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Adipofascial turn-over flap for reconstruction of the dorsum of the foot
Britirh .loumal o/Plastic Surgery (1991), 44, 170-174 0 1991 The T&em of B&i& Association of Plastic Surgeons
Adipofascial turn-over flap for reconstruction of the dorsum of the foot C.-S. Lai, S.-D. Lin, C.-C. Yang and C-K. Chou Division of Plastic and Reconstructive Surgery, Chung-Ho Memorial Hospital, Kaohsiung Medical College, Kaohsiung, Taiwan, Republic of China SUMA4AR Y. Local adipofascial turn-over flaps with shin grafts were successfully used to reconstruct complicated shin defects over the dorsmn of the foot in 7 patients. The blood supply of the flap comes from perforators in the base and from the surromuling subcutaneous and fascial plexuses. A new concept of base-to-flap area ratio is proposed to predict the survival of the turn-over flaps in addition to the conventional base-to-length ratio. This appears to be a valuable technique for ditlicult wounds of the dorsmu of the foot.
silver sulfadiazine ointment. A skin defect with exposure of extensor tendons in the distal portion of the wound remained. A proximally-based adipofascial turn-over flap, measuring 7 x 7 cm with a 2 cm deep base, was raised to cover the defect and the exposed extensor tendons. The grafted wound healed without complication (Fig. 2).
The use of local adipofascial turn-over flaps for the dorsum of the hand and fingers has been reported in an earlier paper (Lai et al., 1991). Our experience with seven flaps on the dorsum of the foot has also been quite encouraging. Materials and Methods
Results
Between August 1989 and May 1990, seven cases with complicated skin defects over the dorsum of the foot were resurfaced with local adipofascial turn-over flaps and skin grafts. There were 5 males and one female. The size of the flaps ranged from 5.0 x 2.5 cm to 7 x 7 cm. The length to breadth ratio of flaps ranged from 0.9 to 2.0 and the base area-to-flap area ratio was from 1:3.0 to 1:4.3. The ages ranged from 5 to 72 years. Follow-up was from 1 month to 8 months (mean, 4 months).
All flaps survived completely except case 3 who suffered distal necrosis. The very thin adipofascial tissue of old age and a too large base-to-flap area ratio (1:4.3) may have been the causes. Desquamation occurred in the reapproximated skin in two cases. All patients can wear normal footwear and have gained a full-range of dorsiflexion of the involved foot.
Case reports
Discussion
Case 1 A 32-year-old man suffered a motorcycle accident resulting in a skin defect with exposure of ruptured extensor tendons over the dorsum of his left foot. The dubiously viable skin surrounding the wound edge was excised and the ruptured tendons repaired. An adipofascial flap was raised over the medial aspect of the foot, measuring 6 x 3.5 cm with a 2 cm deep base, and turned over to cover the defect. The raw surface of the flap was then covered with full-thickness skin graft taken from the groin. The flap donor wound was closed primarily. The superficial peroneal nerve was carefully preserved. Healing was uneventful both in the primary defect and the flap donor site (Fig. 1).
In soft tissue loss of the dorsum of the foot local rotation, advancement and transposition flaps are limited by the area of mobile skin available. Few local flaps are recognized in the literature for reconstruction of the dorsum of the foot : the dorsalis pedis axial flap (McGraw and Furlow, 1975), the de-epithelialised turn-over flap (Thatte et al., 1983) and the distallybased first web flap (Earley and Milner, 1989). The dorsalis pedis flap may not be available in cases with major skin loss or severe trauma over the dorsum of the foot. The de-epithelialised turn-over flap is a reliable method, but the flap donor-site skin is sacrificed. A larger amount of skin graft is therefore needed to resurface the wound, and there may be a tendency to form epithelial cysts. The use of the first web flap is limited to a defect of the distal foot. The application of reverse flow island flaps including the peroneal (Donski and Fogdestam, 1983; Yoshimura et al., 1984), the anterior tibia1 (Wee, 1986; Morrison
Case 2 A 54-year-old diabetic woman received a minor injury over the dorsum of her left foot. Secondary infection caused partial necrosis of the involved skin. The infection was controlled by systemic antibiotics and local application of 170
Adipofascial Turn-over Flap for Reconstruction
of the Dorsum of the Foot
171
Fig.
Figure l--(A) Post-traumatic skin defect with exposure of repaired ruptured tendons. An adipofascial flap, measuring 6 x 3.5 cm with a 2 cm deep base, designed over the medial aspect of the wound. (B) With extra care, the superficial branch of the peroneal nerve can be spared during flap elevation. (C)The flap turned over to cover the defect, and the flap donor-site skin closed primarily. A sheet of full-thickness skin taken from the groin area was grafted on the raw surface of the flap. (D) Uneventful healing 8 months after surgical intervention.
British Journal of Plastic Surgery
172
Fig.
Figure 2-(A) Skin defect caused by superimposed infection in a diabetic foot. A proximally-based adipofascial flap, measuring 7 x 7 cm with a 2 cm deep base, marked. (B) Adequate debridement resulted in exposure of extensor tendons of the distal foot. The flap is already elevated and drains placed in the dependent position under the re-approximated donor-site skin. (C) The flap turned upside-down to cover the defect and anchored to the wound edges with 4-O catgut. (D) View two months after operation to show complete take of the full-thickness skin graft.
Adipofascial Turn-over Flap for Reconstruction
of the Dorsum of the Foot
173
Table 1
Adipofascial turn-over flaps for complicated skin defects of the dorsum of the foot
Case
Sex/age
lesion
Size of the defect (cmz)
Size of the flap (cm2)
Size of the base (cm2)
Ratio of base-to-flap areas
1 2 3 4 5 6 7
M/32
avulsion injury infected diabetic foot avulsion injury crushing injury electric bum cancer excision avulsion injury
4.0 x 3.5 5.0 x 6.5 3.8 x 5.5 3.3 x 2.5 4.0 x 4.5 4.8 x 6.0 10 x5.0
6.0 x 3.5 1.0 x 7.0 6.5 x 5.5 5.0 x 2.5 6.0x4.5 7.0 x 6.0 5.0x5.5
2.0 x 3.5 2.0 x 7.0 1.5 x 5.5 1.5x2.5 2.0 x 4.5 2.0 x 6.0 1.5x5.5
1:3.0
Cause of the
F/50 M/l4 M/33 M/52 M/34 Ml5
1:3.5 1:4.3 1:3.6 1:3.0 1:3.5 1:3.3
Result
survival survival distal necrosis survival survival survival survival
*M = male, F = female.
and Shen, 1987) and the posterior tibia1 fasciocutaneous flaps (Hong et al., 1989) offers an alternative reliable technique. However, the need to sacrifice an important artery in the leg and the obvious contour deformity of the donor site are potentially serious disadvantages. The lateral supramalleolar flap (Masquelet et al., 1988) has the same drawback. Compound skin and muscle free flaps tend to be bulky for reconstruction of the dorsum of the foot (Hidalgo and Shaw, 1986). However, transplantation of the denervated gracilis muscle flap progressively loses bulk and is suitable for infected wounds of the foot (Lai er al., 1990). The thinness of the fascial free flap is ideal (Brent et al., 1985). Elevation of a local adipofascial turn-over flap is quite easy and rapid (Lai et al., 1990). The length to breadth ratio is considered as an index of survival of local random flaps. The base of the traditional random flap is however quite different from that of the local turnover flap. The blood supply of the former is in continuity withnormal tissue. However, the continuity of circulation of the base of the adipofascial turn-over flap is interrupted by the primary defect, only a narrow strip of the base being left adherent to the underlying and surrounding tissue. It would be more accurate to predict the survival of the turn-over flap by ratio of the area of the flap per se to that of the base. The microarterial anatomy of the dorsalis pedis artery which mainly supplies the dorsal skin of the foot has been studied by Man and Acland (1980). The blood supply of the adipofascial turn-over flaps was observed in two fresh below-knee amputees by injection of Chinese ink to the dorsalis pedis artery. Skin defects with exposure of tendons were artificially made on the dorsum of the distal foot of the amputated limbs and the size of the proximally attached base of both flaps was 2 x 7 cm. Vascular plexuses were identified in the base. There were two to three perforators entering the base and branching to the flap. Obviously the blood supply of the flap comes from perforators in the base and from the surrounding subcutaneous and fascial plexuses. The clinical results suggest that a base-toflap area ratio of 1:4.0 is quite safe for flap survival. However, tension should be avoided completely when the turn-over flap is sutured to the defect, otherwise jeopardized circulation may lead to flap failure. A local adipofascial turn-over flap for the dorsum of the foot is possible as long as there is available adipofascial tissue surrounding the primary defect. Care should be taken not to damage the paratenon
under the flap donor-site skin. With care, the superficial branch of the peroneal nerve can be spared during elevation of the flap. Rich dermal plexuses ensure the survival of the re-approximated skin flaps. However, desquamation may occur in patients with relatively thin skin on the foot. The technique described for the dorsum of the foot provides several advantages which include : 1) a onestage operation which is a simple and rapid procedure, 2) thinness of the flap, 3) minimal donor site deformity, 4) easy transposition and 5) no necessity to sacrifice the main artery of the leg or foot. Nevertheless, where the skin defect is extensive or the patient old with extremely thin skin, or the circulation poor, use of the flap is contraindicated. The ideal flap for the dorsum of the foot must provide durable coverage of the exposed vital structures and offer subcutaneous fat that tendons can glide through. The use of normal footwear would be difficult if the flap is bulky. The local adipofascial turn-over flap appears to be a useful technique for the skin defect over the dorsum of the foot.
References Brent, B., Upton, J. and Acland, R. D. (1985). Experience with the temporoparietal fascial free flap. Plastic and Reconstructiue Surgery, 76,1 II. Don&l, P. K. and Fogdestam, J. (1983). Distally based-fasciocutaneous flap from the sural region. Scandinavian Journal of Plastic and Reconstructiue Surgery, 17, 119. Earley, M. J. and Miher, R. H. (1989). A distally based first web flap in the foot. British Journal of Plastic Surgery, 42,507. Hidaleo. D. A. and Sbaw. W. W. (1986). Reconstruction of foot inju’riks. Clinics in Plastic Surgery, i3,663. Hong, G., StetTem, K. and Wang, B. (1989). Reconstruction of the
lower leg and foot with reverse pedicled posterior tibia1 fasciocutaneous flap. British Journalof Plastic Surgery, 42,512. Lpi, C. S., Lln, S. D., Yang, C. C., chon, C. C., Wn, S. F. and Chang, C. H. (1990). Limb salvage of infected diabetic foot ulcers with microsurgical free muscle flap. Annals of Plastic Surgery, Vol. 26 (In press). Lal, C. S., Lll, S. D., Yang, C. C. and Chou, C. C. (1990). The adipofascial turn-over gap for complicated dorsal skin defect of the hand and fingers. British Journal of Plastic Surgery, 44,165. MM, D. and Acid, R. D. (1980). The microarterial anatomy of the dorsalis pedis flap and its clinical application. Plastic and Reconstructive Surgery, 65,419. Masquelet, A. C., Beveridge, J., Romana, C. and Gerber, C. (1988). The lateral supramalleolar flap. Plastic and Reconstructive Surgery, 81,74. M&raw, J. B. and Furlow, L. T., Jr. (1975). The dorsalis arterialized flap: a clinical study. Plastic and Reconstructive Surgery, 55, 171.
British Journal of Plastic Surgery
174 Monkon, W. A. and shen, T. Y. (1987). Anterior tibia1 artery flap: anatomy and case report. British Journal of Plastic Surgery, 40, 230.
Thatte,R. L.,Dhami,L. D. andPatil,U. A. (1983). De-epithelialised turn-over flaps for “salvage” operations. British Journal of Plastic Surgery, 36,178.
Wee, J. T. K. (1986). Reconstruction of the lower leg and foot with the reverse-pedicled anterior tibia1 flap: preliminary report of a new fasciocutaneous flap. British Journal of Plastic Surgery, 39, 327.
Yoshimura, M., Inmra, S., Sldmamura, K., Yamauchi, S. and Nomura, S. (1984). Peroneal flap for reconstruction in the extremity: preliminary report. Plastic and Reconstructiue Surgery, 14,402.
The Authors Clnmg-Sheng Lai, MD, Associate Professor. Sin-Daw Km, MD, Professor. Chin-Chiang Yang, MD, Associate Professor. Chih-Kang Chon, MD, Assistant Professor. Divisionof Plastic and Reconstructive Surgery, Kaohsiung Medical College and Chung-Ho Memorial Hospital, 100 Shihchuan 1st Road, Kaohsiung, Taiwan. Requests for reprints to Dr Lai at the above address. Paper received 1 August 1990. Accepted 3 December 1990.
Adipofascial turn-over flap for reconstruction of the dorsum of the foot C.-S. Lai, S.-D. Lin, C.-C. Yang and C-K. Chou Division of Plastic and Reconstructive Surgery, Chung-Ho Memorial Hospital, Kaohsiung Medical College, Kaohsiung, Taiwan, Republic of China SUMA4AR Y. Local adipofascial turn-over flaps with shin grafts were successfully used to reconstruct complicated shin defects over the dorsmn of the foot in 7 patients. The blood supply of the flap comes from perforators in the base and from the surromuling subcutaneous and fascial plexuses. A new concept of base-to-flap area ratio is proposed to predict the survival of the turn-over flaps in addition to the conventional base-to-length ratio. This appears to be a valuable technique for ditlicult wounds of the dorsmu of the foot.
silver sulfadiazine ointment. A skin defect with exposure of extensor tendons in the distal portion of the wound remained. A proximally-based adipofascial turn-over flap, measuring 7 x 7 cm with a 2 cm deep base, was raised to cover the defect and the exposed extensor tendons. The grafted wound healed without complication (Fig. 2).
The use of local adipofascial turn-over flaps for the dorsum of the hand and fingers has been reported in an earlier paper (Lai et al., 1991). Our experience with seven flaps on the dorsum of the foot has also been quite encouraging. Materials and Methods
Results
Between August 1989 and May 1990, seven cases with complicated skin defects over the dorsum of the foot were resurfaced with local adipofascial turn-over flaps and skin grafts. There were 5 males and one female. The size of the flaps ranged from 5.0 x 2.5 cm to 7 x 7 cm. The length to breadth ratio of flaps ranged from 0.9 to 2.0 and the base area-to-flap area ratio was from 1:3.0 to 1:4.3. The ages ranged from 5 to 72 years. Follow-up was from 1 month to 8 months (mean, 4 months).
All flaps survived completely except case 3 who suffered distal necrosis. The very thin adipofascial tissue of old age and a too large base-to-flap area ratio (1:4.3) may have been the causes. Desquamation occurred in the reapproximated skin in two cases. All patients can wear normal footwear and have gained a full-range of dorsiflexion of the involved foot.
Case reports
Discussion
Case 1 A 32-year-old man suffered a motorcycle accident resulting in a skin defect with exposure of ruptured extensor tendons over the dorsum of his left foot. The dubiously viable skin surrounding the wound edge was excised and the ruptured tendons repaired. An adipofascial flap was raised over the medial aspect of the foot, measuring 6 x 3.5 cm with a 2 cm deep base, and turned over to cover the defect. The raw surface of the flap was then covered with full-thickness skin graft taken from the groin. The flap donor wound was closed primarily. The superficial peroneal nerve was carefully preserved. Healing was uneventful both in the primary defect and the flap donor site (Fig. 1).
In soft tissue loss of the dorsum of the foot local rotation, advancement and transposition flaps are limited by the area of mobile skin available. Few local flaps are recognized in the literature for reconstruction of the dorsum of the foot : the dorsalis pedis axial flap (McGraw and Furlow, 1975), the de-epithelialised turn-over flap (Thatte et al., 1983) and the distallybased first web flap (Earley and Milner, 1989). The dorsalis pedis flap may not be available in cases with major skin loss or severe trauma over the dorsum of the foot. The de-epithelialised turn-over flap is a reliable method, but the flap donor-site skin is sacrificed. A larger amount of skin graft is therefore needed to resurface the wound, and there may be a tendency to form epithelial cysts. The use of the first web flap is limited to a defect of the distal foot. The application of reverse flow island flaps including the peroneal (Donski and Fogdestam, 1983; Yoshimura et al., 1984), the anterior tibia1 (Wee, 1986; Morrison
Case 2 A 54-year-old diabetic woman received a minor injury over the dorsum of her left foot. Secondary infection caused partial necrosis of the involved skin. The infection was controlled by systemic antibiotics and local application of 170
Adipofascial Turn-over Flap for Reconstruction
of the Dorsum of the Foot
171
Fig.
Figure l--(A) Post-traumatic skin defect with exposure of repaired ruptured tendons. An adipofascial flap, measuring 6 x 3.5 cm with a 2 cm deep base, designed over the medial aspect of the wound. (B) With extra care, the superficial branch of the peroneal nerve can be spared during flap elevation. (C)The flap turned over to cover the defect, and the flap donor-site skin closed primarily. A sheet of full-thickness skin taken from the groin area was grafted on the raw surface of the flap. (D) Uneventful healing 8 months after surgical intervention.
British Journal of Plastic Surgery
172
Fig.
Figure 2-(A) Skin defect caused by superimposed infection in a diabetic foot. A proximally-based adipofascial flap, measuring 7 x 7 cm with a 2 cm deep base, marked. (B) Adequate debridement resulted in exposure of extensor tendons of the distal foot. The flap is already elevated and drains placed in the dependent position under the re-approximated donor-site skin. (C) The flap turned upside-down to cover the defect and anchored to the wound edges with 4-O catgut. (D) View two months after operation to show complete take of the full-thickness skin graft.
Adipofascial Turn-over Flap for Reconstruction
of the Dorsum of the Foot
173
Table 1
Adipofascial turn-over flaps for complicated skin defects of the dorsum of the foot
Case
Sex/age
lesion
Size of the defect (cmz)
Size of the flap (cm2)
Size of the base (cm2)
Ratio of base-to-flap areas
1 2 3 4 5 6 7
M/32
avulsion injury infected diabetic foot avulsion injury crushing injury electric bum cancer excision avulsion injury
4.0 x 3.5 5.0 x 6.5 3.8 x 5.5 3.3 x 2.5 4.0 x 4.5 4.8 x 6.0 10 x5.0
6.0 x 3.5 1.0 x 7.0 6.5 x 5.5 5.0 x 2.5 6.0x4.5 7.0 x 6.0 5.0x5.5
2.0 x 3.5 2.0 x 7.0 1.5 x 5.5 1.5x2.5 2.0 x 4.5 2.0 x 6.0 1.5x5.5
1:3.0
Cause of the
F/50 M/l4 M/33 M/52 M/34 Ml5
1:3.5 1:4.3 1:3.6 1:3.0 1:3.5 1:3.3
Result
survival survival distal necrosis survival survival survival survival
*M = male, F = female.
and Shen, 1987) and the posterior tibia1 fasciocutaneous flaps (Hong et al., 1989) offers an alternative reliable technique. However, the need to sacrifice an important artery in the leg and the obvious contour deformity of the donor site are potentially serious disadvantages. The lateral supramalleolar flap (Masquelet et al., 1988) has the same drawback. Compound skin and muscle free flaps tend to be bulky for reconstruction of the dorsum of the foot (Hidalgo and Shaw, 1986). However, transplantation of the denervated gracilis muscle flap progressively loses bulk and is suitable for infected wounds of the foot (Lai er al., 1990). The thinness of the fascial free flap is ideal (Brent et al., 1985). Elevation of a local adipofascial turn-over flap is quite easy and rapid (Lai et al., 1990). The length to breadth ratio is considered as an index of survival of local random flaps. The base of the traditional random flap is however quite different from that of the local turnover flap. The blood supply of the former is in continuity withnormal tissue. However, the continuity of circulation of the base of the adipofascial turn-over flap is interrupted by the primary defect, only a narrow strip of the base being left adherent to the underlying and surrounding tissue. It would be more accurate to predict the survival of the turn-over flap by ratio of the area of the flap per se to that of the base. The microarterial anatomy of the dorsalis pedis artery which mainly supplies the dorsal skin of the foot has been studied by Man and Acland (1980). The blood supply of the adipofascial turn-over flaps was observed in two fresh below-knee amputees by injection of Chinese ink to the dorsalis pedis artery. Skin defects with exposure of tendons were artificially made on the dorsum of the distal foot of the amputated limbs and the size of the proximally attached base of both flaps was 2 x 7 cm. Vascular plexuses were identified in the base. There were two to three perforators entering the base and branching to the flap. Obviously the blood supply of the flap comes from perforators in the base and from the surrounding subcutaneous and fascial plexuses. The clinical results suggest that a base-toflap area ratio of 1:4.0 is quite safe for flap survival. However, tension should be avoided completely when the turn-over flap is sutured to the defect, otherwise jeopardized circulation may lead to flap failure. A local adipofascial turn-over flap for the dorsum of the foot is possible as long as there is available adipofascial tissue surrounding the primary defect. Care should be taken not to damage the paratenon
under the flap donor-site skin. With care, the superficial branch of the peroneal nerve can be spared during elevation of the flap. Rich dermal plexuses ensure the survival of the re-approximated skin flaps. However, desquamation may occur in patients with relatively thin skin on the foot. The technique described for the dorsum of the foot provides several advantages which include : 1) a onestage operation which is a simple and rapid procedure, 2) thinness of the flap, 3) minimal donor site deformity, 4) easy transposition and 5) no necessity to sacrifice the main artery of the leg or foot. Nevertheless, where the skin defect is extensive or the patient old with extremely thin skin, or the circulation poor, use of the flap is contraindicated. The ideal flap for the dorsum of the foot must provide durable coverage of the exposed vital structures and offer subcutaneous fat that tendons can glide through. The use of normal footwear would be difficult if the flap is bulky. The local adipofascial turn-over flap appears to be a useful technique for the skin defect over the dorsum of the foot.
References Brent, B., Upton, J. and Acland, R. D. (1985). Experience with the temporoparietal fascial free flap. Plastic and Reconstructiue Surgery, 76,1 II. Don&l, P. K. and Fogdestam, J. (1983). Distally based-fasciocutaneous flap from the sural region. Scandinavian Journal of Plastic and Reconstructiue Surgery, 17, 119. Earley, M. J. and Miher, R. H. (1989). A distally based first web flap in the foot. British Journal of Plastic Surgery, 42,507. Hidaleo. D. A. and Sbaw. W. W. (1986). Reconstruction of foot inju’riks. Clinics in Plastic Surgery, i3,663. Hong, G., StetTem, K. and Wang, B. (1989). Reconstruction of the
lower leg and foot with reverse pedicled posterior tibia1 fasciocutaneous flap. British Journalof Plastic Surgery, 42,512. Lpi, C. S., Lln, S. D., Yang, C. C., chon, C. C., Wn, S. F. and Chang, C. H. (1990). Limb salvage of infected diabetic foot ulcers with microsurgical free muscle flap. Annals of Plastic Surgery, Vol. 26 (In press). Lal, C. S., Lll, S. D., Yang, C. C. and Chou, C. C. (1990). The adipofascial turn-over gap for complicated dorsal skin defect of the hand and fingers. British Journal of Plastic Surgery, 44,165. MM, D. and Acid, R. D. (1980). The microarterial anatomy of the dorsalis pedis flap and its clinical application. Plastic and Reconstructive Surgery, 65,419. Masquelet, A. C., Beveridge, J., Romana, C. and Gerber, C. (1988). The lateral supramalleolar flap. Plastic and Reconstructive Surgery, 81,74. M&raw, J. B. and Furlow, L. T., Jr. (1975). The dorsalis arterialized flap: a clinical study. Plastic and Reconstructive Surgery, 55, 171.
British Journal of Plastic Surgery
174 Monkon, W. A. and shen, T. Y. (1987). Anterior tibia1 artery flap: anatomy and case report. British Journal of Plastic Surgery, 40, 230.
Thatte,R. L.,Dhami,L. D. andPatil,U. A. (1983). De-epithelialised turn-over flaps for “salvage” operations. British Journal of Plastic Surgery, 36,178.
Wee, J. T. K. (1986). Reconstruction of the lower leg and foot with the reverse-pedicled anterior tibia1 flap: preliminary report of a new fasciocutaneous flap. British Journal of Plastic Surgery, 39, 327.
Yoshimura, M., Inmra, S., Sldmamura, K., Yamauchi, S. and Nomura, S. (1984). Peroneal flap for reconstruction in the extremity: preliminary report. Plastic and Reconstructiue Surgery, 14,402.
The Authors Clnmg-Sheng Lai, MD, Associate Professor. Sin-Daw Km, MD, Professor. Chin-Chiang Yang, MD, Associate Professor. Chih-Kang Chon, MD, Assistant Professor. Divisionof Plastic and Reconstructive Surgery, Kaohsiung Medical College and Chung-Ho Memorial Hospital, 100 Shihchuan 1st Road, Kaohsiung, Taiwan. Requests for reprints to Dr Lai at the above address. Paper received 1 August 1990. Accepted 3 December 1990.