Modelling emboli with floating fir cones
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《英国医生杂志》
1 Institute of Cell and Molecular Science, Barts and The London School of Medicine and Dentistry, London E1 2AD s.e.greenwald@qmul.ac.uk
The study by Knight draws attention to the phenomenon that repeated transient ischaemic attacks often produce similar symptoms and proposes that if the emboli are shed from the same or nearby locations, they are likely to lodge finally in the same place, thus producing ischaemia in the same region of the brain.1
The cones used by Knight to simulate emboli did indeed come to rest in a limited number of locations, a result that is consistent with the hypothesis proposed. Statistical analysis suggests that this aggregation was unlikely to have occurred by chance.
The river Authie and the entrance to the mill stream provide a model of the aortic arch and origin of the left common carotid artery. Note the temporary occlusive lesion
The limitations of this appealing model prompt some questions and comments. Firstly, the flow in the river, although possibly laminar, as is blood flow in most arteries, is essentially steady, whereas flow in large arteries is pulsatile, giving rise to flow patterns that vary with time. How placid or vigorous was the flow in the river and did it undergo any low frequency oscillations? If oscillations did occur, the pattern of the pine cones' arrivals at particular points might change with time; if oscillations did not occur, the cones would probably have arrived randomly at the collection points. Secondly, the vascular system consists of a many branched network in three dimensions whereas, as pointed out by a colleague (C D Bertram), floating objects inhabit a two dimensional system that can contain closed eddies. A true "flow tracer" (that is, a massless object that faithfully follows streamlines) cannot enter such a closed eddy, but one with inertia, such as a pine cone, can be impelled across the boundary. Once inside, it may have insufficient inertia to escape. Sooner or later, most paths will jostle such an inertial object into a closed eddy and the stream may provide copious eddies. Thus in two dimensions (cones floating on a stream), there is a strong likelihood of collection. However, this mechanism would not operate in the vascular system.
Turbulent flow does occur in the aorta during systole, so one might suppose that emboli arising in or passing through the heart and ascending aorta would be randomly distributed owing to the chaotic nature of such flow. However, many chaotic systems are characterised by "strange attractors," as originally described by Lorenz,2 so emboli arising from the same place could end up in proximity in spite of the chaotic nature of the flow.
I tried to improve on the experiment by visualising flow in the river Authie (in northern France) near to the inlet of a millstream. The geometry of this junction bears a noticeable resemblance, at least in two dimensions and in certain lights, to that of the aorta and the left common carotid. A boat manned by me and three companions (one canine) was positioned upstream of the junction, and we poured milk (UHT skimmed, Intermarché, Hesdin, Pas-de-Calais) in a thin stream from each side of the hull so that one stream tended to flow towards the river and the other towards the mill stream. The flow was largely laminar, and the streamlines remained remarkably coherent and showed little deviation during the course of the experiment (about 30 seconds). Photographs were taken but, disappointingly, navigational and other inexplicable stability problems rendered them unfit for publication. Fortunately this type of flow behaviour is well known on a larger scale from aerial views of the sediment carried by converging tributaries of rivers carrying glacial melt water, in which streamlines consisting of sediment from the two sources travel side by side for many miles without mixing.
The observation that prompted Knight's study is of considerable interest, and the hypothesis and experimental results are thought provoking. The possibility of predicting the likelihood of repeated transient ischaemic attacks suggests that more formal modelling of the system as well as numerical simulations of the shedding, transport, and capture of emboli would be a worthwhile enterprise both clinically and scientifically.
Competing interests: None declared.
References
Knight R. The Poohsticks phenomenon. BMJ 2004;329: 1432-3.
Lorenz EN. Deterministic non-periodic flow. J Atmospheric Sci 1963;20: 130-41.(Stephen E Greenwald, prof)
The study by Knight draws attention to the phenomenon that repeated transient ischaemic attacks often produce similar symptoms and proposes that if the emboli are shed from the same or nearby locations, they are likely to lodge finally in the same place, thus producing ischaemia in the same region of the brain.1
The cones used by Knight to simulate emboli did indeed come to rest in a limited number of locations, a result that is consistent with the hypothesis proposed. Statistical analysis suggests that this aggregation was unlikely to have occurred by chance.
The river Authie and the entrance to the mill stream provide a model of the aortic arch and origin of the left common carotid artery. Note the temporary occlusive lesion
The limitations of this appealing model prompt some questions and comments. Firstly, the flow in the river, although possibly laminar, as is blood flow in most arteries, is essentially steady, whereas flow in large arteries is pulsatile, giving rise to flow patterns that vary with time. How placid or vigorous was the flow in the river and did it undergo any low frequency oscillations? If oscillations did occur, the pattern of the pine cones' arrivals at particular points might change with time; if oscillations did not occur, the cones would probably have arrived randomly at the collection points. Secondly, the vascular system consists of a many branched network in three dimensions whereas, as pointed out by a colleague (C D Bertram), floating objects inhabit a two dimensional system that can contain closed eddies. A true "flow tracer" (that is, a massless object that faithfully follows streamlines) cannot enter such a closed eddy, but one with inertia, such as a pine cone, can be impelled across the boundary. Once inside, it may have insufficient inertia to escape. Sooner or later, most paths will jostle such an inertial object into a closed eddy and the stream may provide copious eddies. Thus in two dimensions (cones floating on a stream), there is a strong likelihood of collection. However, this mechanism would not operate in the vascular system.
Turbulent flow does occur in the aorta during systole, so one might suppose that emboli arising in or passing through the heart and ascending aorta would be randomly distributed owing to the chaotic nature of such flow. However, many chaotic systems are characterised by "strange attractors," as originally described by Lorenz,2 so emboli arising from the same place could end up in proximity in spite of the chaotic nature of the flow.
I tried to improve on the experiment by visualising flow in the river Authie (in northern France) near to the inlet of a millstream. The geometry of this junction bears a noticeable resemblance, at least in two dimensions and in certain lights, to that of the aorta and the left common carotid. A boat manned by me and three companions (one canine) was positioned upstream of the junction, and we poured milk (UHT skimmed, Intermarché, Hesdin, Pas-de-Calais) in a thin stream from each side of the hull so that one stream tended to flow towards the river and the other towards the mill stream. The flow was largely laminar, and the streamlines remained remarkably coherent and showed little deviation during the course of the experiment (about 30 seconds). Photographs were taken but, disappointingly, navigational and other inexplicable stability problems rendered them unfit for publication. Fortunately this type of flow behaviour is well known on a larger scale from aerial views of the sediment carried by converging tributaries of rivers carrying glacial melt water, in which streamlines consisting of sediment from the two sources travel side by side for many miles without mixing.
The observation that prompted Knight's study is of considerable interest, and the hypothesis and experimental results are thought provoking. The possibility of predicting the likelihood of repeated transient ischaemic attacks suggests that more formal modelling of the system as well as numerical simulations of the shedding, transport, and capture of emboli would be a worthwhile enterprise both clinically and scientifically.
Competing interests: None declared.
References
Knight R. The Poohsticks phenomenon. BMJ 2004;329: 1432-3.
Lorenz EN. Deterministic non-periodic flow. J Atmospheric Sci 1963;20: 130-41.(Stephen E Greenwald, prof)