Kehl, Lois J.1; Fairbanks, Carolyn A.2 3 4
Clinically treated pain states principally involve pain of muscle, joint, or visceral origin. Unfortunately, most of our knowledge regarding pain mechanisms is based on studies of cutaneous tissue. Relatively little is known about the activation of joint or visceral nociceptors, and perhaps least of all about muscle nociceptors. This is largely because of the multiple inputs that influence muscle sensation, including muscle spindles, tendon receptors, joint receptors, and skin receptors as well as CNS processing of these inputs. The complexity of these many inputs complicates the process of elucidating the mechanisms involved in transmitting and modulating pain from the deep tissues of the musculoskeletal system. In practical terms, this lack of knowledge reflects a real void in the understanding needed to treat musculoskeletal pain effectively, even though it is one of the most frequent symptoms for which patients seek medical treatment.
In the clinical setting, pain may be refractory to pharmaceutical interventions or patients may refuse to take pain medication because of adverse side effects. Furthermore, pain originating from different tissues or as the result of different disease processes responds differently to various drugs or therapies (e.g., ultrasound, transcutaneous electrical nerve stimulation, iontophoresis) used for pain management for reasons that may not be fully understood. The mechanistic differences governing the multiplicity of clinical pain conditions has received recognition relatively recently by scientists studying nociception and analgesia. Refinement of animal models and methods for assessing pain thresholds under varied conditions has greatly expanded the potential for identifying those differences.
Previously, standard animal models used to study pain mechanisms relied on various nerve injuries and tissue inflammation of the paw to evaluate pain responses and the efficacy of analgesics. Most standard dependent measures assess the subject’s response to stimulation of nerve endings that innervate the epidermis (of the paw, for example). However, pain is a response to stimulation of nerve endings in a variety of tissues, not merely epidermal tissue. The impact of exercise and movement on pain thresholds and efficacy of analgesics has received limited attention in basic science investigations. Development of several new models that specifically assess hypersensitivity caused by noxious stimuli in muscle may help to understand pain originating from muscle. This paper profiles these new animal models that are improving our understanding of muscle hyperalgesia and analgesia. Hyperalgesia is a term the describes the increase in sensitivity to normally noxious stimuli that an organism may experience after inflammation, injury, or another physiologic change that lowers the threshold to pain. Analgesia refers to the reduction in sensitivity to noxious stimuli that an organism detects, often as a result of the administration of pain-relieving drugs, such as morphine.
EXERCISE-INDUCED MUSCLE HYPERALGESIA
Prolonged eccentric exercise is well known to produce muscle injury, inflammation, and delayed-onset muscle soreness (DOMS) in humans (3). DOMS is characterized by muscle weakness and infiltration of inflammatory cells into the affected tissues. Consequently, to elucidate mechanisms of human muscle pain, some investigators have attempted to reproduce this phenomenon in animal models.
One such animal model used eccentric treadmill exercise to model DOMS in rats as follows. Sprague Dawley rats performed one of two exercise protocols: (a) in the experimental group, rats ran on a treadmill (60 m·min−1 at an approximately 30° downhill incline for 15 min, twice in 2 h; or (b) in the control group, rats were placed on a treadmill at a walking pace (6 m·min−1 for 15 min, twice in 2 h). After this exercise protocol, animals were tested at intervals over the next several hours for their capacity to perform resisted flexion of their forelimbs against a force transducer (also known as forelimb grip force) (4). In the experimental group, prolonged eccentric exercise resulted in a significant time-dependent reduction in forelimb grip force over the 48-h observation period (P < 0.005) with peak reduction in forearm grip force occurring 18 to 24 h after exercise (Fig. 1). Reduction in grip force was reversed by the μ opioid agonist levorphanol (3 mg·kg−1 intraperitoneally [i.p.]; P < 0.05) but not levorphanol coadministered with the opioid antagonist naltrexone (3 mg·kg−1 i.p.;Fig. 2). Because opioids are not known directly to affect (e.g., enhance) muscle force, the observed reversal of grip force reduction by the opioid is consistent with an analgesic effect rather than the result of increased muscle force production. This result provided evidence that the eccentric exercise protocol described above produced muscle hyperalgesia. Unfortunately, because of the labor-intensive nature of this protocol and because the magnitude of hyperalgesia (measured by reduction in grip force) was not large enough to discriminate drug effects in pharmacologic experiments, this model for DOMS was not developed further.
CARRAGEENAN-INDUCED MUSCLE HYPERALGESIA
A second experimental paradigm reproduces the muscle inflammation associated with DOMS without the possible confound that eccentric exercise-induced muscle fatigue or analgesia could produce. This model (5) uses bilateral intramuscular injections of carrageenan (4 mg·75 μL−1 phosphate buffered saline [PBS]) into the triceps muscles of rodents to produce a localized inflammatory response similar to the inflammation produced during eccentric exercise. Carrageenan is an extract of seaweed that causes localized inflammation when administered to various tissues and is used in some standard animal models of inflammatory pain as a pain-producing stimulus. In this model of muscle hyperalgesia, the amount of forelimb force (i.e., forelimb grip force) exerted by rodents after carrageenan injection is compared with force exerted before injection and used as a behavioral dependent measure of hyperalgesia.
Several studies have shown that patients with chronic muscle pain exert reduced force with their tender muscles. Furthermore, reduced muscle strength strongly correlates with increased numbers of tender points in pain patients. This reduction in force exertion by painful muscles most likely is the result of a reduction in the activity of agonist muscles and an increase in the activity of antagonist muscles. These reports and others formed the basis for choosing reduced forelimb grip force as a behavioral index of hyperalgesia in the rodent model of muscle hyperalgesia described next.
In this model, forelimb grip force measurements are acquired before carrageenan is injected and then at various intervals after carrageenan. Typically, rats exhibit a 160-g reduction in forelimb grip force 12 to 24 h after carrageenan administration, whereas mice exhibit a 40-g peak reduction 48 h after carrageenan administration. Several experimental results validated the reduction of forelimb grip force after intramuscular carrageenan administration as a measure of muscle hyperalgesia (5,15). In particular, the peak reduction in forelimb grip force was reversed within 30 min after administration of several drug classes (i.e., the opioids levorphanol [1 mg·kg−1 i.p. in rats] and morphine [ED50 5.3 mg·kg−1 i.p. in mice], the nonsteroidal antiinflammatory drug indomethacin [4 mg·kg−1 i.p. in rats], and the steroid dexamethasone [4 mg·kg−1 i.p. in rats]) used clinically to treat muscle pain. If the reduction in grip force had been the result of muscle fatigue, analgesic drugs would not have been able to reverse this effect. Furthermore, if muscle injury had been responsible for the reduced forelimb force, then this effect would not have been reversible within 30 min after drug administration. Collectively, these studies provide support that reduction in forelimb grip force is a valid assessment of muscle hyperalgesia.
Behavioral models of nociception are widely used efficiently to screen potential analgesic compounds for therapeutic efficacy in the treatment of human pain. Although not always mirroring naturally occurring painful conditions (e.g., tail flick test, formalin test, intrathecal substance P test), the value of these models lies in their capacity to predict reliably which pharmacologic compounds will be analgesic when administered to pain patients. Therefore, because the model of carrageenan-evoked muscle hyperalgesia reliably evokes a behavioral response reported by muscle pain patients (i.e., reduction in grip force), is reversed by several clinically useful analgesic agents, demonstrates an amplitude of effect that allows pharmacologic testing, and shares an inflammatory component with DOMS, this model has gained popularity.
TUMOR-INDUCED MOVEMENT-RELATED PAIN
Another type of movement-related pain, termed breakthrough pain, is a common problem for patients with cancer pain and is considered to be a predictor of poor response to conventional analgesic agents. Recently, a new animal model of movement-evoked cancer pain was developed to facilitate the investigation of mechanisms contributing to breakthrough pain (15). It uses the implantation of NCTC 2472 sarcoma cells into the humerus bones of C3H/He mice to simulate the development of osteolytic sarcoma, a form of bone cancer, in these animals. As in the carrageenan model described above, the investigators inferred the degree of insult-induced, movement-related hyperalgesia from changes in the level of peak force exerted by these animals’ forelimbs using the grip force assay.
In addition, to determine whether secondary mechanical allodynia of the forepaws contributed to the reductions in grip force observed in this assay, cutaneous forepaw hypersensitivity was evaluated using von Frey filaments. von Frey filaments are a series of approximately 2-cm long nylon monofilaments, similar to fishing line, with increasing diameters that bend when a known amount of force (1–358 mN) is applied to them. During a typical experiment, mice are placed on a wire mesh platform and are allowed to acclimate to their surroundings for a minimum of 15 min before testing. von Frey filaments delivering varying levels of force (1–15 mN is the typical range for mice) corresponding to varying diameters of the filament are applied to the point of bending to the plantar surface of the paw. Each test stimulation lasts approximately 3 s. When the stimulus is of sufficient force, the rodent licks, withdraws, or shakes the paw, or a combination thereof; this action represents the behavioral endpoint. The stimulus terminates completely after 1 to 3 s or immediately after paw withdrawal. Based on the forces at which the animal withdraws, a threshold can be calculated to predict the force at which an animal would withdraw 50% of the time, which is somewhat analogous to an ED50 dose in pharmacology. Normal rats do not respond even to high forces delivered by von Frey monofilaments applied to the point of bending (normal mice respond at 10 mN). Rats subjected to inflammation or nerve injury will withdraw to low forces (approximately 115 mN, injured mice at 1 mN). This is considered a manifestation of mechanical hypersensitivity or hyperalgesia indicating that the thresholds to activation of the pain pathways have been lowered. The reduction in the force that elicits this withdrawal is used as a measure of hyperalgesia.
Using this model of movement-evoked pain, Wacnik et al. (15) performed a series of experiments to compare the relative effectiveness of two different analgesic agents for reversing tumor-evoked and carrageenan-evoked deep tissue hyperalgesia. The first study evaluated the analgesic potency of the μ opioid agonist morphine. Behavioral indices of hyperalgesia (i.e., plantar forepaw von Frey fiber testing and peak forelimb grip force) were measured at baseline, before injection of tumor cells (bilateral humeral injections of 2 × 105 2472 cells in a volume of 10 μL PBS) or carrageenan (bilateral injections of 4–8% carrageenan in 40 μL PBS to the triceps), and repeated at various intervals up to 10 d (tumor) or 17 d (carrageenan) after insult. Morphine was administered intraperitoneally at the time when peak hyperalgesia was present in both animal models (10 d after tumor cell implantation and 48 h after carrageenan injection), and grip force was measured 30 min later. In this study, 3 to 30 mg·kg−1 morphine dose dependently returned grip force measurements toward baseline levels in both tumor-bearing (ED50 19.8 mg·kg−1) and carrageenan-injected (ED50 5.3 mg·kg−1) mice. Both tumor cell implantation and injection of 4% carrageenan produced apparent forelimb hyperalgesia without mechanical allodynia in the forepaws, whereas 6% and 8% carrageenan did evoke significant cutaneous allodynia of the forepaws. Control groups receiving identical implants, injections of PBS, or no treatment at all did not manifest this forelimb hyperalgesia.
In a follow-up study, Kehl et al. (6) used a very similar experimental paradigm to compare the analgesic potency of the cannabinoid agonist WIN55,212–2 for reversing tumor- and carrageenan-evoked hyperalgesia. This compound acts nonselectively at two subtypes of cannabinoid receptors: CB1 receptors, located primarily in the CNS and on primary afferent fibers, and CB2 receptors, located primarily on immune cells. In a series of experiments, these investigators evaluated whether WIN55,212–2 dose dependently reversed tumor- and carrageenan-evoked movement-related hyperalgesia and which receptor subtypes participated in the cannabinoid’s analgesic effects. The results of this study indicated that WIN55,212–2 is approximately four times more potent in reversing carrageenan-evoked hyperalgesia (ED50 = 5.6 mg·kg−1) than tumor-evoked hyperalgesia (ED50 = 23.3 mg·kg−1). Furthermore, in the cancer pain model, WIN 55,212–2’s antihyperalgesic effect was partially blocked by pretreatment with the CB1 (SR141716A) but not the CB2 (SR144528) receptor antagonist. In contrast, both the CB1 and CB2 receptor antagonists blocked antihyperalgesic effects of WIN55,212–2 in the carrageenan model of muscle hyperalgesia. These results provide evidence that CB1 receptors participate in the antihyperalgesia produced by WIN55,212–2 in the cancer pain model but that both receptor subtypes contribute to the antihyperalgesia observed in the carrageenan model that uses an inflammatory pain stimulus. These data provide evidence that cannabinoids differentially modulate tumor- and carrageenan-evoked hyperalgesia and suggest that differences in underlying mechanisms may exist between these two models of deep tissue pain.
Collectively, the studies described above provide evidence that the humeral implantation of osteolytic sarcoma cells in conjunction with forelimb grip force testing provides an animal representation of the movement-related hyperalgesia, or breakthrough pain, frequently associated with cancer. This animal model likely will provide a useful tool to assist in discerning the peripheral and central mechanisms underlying pain that accompanies bone metastases and will allow testing of new analgesic agents for management of cancer pain.
ACID-INDUCED MUSCLE SORENESS
A third approach for modeling muscle hypersensitivity in rodents takes advantage of the observations that tissue pH decreases after inflammation and isometric exercise. This approach is supported further by observations in human clinical experiments that low pH (5.2) evokes some mild detectable muscle pain sensations. Sluka et al. (12) characterized the nociceptive responses of rodents subjected to injections of a wide range of low pH saline in the gastrocnemius muscle. Halothane-anesthetized male Sprague-Dawley rats (250–400 g) were administered 100 μL of sterile saline acidified to a pH of either 4, 5, 6, or 7.2 (nonacidic). These injections reduce the pH of the injected tissue to a level within the pH range that occurs after tissue injury, inflammation, and exercise. These injections were repeated at different intervals ranging from 2 to 10 d. When spaced between 2 and 5 d apart, injections of pH 4.0 saline will cause a long-lasting (30 d) mechanical (but not thermal) hyperalgesia. Mechanical hypersensitivity was assessed using the von Frey monofilament method. The muscle hypersensitivity in rodents does not appear to be accompanied by inflammation or necrosis (determined by histologic examination). Consequently, Sluka et al. currently are investigating the mechanistic source of the observed acid-induced muscle hypersensitivity. Injection of low pH saline into the gastrocnemius muscle could act directly on a newly discovered ion channel thought to be involved in pain signaling (10). Acid-sensing ion channels have been localized to small and medium primary afferent neurons and in synaptic terminals in the superficial dorsal horn, a region in the spinal cord that mediates pain signaling. Activation of these channels results in electrical currents that are consistent with those that are thought to signal pain. Decreasing pH in the region of primary afferent peripheral terminals in the gastrocnemius muscle could activate this channel and could drive an electrical signal of pain. Evidence to support this hypothesis was shown in a study where genetically altered mice that do not have the gene for the ASIC channel found in the dorsal root ganglion (DRASIC) were tested to see if they would develop mechanical hyperalgesia in response to injection of pH 4.0 saline. Normal (DRASIC-containing) litter mate controls to the knock-out mice did, as expected, experience mechanical hypersensitivity after injection of acidic (pH 4.0) saline. In contrast, the DRASIC-KO mice experienced some mechanical hypersensitivity compared with preinjection responses; however, the magnitude of the hypersensitivity was significantly less than their normal litter mate counterparts. This result suggests that DRASIC may, in fact, contribute to acid-induced changes in muscle soreness, at least in this murine model (10). The mechanical hyperalgesia manifested by the acidified saline injections is alleviated by administration of gold standard analgesics such as the μ opioid receptor-selective agonists morphine and DAMGO (D-Ala(2), Me-Phe(4),Gly(ol)(5)]enkephalin) as well as the delta opioid receptor-selective agonist SNC-80 (13). This evidence supported the assertion that the model reflects a true nociceptive event. Furthermore, antagonism of N-methyl-D-aspartate (NMDA) receptors and non-NMDA glutamate receptors by administration of APV (D-(-)-2-amino-5-phosphonovalerate) and NBQX (2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo-[f]-quinoxaline-7-sulfonamide), respectively, 1 week after the second intramuscular injection of acidified saline (pH 4.0) reversed mechanical hypersensitivity (11). These results indicate that, similar to other chronic pain syndromes, NMDA and non-NMDA receptors contribute to the maintenance of mechanical hyperalgesia in this model. This report also suggests that the intramuscular injection of acidified saline model invokes plastic changes within the dorsal horn of the spinal cord that may account for the duration of this chronic mechanical hypersensitivity.
Exercise has been reported anecdotally to increase pain thresholds in patients. Biochemical support for this phenomenon has been provided by animal models of swimming (14). Natural (endogenous) pain relievers (analgesics) that are synthesized and localized in the brain may account for the increase in pain threshold in subjects that are exercised. There are several classes of analgesic neurotransmitters that likely contribute to this phenomenon. The first class includes the “morphine-like” or opioid peptides. These peptides are called endorphin, endomorphin, enkephalin, and dynorphin. They act on proteins that reside in the lipid bilayer of the cell membranes of neurons in the brain and in the spinal cord. These proteins are known as the μ, δ, and κ opioid receptors. Activation of these receptors (by morphine or by these endogenous neurotransmitters) causes a neuron to hyperpolarize such that electrical signals of pain cannot be transmitted through the neuronal circuitry to the brain. Epinephrine and norepinephrine (catecholamines) are neurotransmitters that act on a separate class of neuronal proteins to inhibit pain signaling. When given in combination, norepinephrine and the opioid peptides will “synergize” to give a superadditive analgesic effect that is a level of analgesia greater than the sum of analgesia achieved by the two drugs given individually.
In animal models of exercise, it has been shown that concentrations of β-endorphin (14) and catecholamines (9) are increased centrally and peripherally in exercised rodents compared with nonexercised controls. Similarly, plasma β-endorphin (2) and norepinephrine (8) levels have been observed to rise significantly in humans after acute or chronic exercise, respectively. It is, therefore, possible that the reported exercise-induced analgesia or the increased pain thresholds are attributable to increased basal β-endorphin levels acting on μ or δ opioid receptors to exert an analgesic effect alone or to potentiate exogenously administered analgesics. Recently two more endogenous opioids have been identified: the discovery of mu opioid receptor selective tetrapeptides endomorphins 1 and 2 raise the possibility that those entities also participate in these processes (although this hypothesis remains to be tested). It is likely that further investigations will be conducted to assess the impact of these molecules.
EXERCISE-INDUCED REDUCTION IN ANALGESIA
In contrast to the reports of exercise-induced analgesia, there may be some instances where chronic participation in exercise may, in fact, decrease the efficacy of analgesics. In several rodent models of exercise including wheel running (7) and swimming (1), the analgesic potency of exogenously applied morphine was decreased. Several possibilities may explain this phenomenon. It is conceivable that chronic upregulation of opioid peptides (e.g., enkephalin, endorphin, and endomorphin) or norepinephrine could cause tolerance at their respective cell membrane receptors. Tolerance could result from a decrease in available receptor number or a decrease in the signal transduction machinery such as is depicted in Figure 3. In these studies, it was observed that acutely induced exercise did not reveal tolerance to opioid-induced analgesia and that chronic exposure to exercise was required to observe this effect. However, we have conducted a study that may have detected an acutely induced analgesic tolerance after prolonged exercise during a single session on the rotorod (Ugo Basile, Italy).
MILD ACUTE ANALGESIC TOLERANCE AFTER EXERCISE IN MICE
Substance P (SP) is a neurotransmitter that is released in the spinal cord in response to noxious stimuli at the periphery. SP carries the pain signal to secondary neurons that reside in the spinal cord and subsequently carry the information about pain to higher brain centers. Direct intrathecal injection (5 μL) of exogenous SP (15 ng) in Institute of Cancer Research (ICR) mice results in biting, licking, and scratching behaviors directed to the hind limb for 1 min after the injection. These behaviors can be counted and used for quantification. SP-induced behaviors are dose dependently alleviated by opioid and α2AR agonists in a naloxone-sensitive and idazoxan-sensitive manner, respectively, indicating that this behavior can be used as a model of pain. This model has been approved by the University of Minnesota Institutional Animal Care and Use Committee. The correspondence between results using SP and standard antinociceptive tests (e.g., tail flick) support the usefulness of the SP assay for antinociceptive inference. We used the SP assay to assess the analgesic efficacy of low intrathecal doses of two combined α2AR adrenergic analgesics, clonidine and dexmedetomidine. These drugs are commonly used in the clinic for the treatment of pain and for anesthesia. To simulate exercise, mice were first trained to walk for 300 s on an accelerating rotorod device. The suspended rotorod (diameter is 3 cm) rotates in space and accelerates from 4 to 40 rotations·min−1 within the 5-min session. The rotorod often is used to assess sedation and motor performance after drug administration. In the first training sessions, the mice fall off (6 inches to the platform) the rotorod within the first minute. After being reintroduced to the rotorod several times, the mice learn to stay on the rotorod for the 5-min training duration. Different strains of mice show different training requirements. ICR mice learn to remain on the rotorod for the 5-min period within two training sessions. C3H mice require three to four training sessions, and a mixed hybrid of C57BL/6 and 129sv mice require five to six training sessions to learn to walk on the rotorod for 5 min. For these experiments, we used ICR mice. After they acquired the skill, they were expected to walk on the accelerating rotorod for 300 s. The rotorod was stopped, and the second session began (initially of slower speed 4 rotations·min−1 ramping up to 40 rotations·min−1 within the 5 min). Therefore, the exertion level was variable during the 30 min that comprised the five sessions of accelerated walking.
Immediately after the end of the 30 min, the mice were given the SP nociceptive behavioral test either without (to establish a baseline control group) or with the analgesic combination of clonidine plus dexmedetomidine (the dose of both drugs was either 0.3 pmole·5 μL−1 or 1 pmole·5 μL−1). In animals that had been trained to walk on the rotorod a day earlier but had not been acutely exercised, those two doses of clonidine plus dexmedetomidine demonstrated partial efficacy in inhibiting the SP-evoked behavior (Fig. 4). However, the analgesic efficacy of those two dose combinations was completely abolished in mice that had been acutely exercised (as described above) on the rotorod (Fig. 4). Higher doses of either drug given alone were effective in the acutely exercised mice on the rotorod. We only observed this ablated analgesic efficacy at the very low dose-combination of lower analgesic efficacy doses. Given the fact that in the previous studies the analgesic tolerance was only observed in chronically exercised animals, it is probable that a mild acute tolerance or acute cross-tolerance from potential exercise-induced release of endogenous analgesic neurotransmitters (e.g., enkephalin, endomorphins 1–2, endorphin) may be detectable only at very low doses of exogenous analgesics. We have reported previously that acute tolerance to exogenous spinal administration of the endogenous neurotransmitter endomorphins 1–2 can occur in ICR mice, and so it is conceivable that this could be an explanation, but more studies would be needed to test that hypothesis.
The recognition that “pain” originates from diverse dysfunctional physiologic states is a relatively recent development in the field of pain research. Previously, most information available regarding the transmission and modulation of pain was based on studies performed on cutaneous tissue. However, this new appreciation by basic scientists, that clinical pain states result from a variety of causes, has inspired development of new models specifically to examine pain originating from peripheral (i.e., neuropathic pain) or central nervous system (i.e., spinal cord injury pain) disruption as well as from viscera (i.e., cardiac ischemia, painful bowel distention) and deep tissues (i.e., cancer pain, muscle pain, fibromyalgia, arthritis). These and other painful conditions currently are being evaluated for differences that may facilitate specific and targeted treatment strategies.
One excellent example of the value that animal models have for improving clinical pain management is the rapid advances made in neuropathic pain management since the development of a few animal models for neuropathic pain in the late 1980s and early 1990s. These animal models established precedent for Food and Drug Administration approval of new uses for existing drugs (i.e., antidepressants) as well as development of new drugs specifically targeted to block pathophysiologic mechanisms specific to neuropathic pain. Unfortunately, our understanding of deep tissue pain mechanisms lags behind. Currently, the best therapeutic result that many patients with chronic deep tissue pain can achieve is only partial relief of symptoms. The inability to manage these chronic pain states fully results in substantial time lost from work for those affected as well as disruption of family function and frequently in depression. In the absence of animal models, determination of the mechanisms underlying muscle pain and exercise-induced analgesia (or diminished analgesia) would not be possible. Development of novel pharmaceutical agents and therapeutic methods that specifically target these painful conditions will increase in precision as these new models are more widely applied in research and as new models expand the experimental repertoire.
The authors thank Dr. Ken Hargreaves and Mr. Tom Trempe for their contributions to development of the forelimb grip force assay and the exercise- and carrageenan-evoked muscle hyperalgesia studies described here. A Mentored Scientist Career Development Award (K01-DA00509) provided by the National Institute on Drug Abuse (NIDA) supported CAF’s contribution to this manuscript. A NIDA Scientist Development Award (K21-DA00240) supported development of the models reported by LJK.
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