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Convergent Evolution $113.11 Convergent evolution describes the acquisition of the same biological trait in unrelated lineages. The wing is a classic example of convergent evolution in action. Although their last common ancestor did not have wings, birds and bats do, and are capable of powered flight. The wings are similar in construction, due to the physical constraints imposed upon wing shape. Similarity can also be explained by shared ancestry, as evolution can only work with what is already therethus wings were modified from limbs, as evidenced by their bone structure. Traits arising through convergent evolution are termed analogous structures, in contrast to homologous structures, which have a common origin. Bat and pterodactyl wings are an example of analogous structures, while the bat wing is homologous to human and other mammal forearms, sharing an ancestral state despite serving different functions. Similarity in species of different ancestry which is the result of convergent evolution, is called homoplasy. The opposite of convergent evolution is divergent evolution, whereby related species evolve different traits. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 154 Publication Date: 2010/01/04 Language: English Dimensions: 5.98 x 9.01 x 0.35 inches

Convergent (Continued Fraction) $82.85 A convergent is one of a sequence of values obtained by evaluating successive truncations of a continued fraction. The nth convergent is also known as the nth approximant of a continued fraction.Every real number can be expressed as a regular continued fraction in canonical form. Each convergent of that continued fraction is in a sense the best possible rational approximation to that real number, for a given number of digits. Such a convergent is usually about as accurate as a finite decimal expansion having as many digits as the total number of digits in the nth numerator and nth denominator. For example, the third convergent 333/106 for (Pi) is roughly 3.1415094, which is not quite as accurate as the 6digit 3.14159; the fourth convergent 355/113 = 3.14159292 is more accurate than the 6digit decimal. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 114 Publication Date: 2010/08/03 Language: English Dimensions: 6.00 x 9.02 x 0.27 inches

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From Scalp to Brow: Eyebrow Transplants are Hair Transplants Too

Eyebrow reconstruction as a hair transplant technique is based on the technology first reported by Krusis in Germany in 1914 and later by the Japanese in the 1930 and 40s. In 1943, Tamara reported that single-hair grafts should be used for the hair restoration as these would look the most natural. Nearly a half-century later, when the most advanced type of scalp hair transplantation consists of using naturally occurring follicular units containing 1-4 hairs, the most refined type of eyebrow transplant still consists of using individual hair follicles.

The advance in eyebrow hair restoration lies, therefore, not in the use of individual hairs - this has been known for a long time - but in the adoption of techniques used in scalp hair transplantation that enable the physician to carefully isolate these individual hair follicles from the donor scalp.

The specific technique is called stereo-microscopic dissection, and it enables the surgeon to generate a hair follicle that contains all the essential anatomic structures necessary for maximum survival and growth, but that is devoid of the excess tissue that makes traditional grafts too cumbersome for the nuanced restoration of the eyebrows.

A carefully dissected single-hair micro-graft, trimmed of excess epidermis, dermis and fat, has the flexibility to be inserted into the tiny opening made with a fine hypodermic needle and placed at an angle almost flush with the skin - two techniques that are essential for the most natural restoration. The tiny recipient sites allow the grafts to be placed very close together. However, when closely placed grafts are angled so acutely, the base of one follicle literally lies under the shaft of the next, so that any extra volume to the graft can leave an unnatural lumpiness on the brow. The slender, microscopically dissected grafts have no volume other than the functional follicle, so they are perfectly suited for this closely spaced, acutely angled graft placement.

The Hair Cycle

The normal hair cycle varies from months to years; depending upon the part of the body the hair is located. Each hair regenerative cycle has a growth phase called anagen and a resting phase called telogen. The anagen phase for scalp hair ranges from 3-6 years while the anagen phase of the eyebrow hair is significantly shorter. The rate of growth for scalp hairs ranges from .30-.41 mm per day (about a half inch per month), while the growth rate of the eyebrow hair is half of that.

When scalp hair is transplanted to the eyebrow, the longer hair cycle of the scalp hair makes it grow to a cosmetically unacceptable long length. This necessitates frequent trimming of the eyebrows that is not only a nuisance, but that produces a cut end that is less elegant than the finely pointed tip of an uncut hair.

Over time, the transplanted hair will assume some of the characteristics of the site that it was transplanted into and the length of the transplanted hair will begin to gradually decrease. It is not known if the transplanted follicles will eventually assume the full characteristics of the surrounding eyebrow hair, but work by Wang et al. suggests that influences of the recipient are more significant than was previously thought.

Indications for Eyebrow Hair Restoration and Reconstruction

A variety of conditions can result in a loss or alteration of the eyebrows. Probably the most common is self induced - caused by repeated plucking of the eyebrows for aesthetic reasons, or less often from a compulsive disorder called trichotillomania. Those who pluck hair as an obsessive-compulsive disorder (OCD) should not be transplanted without addressing the OCD first, since transplanting the eyebrow will fail as the patient returns to old habits.

Other forms of physical trauma that may result in loss of eyebrows include car accidents, burn injuries, defects from surgical procedures, and radio- and chemotherapy. Burns or trauma may result in the formation of scar tissue that initially precludes hair transplantation. In these cases, reconstructive surgery may be necessary before the eyebrow hair transplant can be accomplished. Thickened scars may respond to injections of corticosteroids and, once thin, may readily support the growth of transplanted hair.

Women with eyebrows that they deem to be too thin occasionally have them tattooed, but this almost invariably looks unnatural. The situation worsens as the pigment is engulfed by macrophages and brought deeper into the dermis causing the black-brown color to take on a bluish hue. The pigment can be successfully removed with lasers, but then the once thin eyebrows become totally devoid of hair.

A common dermatologic condition that may cause the loss of the eyebrows (and eyelashes as well) is alopecia areata. This is a genetic, auto-immune condition that manifests with the sudden onset of discrete, round patches of hair loss with normal underlying skin. It can be treated with injections of cortisone, but tends to re-occur.

Systemic diseases may also cause the loss of one's eyebrows and there are also congenital abnormalities that are associated with the absence of eyebrows and/or eyelashes.

In some patients, the disappearance of one's eyebrows is a normal occurrence with age and genetic hair loss results from the progressive thinning (miniaturization) of the hair until it is barely noticeable.

For any eyebrow transplant procedure to be successful, one must be certain that the underlying condition that caused the hair loss in the first place has been corrected. Once the hair loss is stable, hair restoration may be contemplated.

The Design

Persons who seek eyebrow hair restoration (or any hair transplant, for that matter) generally have particular desires, goals and prejudices on what the ideal shape of their hair should be. Creating natural looking eyebrows can be a difficult task because of the differences between a patient's prejudices and normal eyebrow design. Eyebrows are as different as faces, so "normal" is a relative term. If beauty is the focus for females, there are rules that can be applied to help define a beautiful eyebrow. Men, who are not satisfied with their eyebrow shape, often want their eyebrows to have a special character, such as the look of Albert Einstein. Some men think that bushy eyebrows are the most desirable as they represent male virility or genius. Women, on the other hand, want delicacy and more well defined shapes. These differences in the preferences of each sex must be understood and incorporated in the design of the restoration from the outset.

Beauty is not just determined by a specific angle or a precise number of grafts. The art of the restoration requires that the surgeon gets "inside the head" of the patient and understands what he or she wants to achieve. In contrast to balding men, who often cannot remember where their hair was when they were young and who are thus open to any design that will give them hair, the person seeking eyebrow restoration often has very specific ideas in mind. The doctor's job is to moderate the patient's perspective and make sure that it is reasonable. Mistakes are in full view and can leave a patient with a problem that may require years of plucking to correct.

Proper angulation is the most important aspect of any eyebrow transplant. The hair in the upper part of the central edge of the eyebrow usually points upward to the hairline, while the hair on the lateral aspects points horizontally, towards the ears. The hair in the upper part of the eyebrow should be pointed slightly downward and the lower portion slightly upward, so that they will converge in the middle, forming a slight ridge and resembling the pattern of a feather.

The eyebrows must be put in flat, or they will stick out pointing forward. The surgeon controls the direction and the distribution as the hair is transplanted into the eyebrow, and fine skills are required to densely pack single hairs into the small needle tracks that make for an undetectable wound.

The Technique

The outline of the eyebrow transplant should be carefully delineated using a fine surgical marker according to the design that the doctor and patient had agreed upon during the consultation. Markings should also be used to indicate the directional change of the hair as one moves medial to lateral. It is often helpful to make these markings above the brow (outside the area that will be transplanted) so that they are not lost as the sites are being made.

Once the markings are complete, the patient should be given a mirror to make sure that this is what they had discussed and that the design is satisfactory. At this point we find it helpful for the physician to leave the room (another staff member should still be present) to give the patient a few minutes to reflect on the design.

A small amount of anesthetic should first be injected in the supra-trochlear and supra-orbital notches to create a nerve block to numb the medial and lateral aspects of the brow. Local infiltration using a mixture of xylocaine or bupivicaine and epinephrine can further anesthetize the area and provide rigidity to the eyebrows. Tumescence enables the physician to keep the recipient sites more superficial and at a more acute angle and minimizes bleeding. Due to the small volume of fluid needed, a separate tumescent mixture is generally not necessary. The use of corticosteroids and other particulate solutions should be avoided when injecting around the eyes.

Recipient sites should be created using 20-22g needles (or equivalent instruments), depending upon the coarseness of the hair. If the patient's scalp hair is very light and fine, 2-hair grafts can be used in the central part of the brow to create extra density, but these grafts should not be placed near the edges.

Recipient sites should be created holding the instrument as flat as possible to the skin surface, as there is always some elevation of the graft in the normal process of healing. In making the sites, the instrument should be gripped between the thumb and the first and second fingers and held nearly flush to the skin surface. The instrument should not be held like a pencil, as this will not allow the angle to be significantly acute.

The number of grafts needed for the eyebrow hair transplant can vary greatly from as few as 75 per brow to as many as 350. Men generally require significant more grafts than women. It is helpful to make the recipient sites first so that one can determine exactly how many hairs need to be harvested. It is important to remember that follicular units will yield 2-3 grafts on average, depending upon the patient's donor density.

If the donor hair is obtained from a strip, then one should excise 1 cm2 of tissue for every 200 grafts required (since there are approximately 100 follicular units averaging 2.3 hairs each per cm2). If hair is obtained via follicular unit extraction, then the staff should dissect the grafts into individual hairs as they are removed from the scalp, so that the doctor can determine exactly how many are needed.

In women, the finer hair in the area over the ears should generally be harvested. In men with fine hair and coarse eyebrows, the area adjacent to the occipital protuberance is usually the coarsest hair on the scalp and may be the best match.

The grafts should be inserted using fine jeweler's forceps under loop magnification. The hair must be literally stuffed, rather than inserted, into the sites, as the site is too small to accommodate both the graft and the forceps.

No dressing is required post op and the patient is instructed to sleep with his/her head elevated. The following morning, the patient should gently irrigate the transplanted area to remove any dried crusts. This should be done in the shower at least three times the day following surgery and twice daily for a week. After each shower, an antibiotic ointment should be applied to the brow to help soften any crusts and enable to them to be more easily removed with the next washing. There is often bruising after the surgery that may take a week or more to subside to normal. Bruising is usually most apparent in older patients with significant sun damage.

As the transplanted hairs grow they will require occasional trimming. Using a gel or wax will help them keep the hairs flat as the hair has a tendency be unruly, particularly when they first start to grow. As mentioned above, the hair growth will tend to slow down over time and the hair will begin to assume some of the characteristics of the surrounding hair due to influence of the recipient site.

Patients should understand that two or more sessions may be required to achieve a desired look. Sessions are best spaced a minimum of eight months apart so that the doctor may have the benefit of seeing the first session actually grow in before planning the second.

Challenges of Eyebrow Transplants

When eyebrows are transplanted using scalp hair, they invariably retain some of their donor area hair characteristics of shape, shaft thickness and growth rates. If a person has coarse hair and fine eyebrows, a transplant from the scalp may not be a good match, particularly for a woman who requires delicacy of the new transplanted eyebrow. It is possible to decrease the diameter of the hair shaft by trimming off part, or all of the bulb, but this risks producing an irregularly shaped hair.

Curly eyebrows from an African American kinky haired person with coarse hair may not produce the directional control that the patient needs in a transplant (as African hair has a strong character, particularly in the coarse haired person). As such, some people may not be good candidates for an eyebrow transplant. With newer placing techniques, it is now possible to place the hair so that the curve is oriented in the appropriate direction.

As part of the normal healing process, wounds tend to contract. As a consequence, the cylindrical defect created by the transplanted hair will tend to contract and orient itself more vertically. This will tend to lift the hair slightly away from the skin giving the brow a bushier, unruly appearance. Making the recipient sites at a very acute angle can partially compensate for this, but some elevation may still occur.

Conclusion

Eyebrow transplantation is a safe, out-patient procedure that can significantly enhance one's appearance. It is particularly helpful for those individuals who have defective eyebrows caused by disease, accidents or that have been self-induced. However, eyebrow restoration is a nuanced procedure that demands technical skills and artistic knowledge beyond that required for the treatment of a balding scalp. For those physicians who have the aesthetic inclination and who are interested in taking time to develop the special skills necessary for this procedure, eyebrow restoration can produce a significant improvement in the appearance of select patients.

About the Author

Dr. Bernstein is Clinical Professor of Dermatology at Columbia University in New York. Dr. Bernstein's hair restoration center in Manhattan is devoted to the treatment of hair loss using his state-of-the-art hair transplant techniques. To read more publications on hair loss, visit http://www.bernsteinmedical.com/.