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1 PNF and Movement, 2019; 17(1): Print ISSN: Online ISSN: Original Article Open Access 뇌졸중환자의직선보행과곡선보행시시공간적변수의비교 최보라 우영근 1 황수진 2 1) 백석대학교보건복지대학원물리치료과, 1 전주대학교의과학대학물리치료학과, 2 백석대학교물리치료학과 Comparison of Spatiotemporal Parameters during Straight and Curve Walking for Patients with Stroke Bo-Ra Choi Young-Keun Woo 1 Su-Jin Hwang 2 Department of Physical Therapy, Graduate School, Baekseok University 1 Department of Physical Therapy, College of Medical Sciences, Jeonju University 2 Department of Physical Therapy, Division of Health Science, Baekseok University Received: February 16, 2019 / Revised: March 14, 2019 / Accepted: March 14, 2019 c 2019 Journal of Korea Proprioceptive Neuromuscular Facilitation Association This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Purpose: This study is a comparison of spatiotemporal parameters between straight and curved walking in individuals with chronic hemiparetic stroke, investigating whether those patients can adapt their walking according to task demands and environmental changes. Methods: Twenty-eight patients who diagnosed with their first stroke at least six months prior to this study were recruited. They were measured for spatiotemporal parameters in three different walking conditions: straight walking, walking with an inner curve to the more-affected leg, and walking with an inner curve to the less-affected leg. This study also measured secondary clinical factors, such as the timed up-and-go test, the trunk impairment scale, and the dynamic gait index. The statistical methods for the three different walking conditions, using the averaged value of each condition, was repeated measures ANOVA. Results: The difference in cadence was statistically significant when comparing straight walking, walking with an inner curve to the more-affected leg, and walking with an inner curve to the less-affected leg. Swing duration (%) was also a statistically significant difference between straight walking and walking with an inner curve to the more-affected leg. However, differences in other spatiotemporal parameters were not statistically significant among the three conditions. Conclusion: The results of this study suggest that stroke survivors could adapt their walking according to straight and curved walking conditions, although cadence and swing duration were different between straight and curved walking groups. Key Words: Kinematics, Stroke, Walking Corresponding Author : Su-Jin Hwang (sujin928@gmail.com)
2 130 PNF and Movement Vol. 17, No. 1 Ⅰ. 서론뇌졸중 (stroke) 은성인에서후천적으로심각한장애를유발하는대표적인원인질환으로우리나라 3대사망원인중하나이다 (O Sullivan et al., 2014; Statistics Korea, 2016). 대부분의뇌졸중생존자는발병초기부터뇌세포손상으로인하여감각 (sensory), 운동 (motor), 인지 (cognition), 지각 (perception) 및언어 (language) 기능의손상과의식수준 (level of consciousness) 변화를포함한다양한신체적 인지적손상이발생한다. 일반적으로, 뇌졸중생존자중에서약 1/3은발병 3개월이후에도보행할수없으며, 생존자의약 30% 는발병 6개월이후에도보조없이보행할수없다 (Olney & Richards, 1996; Von Schroeder et al., 1995). 입원재활을마치고퇴원한지역사회뇌졸중생존자의약 50 74% 는보행제한 (limited ambulation) 으로지역참여에제한되며, 지역사회뇌졸중생존자의약 7% 만이지역사회에서능숙하게보행하기위하여필요한계단이나경사로오르기, 보행속도및거리변경하기등은지역사회뇌졸중생존자의약 7% 만이가능하다 (Durcan et al., 2016; Lord et al., 2008). 따라서뇌졸중생존자의독립적인일상생활동작수행및지역사회참여를위하여보행능력회복은재활초기부터집중적인접근이필요한부분이다. 일반적으로일상생활동작을수행할때, 보행은환경의요구에따라서흔히직선보행 (linear walking) 과돌기 (turning) 와순환보행 (circular walking) 이혼합되며보행시간의약 30% 를곡선보행을수행하는데소비한다 (Courtine & Schieppati, 2003; Courtine & Schieppati, 2004; Courtine et al., 2006). 선행연구에서는정상인을대상으로곡선궤도에서근육활성도 (muscle activation), 운동학 (kinematics), 및운동역학 (kinetics) 에관한연구를실시하였다 (Courtine & Schieppati, 2003; Courtine & Schieppati, 2004; Courtine et al., 2006). 그들은직선보행과곡선보행을할때근육시너지 (muscle synergies) 의미세한조절이보행을조정하고균형을유지하기에충분한추진력을발생시키기에충분한근활성도를 보이며, 근활성도의크기와타이밍에유의한차이를보인다고보고하였다 (Courtine et al., 2006). 반면에, 시공간변수 (spatiotemporal parameters) 인운동학적특징은직선보행과곡선보행에서차이를보이지않았는데, 이것은보행하는동안상위중추에서하달되는보행명령이신체말단이움직이는진폭과위상의변화를생성하여보행의특성에적응하도록조절하기에충분하기때문이라고보고하였다 (Courtine & Schieppati, 2004). 정상인과는달리뇌졸중환자를대상으로직선보행과곡선보행을할때환측다리의신경근전략 (neuromuscular strategies) 을실험한결과는차이를보였다. Duval 등은뇌졸중환자 14명을대상으로직선보행, 큰원보행 ( 길이 12.6m, 반지름 2m, 곡률 0.5m), 중간원보행 ( 길이 6.3m, 반지름 1m, 곡률 1m), 작은원보행 ( 길이 3.1m, 반지름 0.5m, 곡률 2m) 의 4가지조건에서시공간변수를조사하였다. 그들은직선보행에비하여곡선보행일때뇌졸중환자의다리추진력이감소한다고보고하였다 (Duval, 2011). 선행연구에서실제로뇌졸중생존자는과제요구의변화를수용하기위하여보행패턴을수정하는능력이대단히현저한것으로조사되었다 (Reisman et al., 2007). 뇌졸중이후운동재활을진행하는데중요한것은한상황에서새로습득한보행패턴을다른환경에서도일반화하기위하여필요한요인을결정하는것이다 (Reisman et al., 2009). 이것은임상환경을벗어난환경에서보행을지속하기위한재활치료설계에중요한요소이다. 일부뇌졸중환자의보행적응 (locomotor adaptation) 에관한연구는새로운환경이나새로운요구에대한최소한의전이 (transfer) 만을보고하고있다. 본연구의목적은뇌졸중환자를대상으로직선보행과곡선보행을할때운동학적변수에어떤변화가나타나는지조사하고뇌졸중환자의실외보행및지역사회보행과같은환경변화가발생할때변화가발생할수있는요인을제언하기위함이다.
3 뇌졸중환자의직선보행과곡선보행시시공간적변수의비교 131 Ⅱ. 연구방법 1. 연구대상연구대상자는서울에소재한재활병원에서외래환자로재활치료를받고있는뇌졸중환자 28명을대상으로하였다. 해당기관의포털사이트및기관내게시판을이용하여연구의목적및참여자모집내용을게시하였고, 자발적으로참여를희망한뇌졸중환자중에서본연구의선정기준과배제기준에부합하는대상자를선정하였다. 본연구대상자의선정기준은 1 뇌영상- 기반전문의의진단상편마비뇌졸중으로판정받은지 6개월이상인자, 2 연구참여에지장이있는주는인지손상이없는자 ( 간이-정신상태검사 19 점이상 ), 3 보행보조도구유무와상관없이 10m이상 1회보행이가능한자, 4 전문의로부터균형및보행결함을진단받은자, 그리고 5 보행에영향을미칠수있는시지각손상 (visuoperceptual impairment) 이없는자로하였다. 선정된대상자중에서뇌졸중이재발한자, 뇌졸중이외에다른신경학적질환이나정형외과적질환이있는자, 그리고실험중연구에참여의사를철외한자는실험에서배제하였다. 연구참여자는자발적으로연구참여에동의하였고, 본연구는연구자소속기관에서사전연구심의를통과하였다. 2. 측정방법및도구 1) 정적및동적균형 (static and dynamic balance) 일어나걷기검사 (timed up-and-go test, TUG) 는정적및동적균형을모두요구하는개인의이동성을평가하는데사용되는간단한임상평가방법으로, 의자에앉은자세에서시작신호가주어지면일어나서 3m를걸은후에다시돌아와서의자에앉을때까지걸리는시간 ( 초 ) 을측정하는것이다. 일반적으로 10초이하일때정상이라고판단하며, 노인이나장애가있는사람들은 11-20초를정상으로판단하는데, 20초이상은실 외보행시보조가필요하고추가적인검사와치료적중재가필요하다고판단한다. 또한, 30초이상을낙상의위험이있다고판단한다 (Alberta Health services, 2010; American College of Rheumatology, 2010; Podsiadlo & Richardson, 1991). 2) 몸통안정성 (trunk stability) 몸통손상척도 (trunk impairment scale, TIS) 은뇌졸중환자의몸통을평가할목적으로 Verheyden 등 (2004) 에의하여 2004년개발된평가도구이다. 본도구는뇌졸중환자를대상으로앉은자세에서정적및동적앉기균형과몸통협응력을평가한다. 본평가도구는 2점, 3점, 혹은 4점서열척도로구성되어있으며정적앉기균형 7점, 동적앉기균형 10점및협응력 6점으로총 23점이만점이며, 점수가높을수록기능이우수하다고해석할수있다 (Verheyden et al., 2004; Verheyden & Kersten, 2010). 3) 동적보행지수 (dynamic gait index, DGI) 동적보행지수 (dynamic gait index, DGI) 는일상생활에서발생하는복잡한보행과제에보행을적용할수있는능력을평가하는임상평가도구로, 8개다른요구및환경에서보행능력을평가한다. 각항목의점수는 0( 심각한보행능력손상 ) 점에서 3( 정상 ) 점으로 4점서열척도이며, 24점이만점으로점수가높을수록보행능력이우수하다고판단하며 19점이하는낙상의위험이있다고판단한다 (Shumway-Cook et al., 2013). 4) 보행의시공간변수측정본연구는분당걸음수, 큰걸음기간, 디딤기간, 흔듦기, 한다리지지기, 양다리지지기, 골반앞- 뒤경사, 골반가쪽기울기, 골반돌림등보행의시공간변수를측정하기위하여 BTS GWalk (BTS Bioengineering, USA) 를사용하였다. BTS GWalk 는움직임의가속도를이
4 132 PNF and Movement Vol. 17, No. 1 용하여보행을분석하는시스템중하나로, 3-축가속도계, 자이로스코프및자력계로구성되어있다. BTS GWalk는신경학적장애 (neurological disorders), 절단 (amputation) 혹은연부조직기능장애 (soft tissue dysfunctions) 에이차적인운동장애환자를대상으로한실외기능적보행분석을위하여개발되었으며, 보행주기를전산화된운동분석은부드럽거나거친실내또는실외의다양한종류의표면에서수행할수있다. 본연구에서 BTS GWALK는 L4 L5 척추사이공간에부착하고, 운동의평면과축을상대각도와함께결정하며샘플링은 100 Hz으로설정하여측정하였다. 3. 실험절차본연구는지역사회뇌졸중생존자가직선보행과곡선보행을수행할때시공간변수를측정하였다. 먼저직선보행은 10m 보행로를이용하였으며, 곡선보행은길이 10m, 반지름 5m의보행로를이용하였다. 대상자는직선보행, 환측을안쪽으로걷기및건측을안쪽으로걷기등의 3가지조건에서보행검사를실시하였으며각조건을 5회실시하여평균값을분석에이용하였다. 환자의보행조건은무작위로선정하였고, 모든평가는신경계질환자를대상으로임상평가를 5년이상실시한경험이풍부한물리치료사가진행하였다. 4. 자료분석본연구에서수집된자료는 SPSS 14.0 for Windows 프로그램을이용하여대상자의일반적특성은기술통계로하였으며, 실험전과후의차이에대한결과를 repeated measures ANOVA 로분석하였고, Bonferroni 사후검정을실시하였다. 통계적유의수준은 0.05로하였다. Ⅲ. 연구결과 1. 연구대상자의일반적인및임상적특성 본연구참여자는만성편마비뇌졸중환자 28명으로남자 13명, 여자 15명이며, 평균연령 62.32±14.02세, 뇌졸중발병기간 29.32±29.09개월, 뇌혈관손상원인은경색 16명, 출혈 12명, 마비측은오른쪽 17명, 왼쪽 11명, 브론스트롬회복단계 (Brunnstrom recovery stage) 는 4단계 10명, 5단계 16명, 6단계 2명, 간이- 정신상태검사는평균 25.75±3.33점, 보행보조도구사용자는 21명, 미사용자는 7명으로조사되었다 (Table 1). 본연구는참여자의임상적특징을알아보기위하여 3가지임상평가를실시하였는데, 일어나걷기검사는평균 19.21±6.68점, 몸통손상척도는 14.86±2.66점, 동적보행지수는 16.11±4.73점으로조사되었다 (Table 1). Table 1. General and clinical characteristics of subjects (n=28) Characteristics Numbers Sex (male/female) 13/15 Age (years) 62.32±14.02 * Post-duration (months) 29.32±29.09 * Etiology (infarction/hemorrhage) 16/12 Paretic side (right/left) 17/11 Brunnstrom stages (4/5/6) 10/16/2 Mini-mental state examination (scores) 25.75±3.33 * Assistive device for walking (with/without) 21/7 Timed up-and-go test (seconds) 19.21±6.68 Trunk impairment scale (scores) 14.86±2.66 Dynamic gait index (scores) 16.11±4.73 *Mean±Standard deviation 2. 직선및곡선보행의시공간적특성 연구참여자는직선선보행에관한시공간적특성은다음과같았다. 분당걸음수는 88.08±17.57 이었으며, 환측의큰걸음기간 1.46±0.37sec, 디딤기간 63.21±7.1%,
5 뇌졸중환자의직선보행과곡선보행시시공간적변수의비교 133 흔듦기 36.79±7.11%, 한다리지지기 30.85±5.01%, 양다리지지기 16.06±4.94%, 골반앞-뒤경사 2.14±0.83, 골반가쪽기울기 9.36±3.85, 골반돌림 2.55±1.16 로조사되었다. 또한직선보행을할때건측의큰걸음기간 1.46±0.36sec, 디딤기간 68.95±5.1%, 흔듦기 31.06±5.1%, 한다리지지기 36.49±7.58%, 양다리지지기 16.59±5.27%, 골반앞-뒤경사 2.09±0.85, 골반가쪽기울기 9.31±4.05, 골반돌림 2.5±1.18 로조사되었다 (Table 2). 또다른보행조건인건측을안쪽으로회전하며곡선보행할때, 분당걸음수는 83.58±21.14, 환측의큰걸음기간 2.14±2.85sec, 디딤기간 63.55±7.41%, 흔듦기 37.67±8.94%, 한다리지지기 33.64±13.15%, 양다리지지기 16.11±4.4%, 골반앞-뒤경사 2.03±0.83, 골반가쪽기울기 12.59±16.2, 골반돌림 2.52±1.22 로조사되었다. 또한건측의큰걸음기간 2.4±4.16sec, 디딤기간 68.52±5.1%, 흔듦기 31.5±4.97%, 한다리지지기 36.18±7.33%, 양다리지지기 16.09±4.22%, 골반앞-뒤경사 1.96±0.85, 골반가쪽기울기 12.55±16.22, 골반돌림 2.47±1.24 로조사되었다 (Table 2). 마지막으로보행조건인환측을안쪽으로회전하며곡선보행할때, 분당걸음수는 83.42±21.49, 환측의큰걸음기간 1.61±0.62sec, 디딤기간 64.41±6.63%, 흔듦기 31.03±5.91%, 한다리지지기 30.95±5.7%, 양다리지지기 16.59±4.75%, 골반앞-뒤경사 1.97±0.69, 골반가쪽기울기 10.24±5.62, 골반돌림 2.5±1.21 로조사되었다. 또한건측의큰걸음기간 1.61±0.62sec, 디딤기간 68.95±5.9%, 흔듦기 31.03±5.91%, 한다리지지기 37.54±11.93%, 양다리지지기 17.09±4.15%, 골반앞-뒤경사 1.93±0.67, 골반가쪽기울기 10.02±5.51, 골반돌림 2.44±1.21 로조사되었다 (Table 2). 수집된자료를분석한결과분당걸음수는직선보 Table 2. Spatiotemporal parameters of gait performance for participants in this study (n=28) More affected side Less affected side Variables Straight walking Curved walking on less-affected side Curved walking on more-affected side Cadence (strides/min) 88.68± ±21.14 * 83.42±21.49 * Stride duration (%) 1.46± ± ± Stance duration (%) 63.21± ± ± Swing duration (%) 36.79± ± ±5.91 * 7.80 <0.01 Single support duration (%) 30.85± ± ± Double support duration (%) 16.06± ± ± Pelvic tilt range ( ) 2.14± ± ± Pelvic oblique range ( ) 9.36± ± ± Pelvic rotation range ( ) 2.55± ± ± Stride duration (%) 1.46± ± ± Stance duration (%) 68.95± ± ± Swing duration (%) 31.06± ± ± Single support duration (%) 36.49± ± ± Double support duration (%) 16.59± ± ± Pelvic tilt range ( ) 2.09± ± ± Pelvic oblique range ( ) 9.31± ± ± Pelvic rotation range ( ) 2.5± ± ± * significantly significant difference compared to straight walking significantly significant difference compared to less-affected side F p
6 134 PNF and Movement Vol. 17, No. 1 행과비교하여건측을안쪽으로회전하며곡선보행할때와환측을안쪽으로회전하며곡선보행할때유의미하게감소하였다. 또한흔듦기간은직선보행과비교하여환측을안쪽으로회전하며곡선보행할때유의하게감소하였고, 곡선보행도건측을안쪽으로회전하며보행할때보다환측을안쪽으로회전하며보행할때유의하게감소하였다 (p<0.05). 반면에다른시공간변수는통계학적으로유의미한차이가없었다 (p>0.05)(table 2). Ⅳ. 고찰본연구는만성편마비뇌졸중환자를대상으로직선보행과곡선보행을할때운동학적특징에어떤변화가발생하는지조사하고자하였다. 연구결과연구참여자들은직선보행을할때보다곡선보행을할때분당걸음수가유의미하게감소하였다. 또한보행시지면에서다리가들리는흔듦기의비율이직선보행을할때보다환측을안쪽으로놓고회전하며곡선보행을할때유의미하게감소하였고, 건측을안쪽으로놓고회전하며곡선보행할때보다환측을안쪽으로놓고회전하며곡선보행할때흔듦기비율이유의미하게감소하였다. 뇌졸중환자의보행은보행속도감소, 비대칭, 양발간격증가등의특징을보인다 (Kao et al., 2014; Mansfield et al., 2015). 일반적으로일상생활동작을수행할때보행은직선보행과돌기및선회보행등이보행환경과주변의요구에따라서혼합되어서출현한다. Chisholm 등 (2015) 은정상인이일상생활동작을수행하는동안안전하게돌기및방향전환을하기위하여출현하는기본보행유형의적응이뇌졸중환자에게서도출현하는지알아보고자 2명의뇌졸중환자를대상으로직선보행, 넓은곡석보행, 좁은곡선보행을수행할때장딴지근의근활성도, 무게중심점 (center of pressure) 의궤적 (trajectory), 균형, 감각운동조절및기능적보행능력을측정하였다. 연구결과다리의감각 운동소상이큰뇌졸중환자일수록무게중심점의앞- 뒤이동이더큰차이를보였으며, 곡선보행의만곡 (curvature) 가증가할수록악화되었고, 환측다리위에는무게중심점을위치시키지못했다. 또한균형능력이더좋은환자는무게중심점을가쪽으로더기울인다고보고하였다. 본연구에서뇌졸중환자를대상으로직선보행및곡선보행을실시한결과, 분당걸음수와흔듦기비율은직선보행과비교하여곡선보행에서통계학적으로유의미하게감소하였다. 반면에다른보행의시공간적변수는유의한차이가없었다. 서론에서언급하였던것처럼, Courtine과 Schieppati (2004) 는정상인을대상으로직선보행과곡선보행을비교한결과운동학적특성인시공간적변수는두보행환경에서유의한차이를보이지않았으며, 이것은환경및과제요구가달라져도보행의특성을지속적으로유지할수있도록상위중추의명령이선행되기때문이라고주장하였다. 뇌졸중환자를대상으로실시한직선보행과곡선보행에서는신경근육학적특성뿐만아니라운동학적특성도차이를보인다고선행연구들의보고가있었다 (Chisholm, 2015; Duval, 2011). 이러한선행연구의보고와는달리, 본연구참여자에서는보행과제가지닌요구가달려져도, 보행적응력 (walking adaptability) 가출현하는것으로조사되었다. 보행의조절은발짝떼기 (stepping), 평형 (equilibrium) 및적응 (adaptability) 로구성된삼자모델로설명된다. 보행적응은보행과제의목표및환경적요구를충족시키기위하여걷기는수정할수있는능력을말한다. 이러한보행적응은뇌졸중발병이후급격히감소되는데, 실제로이러한보행적응력의정량화는임상환경에서상대적으로관심을받지못하고있는현실이다 (Balasubramanian et al., 2014). 본연구결과는직선보행과곡선보행에서분당걸음수및흔듦기의비율은유의한차이를보였지만, 다른보행의시공간변수는유의한차이가없었다. 따라서본연구결과를바탕으로뇌졸중환자의직선보행및곡선보행에서도이러한보행적응이발생한다는제언할수있을것이다. 본연구의목적은뇌졸중환자의실외보행및지역
7 뇌졸중환자의직선보행과곡선보행시시공간적변수의비교 135 사회보행과같은환경변화가발생할때보행특성에어떠한변화가있는지알아보았다. 본연구결과지역사회뇌졸중생존자는보행의특성및환경적요구에따른보행적응이선행되는것으로조사되었다. 본연구는상대적으로큰반지름의곡선보행만을수행하였다. 향후연구에서는반지름을감소시켜서협소한공간에서회전을할때보행특성의변화및보행적응유무를알아볼것을제언하는바이다. Ⅴ. 결론본연구는만성편마비뇌졸중환자를대상으로직선보행과곡선보행을할때운동학적특징을조사하여보행적응의유무를조사하였다. 연구결과, 직선보행을할때보다곡선보행을할때분당걸음수가유의미하게감소하였고, 보행시지면에서다리가들리는흔듦기의비율이직선보행을할때보다환측을안쪽으로놓고회전하며곡선보행을할때유의미하게감소하였으며, 건측을안쪽으로놓고회전하며곡선보행할때보다환측을안쪽으로놓고회전하며곡선보행할때흔듦기비율이유의미하게감소하였다. References Alberta Health Services, Timed up and go test Retrieved American College of Rheumatology. Timed up and go. Retrieved Balasubramanian CK, Clark DJ, Fox EJ. Walking adaptability after a stroke and its assessment in clinical settings. Stroke Research & Treatment. 2014;2014: Chisholm AE, Qaiser T, Lam T. Neuromuscular control of curved walking in people with stroke: Case report. Journal of Rehabilitation Research & Development. 2015;52(7): Countine G, Paraxanthis C, Schieppati M. Coordinated modulation of locomotor muscle synergies constructs straight-ahead and curvilinear walking in humans. Experimental Brain Research. 2006;170(3): Courtine G, Schieppati M. Tuning of a basic coordination pattern constructs straight-ahead and curved walking in humans. Journal of Neurophysiology. 2004;91: Courtine G, Schieppati M. Human walking along a curved path. II Gait features and EMG patterns. European Journal of Neuroscience. 2003;18(1): Durcan S, Flavin E, Horgan F. Factors associated with community ambulation in chronic stroke. Disability & Rehabilitation. 2016;38(3): Duval K, Luttin K, Lam T. Neuromuscular strategies in the paretic leg during curved walking in individuals post-stroke. Journal of Neurophysiology. 2011; 106(1): Kao PC, Dingwell JB, Higginson JS, et al. Dynamic instability during post-stroke hemiparetic walking. Gait Posture. 2014;40(3): Lord S, McPherson KM, McNaughton HK, et al. How feasible is the attainment of community ambulation after stroke? A pilot randomized controlled trial to evaluate community-based physiotherapy in subacute stroke. Clinical Rehabilitation. 2008;22(3): Mansfield A, Wong JS, McIlroy WE, et al. Do measures of reactive balance control predict falls in people with stroke returning to the community? Physiotherapy. 2015;101(4):1-8. Olney SJ, Richards C. Hemiparetic gait following stroke. Part I: characteristics. Gait and Posture. 1996;4(2): O Sullivan SB, Schmitz TJ, Fulk GD. Physical rehabilitation, 6th ed. Philadelphia. F.A. Davis Co Podsiadlo D, Richardson S. The timed up & go: a test of basic functional mobility for frail elderly persons.
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