Background: Transcranial direct current stimulation (tDCS) has been demonstrated to facilitate motor performance in healthy individuals; however, results are variable. The neuromodulatory effects of tDCS during visuomotor tasks may be influenced by extrinsic visual feedback. However, this interaction between tDCS and visual feedback has not been explored for the lower limb. Hence, our objective was to explore if tDCS over the primary lower limb motor cortex differentially facilitates motor performance based on the availability of visual feedback.Methods: Twenty-two neurotypical adults performed ankle plantarflexion and dorsiflexion movements while tracking a sinusoidal target. Spatiotemporal, spatial, and temporal error were calculated between the ankle position and target. Participants attended two sessions, a week apart, with (Stim) and without (No-Stim) anodal tDCS. Sessions were divided into two blocks containing randomized visual feedback conditions: full, no, and blindfold. During Stim sessions, the first block included the application of tDCS to the lower limb M1.Results: Spatiotemporal and spatial error increased as feedback faded (p <.001). A two-way repeated-measures analysis of variance showed a significant interaction between tDCS and visual feedback (p < .05) on spatiotemporal error. Post hoc analyses revealed a significant improvement in spatiotemporal error when visual feedback was absent (p <.01). Spatial and temporal errors were not significantly affected by stimulation or visual feedback.Discussion: Our results suggest that feedback is not available. These findings indicate that visual feedback may play an important role in demonstrating the effectiveness of tDCS.
机构:
Univ Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, EnglandUniv Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, England
Angius, Luca
Pascual-Leone, Alvaro
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Med Sch, Berenson Allen Ctr Noninvas Brain Stimulat, Div Cognit Neurol, Beth Israel Deaconess Med Ctr, Boston, MA USA
Inst Univ Neurorehabil Guttmann, Barcelona, SpainUniv Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, England
Pascual-Leone, Alvaro
Santarnecchi, Emiliano
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Med Sch, Berenson Allen Ctr Noninvas Brain Stimulat, Div Cognit Neurol, Beth Israel Deaconess Med Ctr, Boston, MA USAUniv Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, England
Santarnecchi, Emiliano
[J].
SPORT AND THE BRAIN: THE SCIENCE OF PREPARING, ENDURING AND WINNING, PT C,
2018,
240
: 317
-
339
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Antal, A.
Alekseichuk, I.
论文数: 0引用数: 0
h-index: 0
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Alekseichuk, I.
Bikson, M.
论文数: 0引用数: 0
h-index: 0
机构:
CUNY City Coll, Dept Biomed Engn, New York, NY 10031 USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Bikson, M.
Brockmoeller, J.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Med Ctr Goettingen, Dept Clin Pharmacol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Brockmoeller, J.
Brunoni, A. R.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Sao Paulo, Serv Interdisciplinary Neuromodulat, Dept & Inst Psychiat, Lab Neurosci LIM 27,Appl Neuromodulat Univ Hosp, Sao Paulo, Brazil
Univ Sao Paulo, Interdisciplinary Ctr, Appl Neuromodulat Univ Hosp, Sao Paulo, BrazilGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Brunoni, A. R.
Chen, R.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Toronto, Div Neurol, Dept Med, Toronto, ON, Canada
Krembil Res Inst, Toronto, ON, CanadaGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Chen, R.
Cohen, L. G.
论文数: 0引用数: 0
h-index: 0
机构:
Natl Inst Neurol Disorders & Stroke NIH, Human Cort Physiol & Neurorehabilitat Sect, Bethesda, MD USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Cohen, L. G.
Dowthwaite, G.
论文数: 0引用数: 0
h-index: 0
机构:
Magstim Co, Whitland, WalesGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Dowthwaite, G.
论文数: 引用数:
h-index:
机构:
Ellrich, J.
Floeel, A.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Med Greifswald, Klin & Poliklin Neurol, Greifswald, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Floeel, A.
Fregni, F.
论文数: 0引用数: 0
h-index: 0
机构:
Spaulding Rehabil Hosp, Spaulding Neuromodulat Ctr, Harvard Med Sch, Boston, MA USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Fregni, F.
George, M. S.
论文数: 0引用数: 0
h-index: 0
机构:
Med Univ South Carolina, Brain Stimulat Div, Charleston, SC 29425 USA
Ralph H Johnson Vet Affairs Med Ctr, Charleston, SC USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
George, M. S.
Hamilton, R.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Penn, Dept Neurol, Philadelphia, PA 19104 USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Carl von Ossietzky Univ Oldenburg, European Med Sch, Dept Psychol, Expt Psychol Lab, Oldenburg, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Paris Est Creteil Univ, Henri Mondor Hosp, AP HP, Dept Physiol, Creteil, France
Paris Est Creteil Univ, EA 4391, Nerve Excitabil & Therapeut Team ENT, Fac Med, Creteil, FranceGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Lefaucheur, J. P.
Liebetanz, D.
论文数: 0引用数: 0
h-index: 0
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Liebetanz, D.
Loo, C. K.
论文数: 0引用数: 0
h-index: 0
机构:
Univ New South Wales, Sch Psychiat, Sydney, NSW, Australia
Univ New South Wales, Black Dog Inst, Sydney, NSW, AustraliaGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Loo, C. K.
McCaig, C. D.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Aberdeen, Inst Med Sci, Aberdeen, ScotlandGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
McCaig, C. D.
Miniussi, C.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Trento, Ctr Mind Brain Sci CIMeC, Rovereto, Italy
IRCCS Ctr San Giovanni Dio Fatebenefratelli, Cognit Neurosci Sect, Brescia, ItalyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Miniussi, C.
Miranda, P. C.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Lisbon, Fac Ciencias, Inst Biophys & Biomed Engn, Lisbon, PortugalGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Miranda, P. C.
Moliadze, V.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Kiel, UKSH, Inst Med Psychol & Med Sociol, Campus Kiel, Kiel, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Moliadze, V.
Nitsche, M. A.
论文数: 0引用数: 0
h-index: 0
机构:
Leibniz Res Ctr Working Environm & Human Factors, Dept Psychol & Neurosci, Dortmund, Germany
Univ Hosp Bergmannsheil, Dept Neurol, Bochum, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Nitsche, M. A.
Nowak, R.
论文数: 0引用数: 0
h-index: 0
机构:
Neuroelect, Barcelona, SpainGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Nowak, R.
Padberg, F.
论文数: 0引用数: 0
h-index: 0
机构:
Ludwig Maximilian Univ Munich, Munich Ctr Brain Stimulat, Dept Psychiat & Psychotherapy, Munich, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Padberg, F.
Pascual-Leone, A.
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Med Ctr, Div Cognit Neurol, Boston, MA USA
Beth Israel Deaconess Med Ctr, Berenson Allen Ctr Noninvas Brain Stimulat, Boston, MA 02215 USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Fukushima Med Univ, Dept Neurol, Fukushima, Japan
Fukushima Med Univ, Adv Clin Res Ctr, Fukushima Global Med Sci Ctr, Fukushima, JapanGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Ugawa, Y.
Wexler, A.
论文数: 0引用数: 0
h-index: 0
机构:Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Wexler, A.
Ziemann, U.
论文数: 0引用数: 0
h-index: 0
机构:Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Ziemann, U.
Hallett, M.
论文数: 0引用数: 0
h-index: 0
机构:Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Hallett, M.
Paulus, W.
论文数: 0引用数: 0
h-index: 0
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
MIT, Harvard Mit Div Hlth Sci & Technol, Cambridge, MA 02139 USAHarvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
Castro, Luis Nicolas Gonzalez
Monsen, Craig Bryant
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USAHarvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
Monsen, Craig Bryant
Smith, Maurice A.
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
Harvard Univ, Ctr Brain Sci, Cambridge, MA 02138 USAHarvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
机构:
Univ Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, EnglandUniv Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, England
Angius, Luca
Pascual-Leone, Alvaro
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Med Sch, Berenson Allen Ctr Noninvas Brain Stimulat, Div Cognit Neurol, Beth Israel Deaconess Med Ctr, Boston, MA USA
Inst Univ Neurorehabil Guttmann, Barcelona, SpainUniv Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, England
Pascual-Leone, Alvaro
Santarnecchi, Emiliano
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Med Sch, Berenson Allen Ctr Noninvas Brain Stimulat, Div Cognit Neurol, Beth Israel Deaconess Med Ctr, Boston, MA USAUniv Kent, Endurance Res Grp, Sch Sport & Exercise Sci, Chatham, England
Santarnecchi, Emiliano
[J].
SPORT AND THE BRAIN: THE SCIENCE OF PREPARING, ENDURING AND WINNING, PT C,
2018,
240
: 317
-
339
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Antal, A.
Alekseichuk, I.
论文数: 0引用数: 0
h-index: 0
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Alekseichuk, I.
Bikson, M.
论文数: 0引用数: 0
h-index: 0
机构:
CUNY City Coll, Dept Biomed Engn, New York, NY 10031 USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Bikson, M.
Brockmoeller, J.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Med Ctr Goettingen, Dept Clin Pharmacol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Brockmoeller, J.
Brunoni, A. R.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Sao Paulo, Serv Interdisciplinary Neuromodulat, Dept & Inst Psychiat, Lab Neurosci LIM 27,Appl Neuromodulat Univ Hosp, Sao Paulo, Brazil
Univ Sao Paulo, Interdisciplinary Ctr, Appl Neuromodulat Univ Hosp, Sao Paulo, BrazilGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Brunoni, A. R.
Chen, R.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Toronto, Div Neurol, Dept Med, Toronto, ON, Canada
Krembil Res Inst, Toronto, ON, CanadaGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Chen, R.
Cohen, L. G.
论文数: 0引用数: 0
h-index: 0
机构:
Natl Inst Neurol Disorders & Stroke NIH, Human Cort Physiol & Neurorehabilitat Sect, Bethesda, MD USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Cohen, L. G.
Dowthwaite, G.
论文数: 0引用数: 0
h-index: 0
机构:
Magstim Co, Whitland, WalesGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Dowthwaite, G.
论文数: 引用数:
h-index:
机构:
Ellrich, J.
Floeel, A.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Med Greifswald, Klin & Poliklin Neurol, Greifswald, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Floeel, A.
Fregni, F.
论文数: 0引用数: 0
h-index: 0
机构:
Spaulding Rehabil Hosp, Spaulding Neuromodulat Ctr, Harvard Med Sch, Boston, MA USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Fregni, F.
George, M. S.
论文数: 0引用数: 0
h-index: 0
机构:
Med Univ South Carolina, Brain Stimulat Div, Charleston, SC 29425 USA
Ralph H Johnson Vet Affairs Med Ctr, Charleston, SC USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
George, M. S.
Hamilton, R.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Penn, Dept Neurol, Philadelphia, PA 19104 USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Carl von Ossietzky Univ Oldenburg, European Med Sch, Dept Psychol, Expt Psychol Lab, Oldenburg, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Paris Est Creteil Univ, Henri Mondor Hosp, AP HP, Dept Physiol, Creteil, France
Paris Est Creteil Univ, EA 4391, Nerve Excitabil & Therapeut Team ENT, Fac Med, Creteil, FranceGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Lefaucheur, J. P.
Liebetanz, D.
论文数: 0引用数: 0
h-index: 0
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Liebetanz, D.
Loo, C. K.
论文数: 0引用数: 0
h-index: 0
机构:
Univ New South Wales, Sch Psychiat, Sydney, NSW, Australia
Univ New South Wales, Black Dog Inst, Sydney, NSW, AustraliaGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Loo, C. K.
McCaig, C. D.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Aberdeen, Inst Med Sci, Aberdeen, ScotlandGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
McCaig, C. D.
Miniussi, C.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Trento, Ctr Mind Brain Sci CIMeC, Rovereto, Italy
IRCCS Ctr San Giovanni Dio Fatebenefratelli, Cognit Neurosci Sect, Brescia, ItalyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Miniussi, C.
Miranda, P. C.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Lisbon, Fac Ciencias, Inst Biophys & Biomed Engn, Lisbon, PortugalGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Miranda, P. C.
Moliadze, V.
论文数: 0引用数: 0
h-index: 0
机构:
Univ Kiel, UKSH, Inst Med Psychol & Med Sociol, Campus Kiel, Kiel, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Moliadze, V.
Nitsche, M. A.
论文数: 0引用数: 0
h-index: 0
机构:
Leibniz Res Ctr Working Environm & Human Factors, Dept Psychol & Neurosci, Dortmund, Germany
Univ Hosp Bergmannsheil, Dept Neurol, Bochum, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Nitsche, M. A.
Nowak, R.
论文数: 0引用数: 0
h-index: 0
机构:
Neuroelect, Barcelona, SpainGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Nowak, R.
Padberg, F.
论文数: 0引用数: 0
h-index: 0
机构:
Ludwig Maximilian Univ Munich, Munich Ctr Brain Stimulat, Dept Psychiat & Psychotherapy, Munich, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Padberg, F.
Pascual-Leone, A.
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Med Ctr, Div Cognit Neurol, Boston, MA USA
Beth Israel Deaconess Med Ctr, Berenson Allen Ctr Noninvas Brain Stimulat, Boston, MA 02215 USAGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Fukushima Med Univ, Dept Neurol, Fukushima, Japan
Fukushima Med Univ, Adv Clin Res Ctr, Fukushima Global Med Sci Ctr, Fukushima, JapanGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Ugawa, Y.
Wexler, A.
论文数: 0引用数: 0
h-index: 0
机构:Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Wexler, A.
Ziemann, U.
论文数: 0引用数: 0
h-index: 0
机构:Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Ziemann, U.
Hallett, M.
论文数: 0引用数: 0
h-index: 0
机构:Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
Hallett, M.
Paulus, W.
论文数: 0引用数: 0
h-index: 0
机构:
Georg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, GermanyGeorg August Univ, Univ Med Ctr Gottingen, Dept Clin Neurophysiol, Gottingen, Germany
机构:
Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
MIT, Harvard Mit Div Hlth Sci & Technol, Cambridge, MA 02139 USAHarvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
Castro, Luis Nicolas Gonzalez
Monsen, Craig Bryant
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USAHarvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
Monsen, Craig Bryant
Smith, Maurice A.
论文数: 0引用数: 0
h-index: 0
机构:
Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA
Harvard Univ, Ctr Brain Sci, Cambridge, MA 02138 USAHarvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA