×

Drainage after total knee replacement. (English) Zbl 1201.92041

Summary: A simple lumped hydraulic model of knee drainage following arthroplasty is developed incorporating a pressure-volume equation of state for the knee capsule and a wound healing rate dynamically retarded by the blood flow-induced shear stress. The resulting second-order nonlinear ordinary differential system is examined numerically and qualitatively to map the parameter space. In the model, moderate suction or a slight back-pressure promotes gradual drainage and healing whereas excessive suction can lead to a bifurcation in which healing is retarded or even prevented. Guided, then, by the model, the literature, and experience, continuous drainage with a small constant back-pressure appeared beneficial, so we prospectively evaluated a series of ten patients. The results are consistent with the model and promising.

MSC:

92C50 Medical applications (general)
92C35 Physiological flow

Software:

Octave
Full Text: DOI

References:

[1] Sperber, Acta Orthop. Scand. 69 pp 484– (1998)
[2] Zamora-Navas, Acta Orthopædica Belgica 65 pp 44– (1999)
[3] Gopinath, J. Orthop. 1 pp e6– (2004)
[4] Geborek, J. Rheumatol. 16 pp 1351– (1989)
[5] Eaton, GNU Octave Manual (2002)
[6] DOI: 10.1016/S0883-5403(05)80125-1 · doi:10.1016/S0883-5403(05)80125-1
[7] Berman, Orthopedics 13 pp 309– (1990)
[8] DOI: 10.1146/annurev.fluid.32.1.347 · Zbl 0989.76096 · doi:10.1146/annurev.fluid.32.1.347
[9] Benoni, Acta Orthop. Scand. 68 pp 133– (1997)
[10] Beer, J. Bone Joint Surg. Am. 73 pp 584– (1991)
[11] Adalberth, Acta Orthop. Scand. 69 pp 475– (1998)
[12] Ritter, J. Bone Joint Surg. Am. 76 pp 35– (1994)
[13] DOI: 10.1016/0002-9610(84)90336-2 · doi:10.1016/0002-9610(84)90336-2
[14] DOI: 10.1302/0301-620X.86B8.14839 · doi:10.1302/0301-620X.86B8.14839
[15] DOI: 10.1016/S0883-5403(97)90029-2 · doi:10.1016/S0883-5403(97)90029-2
[16] Murray, Mathematical Biology (1989) · Zbl 0682.92001 · doi:10.1007/978-3-662-08539-4
[17] DOI: 10.1111/j.1445-2197.1987.tb01416.x · doi:10.1111/j.1445-2197.1987.tb01416.x
[18] Lamb, Hydrodynamics (1932)
[19] Kim, Clin. Orthop. 347 pp 188– (1998) · doi:10.1097/00003086-199802000-00021
[20] Holt, Orthopedics 20 pp 1121– (1997)
[21] Hindmarsh, Scientific Computing pp 55– (1983)
[22] DOI: 10.1038/icb.1981.16 · doi:10.1038/icb.1981.16
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.