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Neuroscience Letters 584 (2015) 184–189 Contents lists available at ScienceDirect Neuroscience Letters jo ur nal ho me p age: www.elsevier.com/locate/neulet Gait analysis in three different 6-hydroxydopamine rat models of Parkinson’s disease Ming Zhou a , Wangming Zhang a,, Jingyu Chang b , Jun Wang a , Weixin Zheng a , Yong Yang a , Peng Wen a , Min Li a , Hu Xiao a a Department of Neurosurgery, Zhujiang Hospital, Southern Medical University, Guangzhou 510282, Guangdong Province, China b Neuroscience Research Institute of North Carolina, Winston-Salem, NC, USA h i g h l i g h t s The gait readouts in the MFB and SNC 6-OHDA rats are more profound than the CPU. Many gait parameters show a close correlation with the protein levels of TH. CatWalk system can provide reliable and objective criteria to stratify gait changes arising from 6-OHDA rats. a r t i c l e i n f o Article history: Received 31 July 2014 Received in revised form 11 October 2014 Accepted 16 October 2014 Available online 24 October 2014 Keywords: Parkinson’s disease Gait CatWalk 6-Hydroxydopamine Neurochemical correlation a b s t r a c t Gait deficits are important clinical symptoms of Parkinson’s disease (PD) but are rarely studied. In this study we made three different rat PD models by administration of 6-hydroxydopamine into caudate puta- men (CPU), medial forebrain bundle (MFB) and substantia nigra compact (SNC). We evaluated the gait changes in these models by using a computer-assisted CatWalk system. Correlations of gait parameters with tyrosine hydroxylase protein levels in the CPU and SNC were also investigated. The gait readouts were significantly impaired in both the MFB and SNC groups. However, the MFB group showed a more pronounced impairment than the SNC group. In contrast, only mild and incomplete gait impairment occurred in the CPU group. In addition, some gait parameters demonstrated close correlation with the protein levels of TH. This paper suggests that the 6-hydroxydopamine-induced MFB model is more propi- tious to study gait dysfunction than the other two models and the CatWalk system can provide reliable and objective criteria to stratify gait changes arising from 6-hydroxydopamine lesioned rats. These findings may hold promise in the study of PD disease progression and new therapeutic methods. © 2014 Elsevier Ireland Ltd. All rights reserved. 1. Introduction Parkinson’s disease (PD), a pervasive motor disease, results from the depletion of dopamine (DA) in the nigrostriatal region of the central nervous system [1]. As PD progresses, gait disturbance and postural instability become increasingly prominent [2]. Thus, ameliorating gait disturbance is vital for PD patients to prevent unexpected injury, disability, and improve their qualities of life [3]. The 6-hydroxydopamine (6-OHDA) induced rat model of PD has been extensively used as an animal model to mimic PD patients in basic science studies. The injection of 6-OHDA into different sites of the brain, i.e., the caudate putamen (CPU), the medial fore- brain bundle (MFB) or the substantia nigra compact (SNC), causes Corresponding author. Tel.: +86 13711629226. E-mail address: [email protected] (W. Zhang). different extent of the lesion in the corresponding brain area. Meanwhile, the lesion process in these three injection models can be quite different, leading to various kinds of performance of gait deficits [4–6]. To quantify these deficits, experimenters use behavioral tests including the open field test, the rotarod test, the treadmill test, the cylinder test, and the ladder walking test [7]. However, the accuracy of readouts can be affected by many factors. For example, timing of testing (day or night), training inten- tion and frequencies, and testing environment are very important factors that affect the behavior performance. Animals behavior tested in an involuntary state are hardly repetitive. Test indicators that are limited to monitor either static or dynamic state cannot adequately display both readouts simultaneously [8], and so on. Therefore, although great efforts have been made to measure the gait deficits in these 6-OHDA PD models [5,9,10], the validation and characterization of gait variability is still lacking [11]. In this report we validated gait variability in three different rat PD models of http://dx.doi.org/10.1016/j.neulet.2014.10.032 0304-3940/© 2014 Elsevier Ireland Ltd. All rights reserved.

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Page 1: Gait analysis in three different 6-hydroxydopamine rat ... · 186 M. Zhou et al. / Neuroscience Letters 584 (2015) 184–189 Fig. 1. (A) Graphical representation of gait parameters

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Neuroscience Letters 584 (2015) 184–189

Contents lists available at ScienceDirect

Neuroscience Letters

jo ur nal ho me p age: www.elsev ier .com/ locate /neule t

ait analysis in three different 6-hydroxydopamine rat models ofarkinson’s disease

ing Zhoua, Wangming Zhanga,∗, Jingyu Changb, Jun Wanga, Weixin Zhenga,ong Yanga, Peng Wena, Min Lia, Hu Xiaoa

Department of Neurosurgery, Zhujiang Hospital, Southern Medical University, Guangzhou 510282, Guangdong Province, ChinaNeuroscience Research Institute of North Carolina, Winston-Salem, NC, USA

i g h l i g h t s

The gait readouts in the MFB and SNC 6-OHDA rats are more profound than the CPU.Many gait parameters show a close correlation with the protein levels of TH.CatWalk system can provide reliable and objective criteria to stratify gait changes arising from 6-OHDA rats.

r t i c l e i n f o

rticle history:eceived 31 July 2014eceived in revised form 11 October 2014ccepted 16 October 2014vailable online 24 October 2014

eywords:arkinson’s disease

a b s t r a c t

Gait deficits are important clinical symptoms of Parkinson’s disease (PD) but are rarely studied. In thisstudy we made three different rat PD models by administration of 6-hydroxydopamine into caudate puta-men (CPU), medial forebrain bundle (MFB) and substantia nigra compact (SNC). We evaluated the gaitchanges in these models by using a computer-assisted CatWalk system. Correlations of gait parameterswith tyrosine hydroxylase protein levels in the CPU and SNC were also investigated. The gait readoutswere significantly impaired in both the MFB and SNC groups. However, the MFB group showed a morepronounced impairment than the SNC group. In contrast, only mild and incomplete gait impairment

aitatWalk-Hydroxydopamineeurochemical correlation

occurred in the CPU group. In addition, some gait parameters demonstrated close correlation with theprotein levels of TH. This paper suggests that the 6-hydroxydopamine-induced MFB model is more propi-tious to study gait dysfunction than the other two models and the CatWalk system can provide reliable andobjective criteria to stratify gait changes arising from 6-hydroxydopamine lesioned rats. These findingsmay hold promise in the study of PD disease progression and new therapeutic methods.

© 2014 Elsevier Ireland Ltd. All rights reserved.

. Introduction

Parkinson’s disease (PD), a pervasive motor disease, results fromhe depletion of dopamine (DA) in the nigrostriatal region of theentral nervous system [1]. As PD progresses, gait disturbancend postural instability become increasingly prominent [2]. Thus,meliorating gait disturbance is vital for PD patients to preventnexpected injury, disability, and improve their qualities of life [3].

The 6-hydroxydopamine (6-OHDA) induced rat model of PD haseen extensively used as an animal model to mimic PD patients

n basic science studies. The injection of 6-OHDA into differentites of the brain, i.e., the caudate putamen (CPU), the medial fore-rain bundle (MFB) or the substantia nigra compact (SNC), causes

∗ Corresponding author. Tel.: +86 13711629226.E-mail address: [email protected] (W. Zhang).

ttp://dx.doi.org/10.1016/j.neulet.2014.10.032304-3940/© 2014 Elsevier Ireland Ltd. All rights reserved.

different extent of the lesion in the corresponding brain area.Meanwhile, the lesion process in these three injection modelscan be quite different, leading to various kinds of performance ofgait deficits [4–6]. To quantify these deficits, experimenters usebehavioral tests including the open field test, the rotarod test,the treadmill test, the cylinder test, and the ladder walking test[7]. However, the accuracy of readouts can be affected by manyfactors. For example, timing of testing (day or night), training inten-tion and frequencies, and testing environment are very importantfactors that affect the behavior performance. Animals behaviortested in an involuntary state are hardly repetitive. Test indicatorsthat are limited to monitor either static or dynamic state cannotadequately display both readouts simultaneously [8], and so on.

Therefore, although great efforts have been made to measure thegait deficits in these 6-OHDA PD models [5,9,10], the validation andcharacterization of gait variability is still lacking [11]. In this reportwe validated gait variability in three different rat PD models of
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Table 1Definitions of gait parameters.

Parameter Definition

Max contact area The maximum area of a paw that comes into contactwith glass plate

Mean intensity The mean intensity of the complete pawStride length The distance between successive placements of the

same pawSwing speed The speed of the paw during swingStand The duration in seconds of contact of a paw with the

glass plateStep cycle The time in seconds between two consecutive initial

contact of the same pawDuty cycle Expressed stand as a percentage of step cycleTerminal dual

stanceThe second step in a step cycle of a hind paw that thecontralateral hind paw also makes contact with theglass plate

M. Zhou et al. / Neuroscien

nilateral 6-OHDA lesions using the CatWalk device. As the motoreficits are the direct consequence of DA loss in the nigrostriatalystem [12], we evaluated the temporal expressions of tyrosineydroxylase (TH) protein in the SNC and CPU of 6-OHDA treated ratsnd assessed the neuro-degeneration in the nigrostriatal regionsy studying the correlation of TH expressions with changes of gaitarameters.

. Materials and methods

.1. Animals

Adult male Sprague Dawley rats, weighing 290-310 g at the timef surgery, were housed 2-3 per cage with ad libitum access toood and water during a 12 h light/dark cycle. All procedures werepproved and regulated by the Institutional Animal Ethics Commit-ee of Southern Medical University of China.

.2. Surgical procedure

The rats were randomly divided into three groups. Each groupas comprised of 12 rats. All rats were anesthetized by intraperi-

oneal injection of pentobarbital (40 mg/kg). Rats were placed in stereotaxic frame (Stoelting) and 6-OHDA were injected intohe right brain using a 10 �l Hamilton syringe fitted with alass capillary. Partial lesion of the nigro-striatal pathway wasbtained by injection of 3 �l of 6-OHDA (3.5 �g/�l free base dis-olved in a solution of 0.2 mg/ml l-ascorbic acid in 0.9% w/vaCl) (Sigma) (0.5 �l/min) in the CPU at the following coordinates

flat skull position): antero-posterior: +1.2 mm, medio-lateral:2.5 mm, dorso-ventral: −5.0 mm below dural surface, calculated

elative to bregma according to the stereotaxic atlas of Paxinosnd Watson (1986). Severe lesion of the nigro-striatal pathway wasbtained by injection of the same dose of 6-OHDA in the MFB at theollowing coordinates: antero-posterior: −4.4 mm, medio-lateral:1.1 mm, dorso-ventral: −7.8 mm or above the SNC at the following

oordinates: antero-posterior: −5.3 mm, medio-lateral: −1.7 mm,orso-ventral: −7.2 mm.

.3. Gait analysis

The CatWalk XT (Noldus information Technology, Wageningen,etherlands) was used to analyze gait of unforced moving rats.atWalk XT consists of a hardware system of a long glass walk-ay plate, illuminated with green light that is reflected within the

lass at points being touched, a high-speed video camera, and aoftware package for quantitative assessment of animal footprints4,13]. Table 1 shows the definition of the gait parameters used inhis study.

All rats were trained to cross the runway in a consistent mannert least six times a day for a week before any experimentation. Auccessful run is defined as an animal finishes running the tracksithout any interruption or hesitation. Rats that failed the CatWalk

raining were excluded from the study. An average number of 5eplicate crossings made by each rat was recorded. Rats were sub-ected to computer-assisted CatWalk from day 26 to day 30 afterdministration of 6-OHDA.

.4. Tissue processing and immunohistochemistry

All animals were sacrificed 30 min after the last behavior test.fter being anesthetized, rats were perfused through the ascending

orta with 250 ml saline (0.9% w/v) at room temperature, followedy 250 ml ice-cold paraformaldehyde (4% w/v in 0.1 M phosphateuffered saline). The brain was removed, post-fixed for 12 h in 4%araformaldehyde and cryoprotected overnight in sucrose (25%

Base of support The average width between either the front paws orthe hind paw

w/v in 0.1 M phosphate buffered saline) before being sectioned ona freezing microtome (Leica). Coronal sections were collected in 6series at a thickness of 20 �m.

Immunohistochemical staining was performed on sectionsusing antibodies raised against TH (mouse, 1:1000; sigma). Sectionswere rinsed three times in potassium-phosphate buffer (KPBS)between each incubation period. The sections were quenched for10 min in 3% H2O2/10% methanol. One hour of pre-incubation with5% normal goat serum was followed by incubation overnight withthe primary antibody in 2% serum at 4 ◦C and incubation with1:200 dilution of biotinylated goat anti-mouse antibody, followedwith avidin–biotin–peroxidase complex, and visualized using 3,3-diaminobenzidine (DAB) as a chromogen.

2.5. Cell counting and optical densitometry analysis

Assessment of the total number of TH+ neurons in the SNCwas made according to the optical fractionator principle, using theImage-Pro Plus (Media Cybernetics, Inc., USA). Every 6th sectioncovering the entire extent of the SNC was included in the count-ing procedure. A coefficient of error of <0.10 was accepted. CPUTH+ fiber density was measured by densitometry at four coronallevels (+1.2, 0.8, 0.00 and −0.4 mm). The measured values were cor-rected for non-specific background staining by subtracting valuesobtained from the cortex. The data are expressed as a percentageof the corresponding area from the intact side.

2.6. Statistical analysis

All the data was expressed as mean ± standard error of mean(SEM). The comparison before and after surgery was performedwith a paired-samples t-test. One-way ANOVA analysis followedby Bonferroni post hoc test was used to determine inter-group andintra-group differences. The correlations of the TH expression levelsin the SNC and CPU with the motor parameters in all tests wereevaluated by Pearson’s product-moment correlation coefficient. Ap value <0.05 was considered as to be statistically significant. Allof the data were analyzed using the SPSS 17.0 software (SPSS Inc.,Chicago, USA).

3. Results

3.1. Cell loss and striatal fiber degeneration in the three models

One rat that failed to meet the CatWalk inclusion criteria andtwo rats that died were excluded from this study (n = 3). The final

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186 M. Zhou et al. / Neuroscience Letters 584 (2015) 184–189

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On the other hand, all parameters in the MFB group took amore profound deterioration than the CPU group. Similar to theMFB group, there was also significant difference in all parameters

Table 2Correlation of gait deficits with tyrosine hydroxylase expression in striatum andsubstantia nigra four weeks post 6-OHDA administrations.

Parameters Pearsoncorrelationa

Pearsoncorrelationb

Parameters Pearsoncorrelationa

Pearsoncorrelationb

Max contact area StanceRF .097 .136 RF −.542* −.579*

LF .730* .722* LF −.538* −.576*

RH −.078 −.058 RH −.475* −.509*

LH .670* .680* LH −.474* −.509*

Mean intensity Step cycleRF −.143 −.256 RF −.506* −.555*

LF .621* .618* LF −.504* −.553*

RH −.230 −.348* RH −.508* −.551*

LH .592* .575* LH −.497* −.542*

Stride length Duty cycleRF .559* .570* RF −.493* −.542*

LF .563* .573* LF −.508* −.555*

RH .541* .571* RH −.550* −.595*

LH .541* .569* LH −.573* −.623*

Swing speed Terminal dual supportRF .576* .597* RF −.693* −.716*

LF .574* .595* LF −.647* −.671*

RH .515* .527* RH −.606* −.643*

LH .509* .521* LH −.621* −.649*

BOS offorelimbs

−.063 −.032 BOS ofhindlimbs

−.672* −.707*

ig. 1. (A) Graphical representation of gait parameters. The upper panel (green prinhase lags) shows the stance phase duration of each individual paw in a single steB), CPU (C), MFB (D), or SNC (E) group.

umber of animals included in the data analysis were: CPU n = 11;FB n = 11; SNC n = 11.Using a stereological approach, we estimated the number of TH+

eurons and compared it to that recorded from the contralateralntact side. Quantifications revealed that a severe loss of nigral neu-ons after injection of 6-OHDA in the MFB and SNC (7.3 ± 4.4% forhe MFB group and 12.6 ± 8.2% for the SNC group; P < 0.05 comparedo intact side; Fig. 3D). The lesion was less severe when 6-OHDAas delivered into the CPU (35.3 ± 15% for the CPU group; P < 0.05

ompared to the intact side).Degeneration of striatal DA fibers was assessed by optical den-

itometry of TH immunostained forebrain sections. Similar to thetereological cell counts, ANOVA analysis revealed a severe lossf terminals when 6-OHDA was injected in the MFB and SNC7.7 ± 3.5% for the MFB group and 12.7 ± 8.1% for the SNC group;

< 0.05 compared to intact side; Fig. 3E), while CPU 6-OHDA injec-ion induced a moderate loss of CPU fibers (35.4 ± 14.6% for the CPUroup; P < 0.05 compared to intact side).

The lesion induced by injection of 6-OHDA in the MFB and SNCas significantly more remarkable than that in the CPU (P < 0.05),hile no difference was observed between 6-OHDA injection in theFB and SNC (P > 0.05; Fig. 3).

.2. CatWalk test

The CatWalk system captures a substantial number of gaitarameters, both dynamic and static (Fig. 1A). A brief overview ofhe injured print and gait patterns is presented in Fig. 1B–E. The

ost significant parameters analyzed using CatWalk are described

n Fig. 2.

Gait analysis parameters collected by the CatWalk system wererst analyzed to compare to the pre-test. The max contact area,ean intensity, stride length and swing speed decreased, whereas

black background) shows the digitized prints, while the lower panel (with colorfule. Blue, RF; red, RH; yellow, LF; green, LH. Four walking patterns including normal

the stance, step cycle, duty cycle, terminal dual stance and bases ofsupport increased in varying degrees in the three groups (Fig. 2).

RF: right front, LF: left front, RH: right hind, LH: left hind.* P < 0.05.a CPU.b SNC.

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M. Zhou et al. / Neuroscience Letters 584 (2015) 184–189 187

Fig. 2. Several parameters of CatWalk were affected variously in three kinds of 6-OHDA lesioned rats. The max cantact area (A), mean intensity (B), stride length (C) andswing speed (D) decreased after 6-OHDA injection and the columns indicating the parameters before surgery was covered with the columns indicating the parameters afters e (H) at eters

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etween the SNC and CPU groups except the duty cycle. However,eadouts of gait parameters of mean intensity, stride length, swingpeed, step cycle, duty cycle and terminal dual stance of the MFBnd SNC group were significantly different (all P < 0.05; Fig. 2).

Significant contralateral (‘lesioned’) vs. ipsilateral (‘nonle-

ioned’) differences were observed in the max contact area, meanntensity and terminal dual stance of the MFB and SNC groups (all

< 0.05; Fig. 2A, B, H). There was significant difference of max con-act area between the contralateral and the ipsilateral fore paw

nd base of support (I) increased after 6-OHDA injection and the columns indicatingbefore surgery. *P < 0.05, **P < 0.01 compared to the pre-test. �P < 0.05, ��P < 0.01t and left limbs after surgery.

(contralateral<ipsilateral, P < 0.05; Fig. 2A) and terminal dual stance(contralateral>ipsilateral, P < 0.01) in the CPU group. Besides, otherparameters were similar between the contralateral and the ipsilat-eral side (Fig. 2).

3.3. Correlation of TH with gait variability

Table 2 shows the analysis of the correlation between the lev-els of TH in the SNC and CPU of 6-OHDA treated rats and the

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188 M. Zhou et al. / Neuroscience Letters 584 (2015) 184–189

Fig. 3. Immunolabelling of striatal TH+ fibers (1,2) and midbrain TH+ neurons (3,4) 4 weeks after 6-OHDA in CPU (A), MFB (B) or SNC (C). A marked reduction in striatalfi ll grouw Data ac ay AN

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ber density and nigral DA neurons is observed on the side of injection (right) in aeeks after 6-OHDA lesion. (E) Quantification of the number of TH+ neurons in SN.

ompared to intact side. ��P < 0.01 between compared groups after surgery (one-w

alues derived from a variety of CatWalk tests after four weeks post-OHDA administration. Significantly positive correlations existetween TH levels and values of swing speed, stride length of all

imbs, max contact area, and mean intensity in the left limbs. Sub-tantially negative correlations between TH levels and values oftance, terminal dual support, step cycle, duty cycle in all limbs,nd base of support were noted (Table 2).

. Discussion

.1. Quantitative assessment of gait

In a previous study [4], the parameters investigated displayedimilar numerical output before and after surgery in the shamroup, suggesting that all parameters in the study remain consis-ent and stable over time in neurologically intact rats.

There are a variety of tests that can be used to model bradyki-

esia. An increase in muscle rigidity and hypokinesia may causeemarkable decrease of stride length and swing speed in PD rats14], which is similar to the clinical signs that is often seen inD patients that they usually take smaller steps when trying to

ps. Scale bar: 500 �m. (D) Quantification of striatal TH+ fiber immunoreactivity 4re percentage of neurons (C) and percentage of striatal fiber immunoreactivity (D)OVA followed by Bonferroni post hoc test).

walk [15]. The measurement of stance, step cycle and duty cyclewas increased in the severely impaired groups of rats of the studydue mainly to the longer contact between the paws and the glassplate [16]. Clinically, PD patients demonstrate gait disturbancessuch as reduced overall velocity, decreased arm swing, reducedstride length, and increased duration of the stance phase [17]. Thedynamic parameter stance and duty cycle illustrate the pitfalls aswell, in which PD patients have increased stance duration of thepart spend in double limb support [18].

In a previous study, Chuang et al. found a persistent reductionin paw pressure and maximal area of paw contact [5]. Similarlywe also found that a reduction in paw pressure and print area ofpaw contact in the affected limbs was due to unilateral dopaminedeficiency. This was most likely because of the rigidity of muscletone and altered use of paw surface in the lesioned side [19].

The terminal dual stance reflects the posture alterations. In ourstudy, we found that, in the fully lesioned models, a significant

increase of terminal dual stance in all limbs existed, suggesting anincreased duration of the postural phase in the 6-OHDA-treatedrats. We, therefore, postulated that the terminal dual stance is animportant parameter mimicking delays of freezing of gait or gait
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esitation in PD [20]. The data also agree with the reports of aonger double limb support time in PD, as a result of patients need toake longer time to prepare for the generation of propulsive forces21,22].

The spatial parameters of base of support for hind limbsncreased substantially in the MFB and SNC lesion group whileemarkable difference between fore limbs in all rats still existed.his result, similar to the finding in a previous study [10], might beelated to the fact that hind limbs playing a more sensitive role inhe balance instability of 6-OHDA-treated rats tested. However, theame result was not seen in a bilateral 6-OHDA lesioned models [4].his might be attributed to the difference of injected brain areas innimals of the two studies.

In our study, we cannot get the conclusion that gait deficits areot (partially) due to loss of LC-noradrenergic neurons, since weid not protect nor-adrenergic cell loss by the injection of des-

mipramine before the injection of 6-OHDA, which is similar to previous gait analysis study [4]. In addition, unilateral 6-OHDAnfusions not only led to gait disturbance in the ipsilateral side pawsut also in the contralateral side paws. We hypothesize that the ratsdapted to the use of the contralateral side paws to compensate forhe loss of the ipsilateral side paws in order to maintain a straightath down the narrow glass walkway.

.2. The injection of 6-OHDA into different location of the brainroduce different models

As described previously, injection of 6-OHDA into the MFB andNC results in a rapid and profound loss of the nigrostriatal DAeurons accompanied by severe motor deficits [1]. In our study,he gait alteration in the CPU group is milder and incomplete. TheNC group has less stable loss of DA neurons compared with theFB group on account of the narrow anatomical structure of SNC. In

rief, the MFB group has a more evident and stable gait impairmenthan the other two models.

.3. The correlation between the gait parameters andeurochemical expression

Various strategies have been employed to verify the correlationetween the motor deficits and the impairment of the nigrostri-tal system [10]. Here, we used correlation analysis of the motorarameters and TH protein levels in the SNC and CPU. Parametersf the max contact area, mean intensity, stride length, swing speed,tance duration, step cycle, duty cycle, terminal dual stance andase of support between limbs in the CatWalk test were stronglyorrelated with TH protein level in the SNC and CPU. This is one ofhe first studies to analyze correlation between gait measures andH protein levels in the SNC and CPU to further confirm gait andosture deficits in the three classic 6-OHDA PD models.

. Conclusion

This study compares the changes of gait dysfunction in threeifferent 6-OHDA models and validates a novel and low-stressethod for analyzing the gait functions of rats. In future studies it

eems advisable to test candidate therapeutic intervention in sev-ral models that complement each other with respect to individualnd interacting mechanisms underlying the gait and pathogenesisf the human disease.

[

ters 584 (2015) 184–189 189

Acknowledgments

The authors are grateful to Dr. Xibin Liang for the help with themanuscript. This study was supported by grants from the funds forthe National Natural Science Foundation of China (no. 81271250)to Professor Wangming Zhang.

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