelial breakdown, allowing penetration of endotoxins, bacteria, and other harmful substances well beyond the initial exposure. This could potentially explain increases in acute mortality after CRI when isolated radiation and burn injury fail to produce similar results. This second hit provides a window in which therapeutics could be administered to attenuate intestinal epithelial damage and assist regeneration of the gut epithelium. Blocking the apoptotic response seems like less of a viable option. Inhibiting caspase-8–mediated apoptosis in some cell lines has induced TNF-α–mediated necrosis (33). However, attenuating gut leakiness could prevent bacterial translocation and the subsequent inflammatory response. Myosin light-chain kinase (MLCK) is an important enzyme in the maintenance of the mucosal barrier of the intestine. Under inflammatory conditions, it has been shown to alter myosin-actin interactions by phosphorylation of the myosin light chain, resulting in cytoskeletal sliding and tight junction disruption (34). Cell-permeating peptide inhibitors of myosin light-chain kinase, such as permeant inhibitor of MLCK (PIK), have been found to reduce occludin disorganization away from tight junctions after inflammatory states, such as in a model of combined ethanol and burn injury. PIK could be used as an investigational agent in our model of CRI as well (35).
The use of nuclear technology and the potential for its implementation in warfare and terrorism highlight the importance of this study. Animal models will be paramount in the development of therapeutics in preparation for such events. Insight into the effects of CRI on the gut will help direct management of survivors of nuclear disaster. Further research into the mechanistic targets underlying gut-related morbidity and mortality associated with CRI may enable the development of effective mitigating agents.
The authors thank Dr. Mashkoor A. Choudhry, Dr. Martin Hauer-Jensen, and Michael Chen for thoughtful discussion.
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