Mathematical Tools For Predicting Facial Surgery

Cosmetic Medicine

Cranio-maxillofacial surgery is a medical specialty focusing on facial and skull reconstruction. This surgery can help patients with such disorders as cleft palate, malformations of the upper or lower jaw, and problems with the facial skeleton due to injury.

Intensive pre-operative planning is needed not only to ensure that the medical purposes of the surgery are achieved, but also to give patients a sense of what their faces will look like after the surgery is performed. In their article "Mathematics in Facial Surgery," Peter Deuflhard, Martin Weiser, and Stefan Zachow (of the Konrad Zuse Zentrum (ZIB), Berlin) describe the mathematical techniques they have used to assist cranio-maxillofacial surgeons to predict the outcomes of surgery.

These techniques have proven to be quite successful in producing predictions that end up matching well the post-operative outcomes. The first step in the planning paradigm for such surgery is to use medical imaging data of the patient to construct a 3-dimensional computer model, called the "virtual patient". The second step, which is the one the article focuses on, uses the data to create a "virtual lab" in which various operative strategies can be tested. The last step is to play back to the patient the outcomes of the various strategies. The second step in the paradigm requires modeling and solving partial differential equations (PDEs), which are equations that represent changing physical systems.

One must identify which PDEs are appropriate for biomechanical modeling of soft facial tissue and bone. Standard methods for handling the equations need to be adapted for this particular application. One must also formulate ways to represent the interface between tissue and bone, as well as their interactions. Generally such PDEs cannot be solved exactly in closed form, so mathematics enters the picture once again to provide numerical techniques for producing approximate solutions. With the "virtual patient" data as input, one can use the approximate solutions to generate an individualized model for that particular patient.

The surgeons can then use the model as a "virtual lab" to predict the effects of surgical procedures and options, and patients can get a picture of approximately how they will look after the surgery. The article by Deuflhard et al states that qualitative comparisons between the outcomes predicted by the model, and the actual surgical outcomes, have been surprisingly good. The authors have also made quantitative comparisons, by creating a post-operative model of the patient and comparing it quantitatively to the predicted outcome.

They found a mean prediction error of between 1 and 1.5mm for the soft tissue, which they write "seems to be a fully acceptable result." "Even though biomechanical tissue modeling turns out to be a tough problem, we are already rather successful in predicting postoperative appearance from preoperative patient data," the authors write. "For the surgeon, our computer assisted planning permits an improved preparation before the actual operation."

Reduce form and cell mathmatical tools...

Best tools of Mathematical and Computer

To intelligently and effectively use crystallographic databases, mathematical and computer tools are required that can elucidate diverse types of intra- and interlattice relationships. Two such tools are the normalized reduced form and normalized reduced cell. Practical experience has revealed that the first tool--the normalized reduced form--is very helpful in establishing lattice metric symmetry as it enables one to readily deduce significant relationships between the elements of the reduced form.

Likewise research with crystallographic databases has demonstrated that the second tool--the normalized reduced cell--plays a vital role in determining metrically similar lattices. Knowledge of similar lattices has practical value in solving structures, in assignment of structure types, in materials design, and in nano-technology. In addition to using the reduced cell, it is recommended that lattice-matching strategies based on the normalized reduced cell be routinely carried out in database searching, in data evaluation, and in experimental work.

Key words: identification; lattice-matching strategies; lattice relationships; lattice similarity; metric lattice; normalized reduced cell and form; symmetry. **********

1. Introduction

The various crystallographic databases [1] now available constitute a large, comprehensive, and rapidly growing scientific resource, serving as an invaluable source of data for the intelligent design of materials, for crystal engineering, and for nanotechnology. To evaluate data entering these databases and to intelligently and effectively use this resource, diverse mathematical tools are required that can establish intralattice relationships or elucidate various types of interlattice relationships. Two such tools are the normalized reduced form and the normalized reduced cell--tools that are ideal for elucidating certain types of intra- and interlattice relationships. For example, with the normalized reduced form, one can determine lattice-metric symmetry and deduce other types of intralattice relationships.

With the normalized reduced cell, one can determine metrically similar lattices (1) via lattice matching techniques against the lattices in the crystallographic databases. Practical experience has revealed that these tools are very useful for routine and complex lattice analyses. Before proceeding with applications of these tools, it is necessary to define the normalized reduced cell and form.

1.1 Definitions

The reduced cell is a unique primitive cell of the lattice, which is based on the three shortest lattice translations. For the precise mathematical definition of the reduced cell and form and for procedures to calculate this cell, see [2] and NBS Technical Note 1290 [3].

The normalized reduced cell of a lattice is determined simply by dividing the cell edges of the reduced cell by the a-cell edge. The normalized reduced form is calculated from the normalized reduced cell and is defined by the vector dot products of the normalized reduced cell edge vectors:

a * a b * b c * c

b * c a * c a * b

As an example, consider the reduced cell for a typical triclinic crystal structure reported in the recent literature [4]:

[a.sub.t] = 9.6907[Angstrom] [b.sub.t] = 10.3119[Angstrom] [c.sub.t] = 11.2549[Angstrom]

[[alpha].sub.t] = 63.954[degrees] [[beta].sub.t] = 70.282[degrees] [[gamma].sub.t] = 87.414[degrees]

The corresponding normalized reduced cell and form are: Cell: a = 1.0000 b = 1.0641 c = 1.1614

[alpha] = 63.954[degrees] [beta] = 70.282[degrees] [gamma]...

Three Funny Jokes

Things to say if caught sleeping at your desk

Face it, we all feel sleepy the moment we enter the office premises. But what if your boss caught you sleeping at your desk? Here is what you can tell him:

• "They told me at the blood bank this might happen."

• "This is just a 15 minute power-nap as described in that time management course you sent me."

• "Whew! Guess I left the top off the White-Out You probably got here just in time!"

• "I wasn't sleeping! I was meditating on the mission statement and envisioning a new paradigm."

• "I was testing my keyboard for drool resistance."

• "I was doing Yoga exercises to relieve work-related stress."

• "Damn! Why did you interrupt me? I had almost figured out a solution to our biggest problem."

• "The coffee machine is broken..."

• "Someone must've put decaf in the wrong pot..."

• " ... in Jesus' name. Amen."

School Gifts

It was at the end of the school year, and a kindergarten teacher was receiving gifts from her pupils. The florist's son handed her a gift. She shook it, held it overhead, and said, "I bet I know what it is. Some flowers." " That's right" the boy said, "but how did you know?"

"Oh, just a wild guess," she said.

The next pupil was the candy shop owner's daughter.

The teacher held her gift overhead, shook it, and said, "I bet I can guess what it is. A box of sweets."

"That's right, but how did you know?" asked the girl.

"Oh, just a wild guess," said the teacher.

The next gift was from the son of the liquor store owner. The teacher held the package overhead, but it was leaking. She touched a drop of the leakage with her finger and touched it to her tongue.

"Is it wine?" she asked.

"No," the boy replied, with some excitement.

The teacher repeated the process, taking a larger drop of the leakage to her tongue.

"Is it champagne?" she asked.

"No," the boy replied, with more excitement.

The teacher took one more taste before declaring, "I give up, what is it?"

With great glee, the boy replied, "It's a puppy!"

Marketing Concepts

You see a gorgeous girl at a party.

You go up to her and say, "I am very rich.Marry me!"

That's Direct Marketing.

You're at a party with a bunch of friends and see a gorgeous girl.

One of your friends goes up to her and pointing at you says, "He's very rich.Marry him.

"That's Advertising.

You see a gorgeous girl at a party.

You go up to her and get her telephone number. The next day you call and say "Hi,I'm very rich.Marry me.

"That's Telemarketing.

You're at a party and see a gorgeous girl. You get up and straightenyour tie, you walk up to her and pour her a drink. You open the door for her, pick up her bag after she drops it, offer her a ride, and then say, "By the way, I'm very rich.Will you marry me?

"That's Public Relations.

You're at a party and see a gorgeous girl. She walks up to you andsays, "You are very rich.." That's Brand Recognition.

You see a gorgeous girl at a party. You go up to her and say, "I'mrich.Marry me" She gives you a nice hard slap on your face.That's Customer Feedback !!!!!

You see a gorgeous girl at a party. You go up to her and say, "I am very rich.Marry me!" And she introduces you to her husbandThat's demand and supply gap.

You see a gorgeous girl at a party. You go up to her and before yousay, "I am very rich.Marry me!" she turns her face towards you ------------ she is your wife !

That's competition eating into your market share

Job Prospects: Librarian

Librarian

If books are your obsession and you love the company of these true silent companions a library is the best place you can be at and what more if you all get the opportunity to work in one. It is a place for those who love the serene work environment and definitely have an analytical mind to absorb large quantity of information.

A library is described as the 'reservoir of knowledge' hence the people who are trained to work in such places are taught how to handle, maintain and improve the knowledge bank. Several institutes today offer courses in 'library science' to students who wish to pursue a career in the field. The course majorly teaches the technique to catalogue books, journals and audio-visual material in the library. It teaches one the skill to acquire and make information available to library members in a limited time span.

A library is one of the places that maintain a very typical and unique work ethics that are seldom altered and is maintained across the globe in a similar fashion. Students of the course are also taught these mannerisms and policies. With the world gradually shifting into the technology era, libraries worldwide too, are concentrating on attaining technological assistance to maintain their knowledge bank and provide accurate information to their members. The librarians therefore, are taught how to use various technology and extract required information from them. The job profile of a librarian is divided into three broad categories namely, customer service, administration and technical assistance.

The customer service part of their job is to help users locate their requirement either on the shelves or from the Internet that is proficiently a part of the knowledge bank these days. The administrative part of a librarian's job involves planning and management. The librarians are expected to negotiate buy and sell from wholesalers, publishers, distributors etc. While managing the smooth running of the library they are supposed to supervise the library physically, set budgets for the library stock and maintenance etc. Activities such as fund raising and public relations are also put under the job responsibility of a librarian.

In a small library set-up all responsibilities are shouldered by one person or sometimes by two librarians who divide their responsibilities, whereas in a larger set up there are a number of people appointed with specific area of functioning depending on their qualification. Apart from being appointed in a library a person with the a similar job profile can also stand chance of being absorbed by other organizations like information centers run by organizations like government aided agencies, museums, professional associations and corporate houses, law firms, ad agencies, medical research centers, hospitals, religious organizations, and various research laboratories.

Sport Personalities: Pete Sampras

Pete Sampras

Pete Sampras known for his aggressive serves and flinging swings carries an easy going straightforward and an extremely candid personality. His competitive style has won him several Grand Slam titles and a vast fan following too. Born on 12th August 1971 in Washington DC, Pete is a Greek immigrant by origin.

Sampras began his professional journey in the game of tennis at the tender age of 17 in 1988 and in only two years he smoothly moved his way up to the top ten strata. He won his very first Grand Slam title the U.S. Open in 1990. His serves in the tournament were such that impressed players like Agassi, Lendl, and McEnroe too. Pete was announced the youngest tennis player ever to win the U.S. Open cup.In 1991, Pete won the IBM World Championship followed by the Davis cup in 1992, where he helped the US regain its first position.

In 1993 he made a record of 1000 aces in a single season that also helped him to win the Wimbledon and the US opens in the same year. Pete's victory in the Australian Open in 1994 made him the first player ever to win three Grand Slam Tournaments in a row. During his career Pete won a total of 64 singles titles, with 14 Grand Slam titles. He won Wimbledon title seven times, the U.S. Open five times and the Australian Open twice in his 15 years of career. Though Pete could never win the French Open tournament ever the fact remains that he is an astounding player who exhibited great caliber on court.

Much on the contrary is his otherwise low-key behaviour and sportsmanlike attitude that kept him from becoming a major celebrity beyond the court. At the age of 32, in August 2003 Pete officially announced his retirement from the game at the US Opens and was the only player in history whose final match was a victory in the Grand Slam Finals so far. Apart from playing tennis professionally Pete is also known to have a liking for Golf as a game and also plays the game as a hobby.

Sport Personalities

Sunil Gavaskar- The Little Master

'The Little Master' as he was fondly called by his co-players and commentators, Sunil Gavaskar was born in 1949. He started playing cricket at the early age of 17 in the year 1966/67. He played in the 1970s and 80s for Bombay and then for India too. He was regarded as the greatest opening batsman of his time. To Gavaskar's credit are world records for the most runs and most centuries ever by a batsman. Gavaskar spent his childhood days in Mumbai where he developed his interest in the game and started playing for the state (Maharashtra) at a very young age. He was given the title of the 'Best Schoolboy Cricketer of the Year' in 1966.

After making a few consecutive centuries in state level matches for the Ranji Trophy team from Mumbai. Gavaskar made his entry into team India in a tour to West Indies. Sunil Gavaskar was the first batsman to score 10,000 runs. Gavaskar started playing his test matches for India in 1971 during India's tour to West Indies where he scored a spectacular 774 runs. Gavaskar's unique techniques and long concentration abilities proved beneficial for his games. Gavaskar holds the record for the highest number of test series – 34 until 2005 when Sachin Tendulkar broke his record. Apart from the numerous records and awards that are credited to his name, Gavaskar has also attained the prestigious 'Padma Bhushan' award. In the year 1994, he was appointed the honorary 'Sheriff of Mumbai' for a year.

Sunil Gavaskar retired from the game in the 1986-87 season of test cricket. But such was his love for the game that he took up TV and print commentary after retirement and also became an active executive member of the ICC board where he serves till date. Even after a decade of retirement from the field, the 'Little Master' still stands an example to young cricketers across the globe. Several records by the player are still unbroken by any player national or international. This makes it reason enough to call the all rounder a 'Living Legend in Cricket' today.

Article About Education and Healthcare by Anjali Prayag

`Education is the best investment'

Entrepreneurship in education and healthcare is a tricky business. Without compromising on quality, cost and pricing parameters have to be carefully watched. While an innovative idea gets applauded, an expensive one will be frowned upon. So how does one tread this difficult path?
"Let me tell you about our business model," says Dr Ramdas Pai, Chairman and President, Manipal Education and Medical Group (MEMG). At the group's medical colleges, one-third of the students are NRIs admitted only on merit. In turn, they subsidise the education of the other two-thirds who cannot afford expensive medical education, he explains.

The same principle holds good in their hospitals too, says Dr Pai. About 80 per cent of the patients in the general wards only pay about 10-15 per cent of the cost and about 10 per cent of the beds are offered free. "We believe that both in education and healthcare, nobody should be stranded or turned away because of lack of money," he says.

He narrates the story of a vegetable vendor who came to him decades ago pleading for a job for his son, who was an SSLC pass. "We could have easily given him a small-time job in one of our set-ups and be done with it. Instead, I advised the young boy to take a loan in a bank and continue his education in our college." He now lives and works in the UK.

Dr Pai firmly believes that the only thing that can change the face of this country is education. Human resource is our country's greatest asset and it's time to tap the potential of the two billion hands, he feels.

"Right now, our population is a liability, but with education and good healthcare we can turn it into an asset." He feels that there is no investment as good as education because of its yield.
MEMG's foray into the two high-pulse sectors began more than half a century ago when Dr Pai's father, Dr T M A Pai, started the Kasturba Medical College in Manipal. The first batch comprised 34 young men.

Today, students from 31 countries come to this university town in the South Kanara district of Karnataka, every year. In fact, the town is known to have more foreign nationals than any other region in the country — about 75,000 at any given point of time.

Kasturba Medical College is also the country's first self-financed college. For its first batch itself, the college was awarded recognition by the Indian Medical Council and the General Medical Council of Great Britain. After taking over the mantle of the group from his father in 1979, Dr Pai decided that MEMG's commitment to education and healthcare would move beyond South Kanara.

Institutes of learning were set up in various fields such as health sciences, technology and management. Dr Pai was responsible for establishing the first joint venture between the State Government and the private sector. The Sikkim Manipal Univeristy was set up with a medical college in Gangtok. This was just the beginning. Next came a teaching hospital and then an engineering college, with the group contributing nearly Rs 200 crore in these projects. Today, all these are part of the Sikkim Manipal University.

Dr Pai had earlier been invited by the Government of Nepal to start a medical school in Pokhara. In 1995, the Melaka Manipal Medical College was set up in Malaysia. Students of the college study in Manipal for two-and-a-half years and continue their clinical training for the same duration at the Melaka General Hospital in Malaysia.

The Manipal Academy of Higher Education was the first private university recognised by the Government of India, in 1993. Today, MEMG has two universities, 24 professional colleges, 11 hospitals (including 6 teaching hospitals) and 33,000 students from over 48 countries.

Technology and innovation have not been ignored here, he says. Through its distance education wing, designed to scale down the cost of education, the Manipal University reaches out to 39,000 students studying in 400 centres — the largest after IGNOU.

New business trends like outsourcing have to be tapped to our advantage, says Dr Pai. For instance, MEMG's healthcare BPO, employing around 1,000 people, has just been launched and business is `just picking up,' he says.

MEMG has also tied up with the National Health Service (NHS) of the UK to send its doctors and nurses abroad for short stints in the areas of ophthalmology and orthopaedics. "So far, NHS was outsourcing medical talent from Canada, Australia, South Africa and New Zealand. Now Indian doctors are getting globally recognised."

Commenting on the opening up of the education sector early next year, Dr Pai says, "I don't know what will happen. Personally I feel it will be good because competition is good for any business. In fact, it is an opportunity for us to benchmark with the world's best schools." Good institutions should not worry, "but unfortunately, the Government's regulations are not very clear," he says, adding, "There are a lot of grey areas which need to be cleared."

Dr Pai was recently awarded the Ernst & Young `Entrepreneur of the Year' 2004 in the services category. The award, celebrates entrepreneurs who are building and leading successful, growing, and dynamic businesses, recognising them through regional, national, and global award programmes in more than 115 cities and 35 countries.