Bupivacaine is a widely used anaesthetic injected locally in clinical practice for short-term neurotransmission blockade. However, persistent side effects on mitochondrial integrity have been demonstrated in muscle parts surrounding the injection site. We use the precise language of metabolic control analysis in the present study to describe in vivo consequences of bupivacaine injection on muscle energetics during contraction. We define a model system of muscle energy metabolism in rats with a sciatic nerve catheter that consists of two modules of reactions, ATP/PCr (phosphocreatine) supply and ATP/PCr demand, linked by the common intermediate PCr detected in vivo by 31P-MRS (magnetic resonance spectroscopy). Measured system variables were [PCr] (intermediate) and contraction (flux). We first applied regulation analysis to quantify acute effects of bupivacaine. After bupivacaine injection, contraction decreased by 15.7% and, concomitantly, [PCr] increased by 11.2%. The regulation analysis quantified that demand was in fact directly inhibited by bupivacaine (−21.3%), causing an increase in PCr. This increase in PCr indirectly reduced mitochondrial activity (−22.4%). Globally, the decrease in contractions was almost fully explained by inhibition of demand (−17.0%) without significant effect through energy supply. Finally we applied elasticity analysis to quantify chronic effects of bupivacaine iterative injections. The absence of a difference in elasticities obtained in treated rats when compared with healthy control rats clearly shows the absence of dysfunction in energetic control of muscle contraction energetics. The present study constitutes the first and direct evidence that bupivacaine myotoxicity is compromised by other factors during contraction in vivo, and illustrates the interest of modular approaches to appreciate simple rules governing bioenergetic systems when affected by drugs.

INTRODUCTION

In clinical practice, bupivacaine (as well as other drugs) is used to induce and maintain local anaesthesia thanks to iterative injections in the vicinity of nerves, where the drug spreads into contact with surrounding muscle tissues. Bupivacaine binds to the intracellular portion of sodium channels and blocks sodium influx into nerve cells, thus preventing depolarization. Although bupivacaine and other anaesthetics offer the benefits of extended analgesia and improved comfort as well as post-operative pain relief in patients, challenges remain for their use, because of their myotoxicity (side effects). In muscle tissues exposed to bupivacaine, several structural and functional alterations have been reported, including alteration of intracellular Ca2+ regulation [1], a wide range of abnormal histological patterns [2], fragmentation of the mitochondrial network [3], inhibition of mitochondrial respiration [4], uncoupling of oxidative phosphorylation [5], opening of the mitochondrial transition pore [5] and reduction in muscle mito-chondrial content [4]. All clinically used local anaesthetics are myotoxic, with a drug-specific and dose-dependent rate of toxicity that worsens with iterative or continuous administration [6].

To evaluate in situ myotoxicity of repeated injections of anaesthetics, a clinically relevant rat model of repeated injections with a femoral nerve block catheter has been developed [7]. To date, the myotoxicity due to drug injection through the catheter has been studied from excised muscle tissues. However, it is worth noting that the limited damages due to the positioning of the catheter offer a great opportunity for in vivo studies. An improved understanding of regulatory effects of the anaesthetics on energy metabolism could thus be gained by combining non-invasive 31P-MRS (31P-magnetic resonance spectroscopy) detection of phosphorylated intermediates in skeletal muscle with iterative injections through the catheter.

Studying regulation of a metabolic system either by drug injection, hormones or other molecules/effectors requires that the metabolic system be studied as a whole, a situation wherein supply and demand processes communicate together [8]. In contracting skeletal muscle, the pathways for supply of energy on one hand, and crossbridges and other processes that utilize energy (e.g. ATPases of the sarcoplasmic reticulum) on the other hand, are necessarily connected because both sets of molecular modules share common metabolic intermediates: ATP, ADP, Pi, Cr (creatine), PCr (phosphocreatine) and H+ ions. The products of myofibril ATPases are signals regulating the activity of energy supply processes and reciprocally the rate of energy supply modulates metabolite concentrations that influence crossbridge kinetics and force output. Actually, only a few reactions are necessary to advance the quantitative understanding of supply and demand processes [9,10]. It was thus demonstrated that these principles allow the ability to obtain critical information concerning energy flux regulation and to discern simple yet powerful rules governing the control of contraction [1113].

The more familiar biochemical approach to regulation is to try to identify the routes by which a drug causes changes in the rate of process or a group of reactions. There exist only few approaches that have the capacity to assess such metabolic regulations in integrated systems. Quantitative answers can yet be obtained from regulation analysis concepts of partial response coefficients (regulatory strengths [14]), an approach apparent from the early days of control analysis [15,16], but to which serious attention has been paid only in application to integrated metabolic systems [1720]. Our group has developed MoCA (modular control analysis) of the energetics of contraction in the beating heart [21] and has applied it to skeletal muscle [13], by combining tools of metabolic control analysis with non-invasive 31P-MRS. By using PCr as a surrogate of energetic intermediates because of a high signal-to-noise ratio for PCr in MRS, the ATP/PCr supply and demand system that is conceptually defined greatly simplifies the experiments that are required and the regulation patterns that are obtained thanks to a systemic approach [2227]. The main principles of MoCA are that the responses of the steady-state flux of ATP/PCr supply and ATP/PCr demand pathways to changes in concentration of their linking intermediate (PCr) are experimentally measured under conditions where other parameters and variables are constant. From these kinetic responses, i.e. modular elasticities, the influence of a change in activity of supply or demand processes on overall steady-state flux (i.e. flux control) can be calculated. The overall structure of internal controls can thus be described quantitatively in contracting skeletal muscle in vivo [13], and regulatory effects of an external effector on such a system can be described quantitatively [21,22,27,28]. Strictly speaking, the requirement in the definition of the elasticity coefficient that all other parameters and variables be held constant during the modulation of a local variable may appear to be hardly satisfied in experiments in vivo. However, with regard to muscle physiology, there exist a number of issues discussed in the present study that indicates that applying MoCA to contraction is reliable and brings outstanding information on muscle bioenergetic control in healthy animals [13] as well as in animals exposed to external stressors [26] or drug delivery (the present study).

In the present study we applied regulation analysis and elasticity analysis in vivo to quantify acute and chronic (long-term) effects of bupivacaine on muscle energetics during contraction respectively. Regulation analysis is carried out from the jump in steady state imposed by acute drug injection and describes the routes through which a single injection of bupivacaine affects contraction and PCr (energy state).

Elasticity analysis compares supply and demand responsiveness (elasticity) to PCr obtained 8 h after several injections of bupivacaine to those obtained in healthy control rats. The method is thus suitable for studying potential dysfunctions due to persistent effects of iterative injections of bupivacaine.

MATERIALS AND METHODS

Ethical approval

The present study complies with the European Community Guidelines for the Care and Use of Laboratory Animals, with the recommendations of the Directive 2010/63/EU of the European Parliament. Experiments were conducted in an authorized laboratory under the supervision of an authorized researcher. All of the protocols used were approved by our local ethics committee, Comité d'éthique Régional d'Aquitaine. The PD permanent license for experimentation is P.D.3308010 (03/17/1999).

Chemicals

Bupivacaine hydrochloride 0.5% (15 mM) was purchased from Astra Zeneca for rat administration.

Animals and injections

Experiments were conducted on adult (weighing 290–350 g) female Wistar rats. Rats were housed in a regulated facility with a 12 h light/12 h dark cycle, fed with chow and allowed free access to tap water. Eight rats served as the control group and eight rats were locally injected with bupivacaine with a sciatic nerve catheter. In the latter group, the day before MRS, rats were anaesthetized with intraperitoneal pentobarbital sodium (40 mg/kg of body weight) and subcutaneous injection of 10 mg of lidocaine. A plexus catheter (20 G, 0.9 mm outer diameter, Pajunk, Geisingen, Germany) was inserted near the right sciatic nerve sheath. It was fixed with stitches on the gracilis muscle, passed under the skin and exited at the neck. Incisions were subsequently closed by suturing. In the treated group of rats, neither self-mutilation following catheter placement nor catheter displacement were observed.

Seven perineural injections 8 h apart induced a decrease in pinprick sensation in the cutaneous distribution of the sciatic nerve, but not complete motor blockade in the first 1 h after each 1 ml/kg of body weight 0.25% bupivacaine injection. Each rat was investigated first at the occasion of the first single-shot injection of bupivacaine, while plantar flexor muscles were electrically stimulated inside the MRS magnet: this analysis is referred to as regulation analysis. At 8 h after the last perineural injection, each rat was investigated again to identify potential toxicity of iterative injections of bupivacaine on the energetics of contraction: this analysis is referred to as elasticity analysis. An additional experiment was carried out in two of the rats: a single-shot 1 ml/kg of body weight 5% (v/v) glucose solution was injected 15 min before the typical single-shot bupivacaine injection. Clearly without bupivacaine, glucose alone had no effect on steady-state levels of energetic intermediates, force output or the variables of the conceptual system studied (see below).

Experimental protocol

The experimental protocol was designed to obtain simultaneous measurements of phosphorylated muscle compounds by 31P-MRS and muscle contraction (force output) in electrically stimulated plantar flexors of rats in vivo as described previously [13]. The experimenter controlled the oxygen delivery (inhaled fraction of O2) through a facemask, the electrical stimulation of plantar flexors and injected the bolus of bupivacaine through the sciatic nerve catheter.

Briefly, rats anaesthetized by continuous delivery of 1.5% isoflurane in air through a facemask were placed inside a 4.7-T supra-conducting magnet (47/50, Biospec; Bruker). A surface coil tuned to 31P frequency was placed facing the plantar flexor muscles. Plantar flexors were electrically stimulated in a transcutaneous manner using surface electrodes (Compex II; Compex Medical SA). Contraction (force output) was measured thanks to a pressure sensor (MLT0699 plus Powerlab; ADInstruments). Muscle stimulation was progressively incremented then maintained at a constant level at least 30 min were allowed for stabilization of muscle activity before measurements of variables of interest (muscle PCr level and force output) were exploited under steady-state conditions.

In each experiment, the ‘reference’ steady state around which regulation analysis and elasticity analysis were carried out was characterized by the following muscle PCr levels: 17.7±1.8 mM in healthy control rats, 17.4±1.7 mM in rats before the first injection of bupivacaine (regulation analysis) and 17.3±2.0 mM 8 h after the last iterative injection (elasticity analysis). No difference was noted between these concentrations, even when expressed relatively to PCr at rest, which were 68±7%, 68±8% and 70±10% respectively.

Definition of the bioenergetic system

As described previously [13], the energy metabolism during muscle contraction was conceptually designed as a two-module system, ATP/PCr supply and ATP/PCr demand, that communicate through a group of energetic intermediates (ATP, ADP, Pi, PCr and Cr), as represented by a 31P-MRS-visible muscle PCr level under our conditions. PCr was chosen as representative of the group, because muscle level can be assessed in vivo by 31P-MRS with reliable signal-to-noise ratio, and because, under our conditions, the relative change in PCr is a surrogate of the relative change in the Gibbs free energy of ATP hydrolysis (ΔGp) or energy state, which is the true energetic intermediate in the two-module system. The supply module is then defined as all the steps from substrates and oxygen supply to mitochondrial PCr production through the PCr–Cr kinase system (Figure 1). The demand module comprises all of the ATP-consuming processes occurring during contraction (myosin ATPases and calcium re-uptake by the sarcoplasmic reticulum and cell membrane). Control and regulation in our modular system can be analysed using MoCA as long as changes in the intermediate (PCr) and module activities (flux) can be studied. Continuous 31P-MRS gives access to all phosphorylated energetic intermediates including our intermediate, PCr. The energetic flux through the system under steady-state conditions was simultaneously quantified by force output (Figure 2).

The conceptual bioenergetic system of contraction

Figure 1
The conceptual bioenergetic system of contraction

The system was conceptually defined as two modules grouping energy supply and energy demand processes. Muscle PCr is representative of the group of energetic intermediates. The steady state during contraction is defined by the system variables, PCr (intermediate) and force output (flux). ox. phos., oxidative phosphorylation.

Figure 1
The conceptual bioenergetic system of contraction

The system was conceptually defined as two modules grouping energy supply and energy demand processes. Muscle PCr is representative of the group of energetic intermediates. The steady state during contraction is defined by the system variables, PCr (intermediate) and force output (flux). ox. phos., oxidative phosphorylation.

Typical recordings of system variables for the study of acute effects of bupivacaine

Figure 2
Typical recordings of system variables for the study of acute effects of bupivacaine

Simultaneous recordings of 31P-magnetic resonance spectra and muscle force output under steady-state conditions effected by a single injection of bupivacaine (acute effect, regulation analysis). Bottom panel, successive spectra were acquired every 3 min, four spectra before injection (front) and four spectra after injection. The analysis of the bupivacaine-induced change in area under PCr peaks provided the ΔPCr required for regulation analysis. Top panel, force output during twitch contractions as recorded by the pressure sensor. The analysis of the bupivacaine-induced change in signal magnitude provided Δflux required for regulation analysis.

Figure 2
Typical recordings of system variables for the study of acute effects of bupivacaine

Simultaneous recordings of 31P-magnetic resonance spectra and muscle force output under steady-state conditions effected by a single injection of bupivacaine (acute effect, regulation analysis). Bottom panel, successive spectra were acquired every 3 min, four spectra before injection (front) and four spectra after injection. The analysis of the bupivacaine-induced change in area under PCr peaks provided the ΔPCr required for regulation analysis. Top panel, force output during twitch contractions as recorded by the pressure sensor. The analysis of the bupivacaine-induced change in signal magnitude provided Δflux required for regulation analysis.

Modulations of the steady state: determination of elasticities

In our MoCA application, the elasticity of one module is calculated from changes in flux (force output) and PCr concentration induced by a slight modulation of the other module. We used oxygen shortage to determine demand elasticity and a slight lowering of muscle electrical stimulation to determine supply elasticity. The reliability of this method is discussed below.

Steady states, either in the presence or absence of modulation, were defined by four to five magnetic resonance spectra (3 min duration for each) acquired concomitantly to force output. Averaged levels of phosphorylated compounds, pH and force output were calculated.

Flux-control coefficients

The flux-control coefficient of each module was calculated from experimentally measured elasticities according to summation and connectivity theorems [9]. These control coefficients represent how a modification of the activity of a module affects the overall contractile activity of the muscle: the more a module responds to changes in the intermediate PCr (high elasticity), the less this module controls contraction (low flux-control coefficient). Elasticity and flux-control coefficients allow the complete description of supply and demand interactions within the defined supply and demand system.

Regulation analysis: regulatory effects of acute injection of bupivacaine

Regulation analysis requires the complete and prior determination of elasticity and control coefficients before injection of bupivacaine. Then, changes in system variables (PCr and force output) induced by acute injection of bupivacaine served to characterize bupivacaine regulation of the steady state. In this scenario, the pattern of regulation is quantified using the principles of top-down analysis established by Ainscow and Brand [19], and applied by our group to the beating heart [21,27].

Regulation analysis has the potential to provide a quantitative description of how bupivacaine modifies muscle contraction, both globally and internally by describing its effect on each module of the supply and demand system. The effects of bupivacaine were quantified in the present study in terms of indirect effects (changes in local rates due to PCr changes) and direct effects on each module. Additionally, the global effect calculated for each module quantified how bupivacaine acts on contraction through each module (Figure 3).

Regulatory effects of a single injection of bupivacaine

Figure 3
Regulatory effects of a single injection of bupivacaine

Bupivacaine effects were calculated as devised by Ainscow and Brand [19]: direct effect refers to integrated elasticity, IE (total effect−indirect effect); global effect refers to integrated partial response coefficients (IR) calculated from IE and flux-control coefficient for each module. The size of the arrows is proportional to the bupivacaine effect as quantified from the percentage changes from control conditions. See the text for information.

Figure 3
Regulatory effects of a single injection of bupivacaine

Bupivacaine effects were calculated as devised by Ainscow and Brand [19]: direct effect refers to integrated elasticity, IE (total effect−indirect effect); global effect refers to integrated partial response coefficients (IR) calculated from IE and flux-control coefficient for each module. The size of the arrows is proportional to the bupivacaine effect as quantified from the percentage changes from control conditions. See the text for information.

Elasticity analysis: chronic effects after repeated injections

Potentially persisting effects of bupivacaine on the behaviour of the energetic control of contraction were tested by elasticity analysis that consists of comparing modular elasticities before any injection (healthy control rats) with those after iterative injections of the anaesthetic. Hence the protocol described above, i.e. modulation of the steady state by hypoxia and lowering of electrical stimulation, was repeated in treated rats 8 h after the last injection.

Statistical analysis

Experimental values are reported as means±S.D. for n independent experiments. Statistical comparisons were performed by ANOVA.

RESULTS

Elasticities and flux control in healthy control rats

The first step in the present work was the determination of modular elasticities in healthy control rats. As indicated in Table 1, the decrease in energy demand (lowering of electrical stimulation) induced an increase in PCr concentration (+20%) and a concomitant decrease in force output (−26%). Hypoxia induced a decrease in PCr (−24%) without a change in ATP, and a concomitant decrease in contraction (−11%). In each animal, co-variations in PCr and force output and the following equations were used to calculate elasticity coefficients:

 
formula

where ∂ indicates variations due to electrical modulation.

 
formula

where ∂ indicates variations due to hypoxia. Average values of elasticities in control rats are shown in Table 1 (together with corresponding data obtained in treated rats for the subsequent elasticity analysis – chronic effects).

Table 1
Experimentally induced changes in system variables and corresponding MoCA coefficients

Healthy control rats were compared with rats treated by iterative injections of bupivacaine (elasticity analysis). There is no statistical difference between control rats and rats treated by iterative injections of bupivacaine

TreatmentMeasurementControl ratsTreated rats
Hypoxia PCr (mmol/kg) 13.4±3.1 14.1±2.0 
Reference PCr (mmol/kg) 17.7±1.8 17.3±2.0 
Low stimulation PCr (mmol/kg) 21.2±2.8 20.7±3.2 
Hypoxia Force output (μV) 237±64 223±29 
Reference Force output (μV) 265±70 244±28 
Low stimulation Force output (μV) 197±92 178±38 
Elasticity Supply −2.0±1.3 −2.1±1.2 
 Demand 0.5±0.2 0.5±0.3 
Flux-control Supply 20% 20% 
 Demand 80% 80% 
TreatmentMeasurementControl ratsTreated rats
Hypoxia PCr (mmol/kg) 13.4±3.1 14.1±2.0 
Reference PCr (mmol/kg) 17.7±1.8 17.3±2.0 
Low stimulation PCr (mmol/kg) 21.2±2.8 20.7±3.2 
Hypoxia Force output (μV) 237±64 223±29 
Reference Force output (μV) 265±70 244±28 
Low stimulation Force output (μV) 197±92 178±38 
Elasticity Supply −2.0±1.3 −2.1±1.2 
 Demand 0.5±0.2 0.5±0.3 
Flux-control Supply 20% 20% 
 Demand 80% 80% 

In healthy control rats, supply elasticity (−2.0±1.3, the minus sign indicates that an increase in PCr reduces mitochondrial activity) was much more responsive to small changes in PCr than contractile processes (elasticity +0.5±0.2) under our conditions. The consequence is a dominant control over the steady-state flux on demand processes (80%) with low control (20%) by supply (Table 1).

Regulation analysis: acute effects of bupivacaine

Under our conditions, a single injection of bupivacaine immediately decreased contraction by 15.7±9.4% (Table 2). No change in ATP level was observed in magnetic resonance spectra following bupivacaine injection but a significant increase in PCr level of, +11.2±6.1% was observed.

Table 2
System variables before and after a single injection of bupivacaine (regulation analysis)

*P<0.05; **P<0.01, significant effect of a single-shot injection of bupivacaine.

MeasurementBefore injectionAfter injectionPercentage change
[PCr] (mM) 17.4±1.7 19.2±1.3* 11.2±6 
Force output (μV) 250±25 210±26** −15.7±9 
MeasurementBefore injectionAfter injectionPercentage change
[PCr] (mM) 17.4±1.7 19.2±1.3* 11.2±6 
Force output (μV) 250±25 210±26** −15.7±9 

These changes in PCr and contraction were used in combination with elasticity and the flux-control coefficient determined in healthy control rats to describe the regulation pattern by acute delivery of bupivacaine in healthy muscles (Figure 3).

First, indirect effects were calculated as the product of the percentage change in PCr and modular elasticities to PCr: supply was indirectly inhibited by −22.4%, but demand was activated by +5.6%. Then direct effects of bupivacaine were calculated as the difference between the total effect on contraction (−15.7%) and these indirect effects: direct effects of bupivacaine were dominantly on demand (−21.3%) with a small positive effect on supply (+6.7%).

Direct effects combined with modular flux-control coefficients allowed the quantification of the strength of the drug on the system through each route (global response through a module). The overall effect of bupivacaine is dominantly through demand inhibition (−17.0%) with negligible effects through supply (+1.4%).

The major outcome of regulation analysis is the absence of a direct negative effect, and even a positive effect (+6.7%) of acute injection of bupivacaine on energy supply during contraction. So bupivacaine in acute injection effectively inhibits ATP demand directly and ATP supply indirectly through changes in energetic intermediates.

Elasticities in treated rats: chronic effects of bupivacaine

The elasticity analysis compares modular elasticities obtained in healthy control rats with those obtained in rats 8 h after iterative injections of bupivacaine. As reported in Table 1, similar modulations of the steady state (hypoxia or decreased electrical stimulation) were carried out in each population.

In treated rats, the decrease of demand induced by the lowering of stimulation induced an increase in PCr (+20%) and a concomitant decrease in contraction (−27%). The effects of hypoxia, used to decrease energy supply activity, amounted to −18% in PCr and −9% in contraction. All of these effects are very similar to those observed in healthy control rats (Table 1). As a consequence, modular elasticities and flux-control coefficients were similar in healthy and in treated animals (Table 1).

DISCUSSION

There are two issues that could be addressed fruitfully by metabolic control analysis: acute effects of bupivacaine on metabolic regulation and secondary chronic effects. First, the application of regulation analysis allowed the quantification of the acute effect of a single injection of bupivacaine on activities of supply and demand parts of the metabolic system of muscle contraction as well as on the overall flux through the system; secondly, the application of elasticity analysis consisted of comparing supply and demand elasticities in healthy control rats to those in treated rats, 8 h after the last injection of the drug (seven injections 8 h apart to mimic the use in clinical practice).

These experiments were motivated by the demonstration by in vitro methodologies that, besides acute neuromuscular blockade and analgesia, bupivacaine also leads to some alteration of mitochondrial bioenergetics and histological damage in skeletal muscles. The major outcome of the present study was the absence of dysfunction in internal energetic control of muscle injected with a massive (iterative) dose of bupivacaine during contraction in vivo, as illustrated by the application of elasticity analysis.

Chronic effects of bupivacaine

The method to determine elasticities in a supply and demand metabolic system requires that the modulations applied to the steady state are specific to either supply or demand. The modulations used in the present study were hypoxia (supply) and the lowering of electrical stimulation (demand) respectively, keeping in mind that the integrative approach is carried out in vivo. Strictly speaking, the requirement in the definition of the elasticity coefficient that all other parameters and variables be held constant during the modulation of a local variable may appear to be hardly satisfied in vivo and we already quoted that MoCA in vivo is a method that gives crude elasticities. The most often mentioned concern is about the parameter intracellular Ca2+ changes during modulation of electrical stimulation, which might alter local rates [glycogenolysis or dehydrogenases in the TCA (tricarboxylic acid) cycle], thereby complicating the estimation of supply elasticity towards energetic intermediates. This potential side effect was neglected in the present study on the basis of previous experimental demonstrations that the characteristics of Ca2+ transients during twitch contractions and the kinetics of mitochondrial Ca2+ uptake [29,30] make intramitochondrial TCA cycle activation unlikely in our conditions. Indeed, we demonstrated that mitochondrial (TCA cycle, ATP synthase) activation effectively occurs in heart [21] and explains the main energetic difference between the heart and skeletal muscle, i.e. homoeostasis of energetic intermediates. Therefore this mitochondrial activation by Ca2+ is minimized in muscle. The control of glycogenolysis and glycolysis by Ca2+ in contracting rat skeletal muscle was recently discarded; rather, the control resides exclusively in factors related to the energy state, our intermediate [31]. At last, a significant implication of electrically induced vasodilatation resulting in increased oxygen availability and supply activation was also discarded because an immediate jump of force output to the new steady state was systematically observed after the electrical switch in our experiments, in a timescale in which a new state of oxygen distribution through vasodilatation could hardly take place.

With regard to hypoxia as a non-specific modulator of supply, we are not aware of any direct effect of acute hypoxia on myofibrillar ATPases, and it is believed that compensatory responses during exposure to hypoxia usually take place in a timescale that is not relevant to the current experiments.

Supply and demand elasticities determined in the present study in healthy control rats (Table 1) are in agreement with previous studies using either similar or different methodologies [11,13]. In skeletal muscle, the elasticity pattern depends on work rate; the values obtained in the present study (−2.0 and 0.5 for supply and demand respectively) are characteristic of intermediate levels of aerobic contraction. When determined by using similar experimental conditions, elasticities and flux-control coefficients were of similar magnitude in rats treated by iterative injections of bupivacaine as classically used in clinical practice (Table 1). These results constitute the first and direct evidence that bupivacaine myotoxicity, as shown by in vitro methodologies, is compromised by other factors during contraction in vivo. Clearly, MoCA points to the few critical rules that govern muscle contraction during moderate work rate. These rules are determined by relevant processes in muscle energetic control. Whereas a large spectrum of mitochondrial defects reported in the literature probably leads to a decline in maximal oxidative capacity of the tissue, a normal response of ATP supply to ATP demand may be preserved, as indicated by our elasticity analysis. Adverse effects on maximal capacity and sensitivity were already reported, for instance in hypoxic rats where citrate synthase activity was reduced, but supply elasticity was improved [25].

Integrated acute effects of bupivacaine

One bolus of bupivacaine injected locally triggered an inhibitory effect on contraction in vivo, characterized by a 15.7% decrease in force output (Table 2). Results obtained from 31P-MRS synchronized to contraction highlighted a concomitant increase in PCr concentration (+11.2%) induced by bupivacaine, without any change in ATP concentration or muscle pH (Figure 2). Such a change in the energy state results from unbalanced effects on supply and demand processes quantified in the present study by direct effects. The direct effect of bupivacaine was dominant on demand, amounting to −21.3% (the minus sign indicates inhibition) compared with a small direct effect on supply amounting to +6.7%, where the plus sign indicates activation. The direct negative effect of bupivacaine on demand is not difficult to explain. It is the well-known consequence of the effect of bupivacaine on sodium channels blocking sodium influx into motor neurons and thereby preventing depolarization. The result is a lower neural input, although electrical stimulation was unchanged, that naturally attenuates Ca2+ pulses, myofibril activation and the rate of energy demand. In contrast, the slight direct activation of ATP/PCr supply processes by a single injection of bupivacaine in vivo is more appealing. In fact, in vitro methodologies reported deleterious effects of bupivacaine on mitochondrial energetics (making inhibition rather than activation expectable). Activation might yet be explained in the light of substantial perturbation of Ca2+ transients by bupivacaine demonstrated previously [32]. After acute injection of the local anaesthetic at the site of action (nerve extremity), the drug generally spreads into contact with neighbouring muscles and nerves, as observed by ultrasonic [33] and magnetic resonance imaging methods [3]. The slight activation of supply quantified in the present study may correlate with immediate damage induced by bupivacaine at the sarcoplasmic reticulum level. Owing to its pronounced lipophilicity, the injected bupivacaine rapidly accumulates in the myoplasm. A previous study revealed that bupivacaine at clinical concentrations not only induces Ca2+ release from the SR, but also inhibits Ca2+ reuptake into the SR, which consequently results in a massive increase in intracellular Ca2+ levels [32]. Although Ca2+ is considered a poor activator of mitochondrial ATP synthesis under physiological conditions in myocytes activated by normal excitation–contraction coupling [11,29,30,34], abnormally high concentrations of cytosolic Ca2+ resulting from sarcoplasmic reticulum disruption might activate mitochondrial dehydrogenases, thus explaining the direct (although slight) activation of our supply module in vivo.

It is worth noting that this positive direct effect on supply local rates after bupivacaine injection is too small to induce significant changes in contraction. This is quantified by the global effect (integrated partial response, IR) on contraction through this mitochondrial activation, which is below +2% due to the low flux control by supply, whereas the global effect through demand is −17% (Figure 3).

Regulation analysis allowed describing how the increase in PCr (and the corresponding decrease in free Cr) after bupivacaine injection blunted mitochondrial activation (indirect effect). Owing to the high elasticity of supply to PCr (−2.0), the increase in PCr (+11.2%) results in a decrease in mitochondrial energy production amounting to −22.4%. In contrast, demand elasticity is low (0.5) and demand therefore responded weakly to the increase in PCr (+5.6%).

To summarize, regulation analysis demonstrates that a single injection of bupivacaine immediately attenuates myofibril activation as the main effect, which in turn constitutes the reason why contraction declines in vivo immediately after drug injection. The concomitant inhibition of energy supply processes does not result from direct mitochondrial impairments by bupivacaine, but is the consequence of changes in energetic intermediates. Therefore this mechanism has no effect on flux at the systems level (contraction).

Conclusion

The main effect of a single injection of bupivacaine on the energetics of contraction in vivo is a decrease in ATP demand, as a result of a neural transmission blockade. This phenomenon fully explains the decrease in contractile performance, since no other significant effects were noted through the supply processes. On the basis of the slight positive direct effect of a single injection on mitochondrial activity, probably due to Ca2+ perturbations, no acute deleterious effects of bupivacaine through integrated mitochondrial regulation of contraction were reported.

Healthy (normal) elasticities of supply and demand processes in rats after several injections of bupivacaine (classic protocol in clinical practice) demonstrate the absence of persistent abnormalities in the mitochondrial response to ATP demand. This does not exclude the myotoxicity of the anaesthetic, but interestingly demonstrates a healthy bioenergetic behaviour of contraction 8 h after the last injection.

The results of the present study illustrate the possible application of MoCA in vivo for the discrimination of physiological/biochemical relevant effects of drugs/hormones on integrated bioenergetic systems.

Abbreviations

     
  • Cr

    creatine

  •  
  • MoCA

    modular control analysis

  •  
  • MRS

    magnetic resonance spectroscopy

  •  
  • PCr

    phosphocreatine

  •  
  • TCA

    tricarboxylic acid

AUTHOR CONTRIBUTION

Rodrigue Rossignol, Karine Nouette-Gaulain and Laurent Arsac designed the experiments. Karine Nouette-Gaulain inserted catheters and supervised bupivacaine injections. Laurent Arsac, Sylvain Miraux and Karine Nouette-Gaulain performed the experiments. Eric Thiaudiere helped to analyse the NMR data. Laurent Arsac, Philippe Diolez and Veronique Deschodt-Arsac carried out the metabolic control analysis. Laurent Arsac wrote the paper with the help of Philippe Diolez and Veronique Deschodt-Arsac.

FUNDING

This work was supported by Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen and Conseil Regional d'Aquitaine.

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