Avian Bone Marrow

A - Let me answer this from two slightly different avenues - Simple and 
Complex: (Make sure to read all of this if you want to know a lot about 
birds!)

Simple - 

Even though birds have relatively hollow bones (with large air spaces) they 
still have bone marrow cells, where red blood cells are produced. The marrow 
cavity is just smaller.  Also, because birds have more efficient lungs than 
mammals, this works just fine for them.

Complex - 

The answer is that although a bird's bones are filled with air, there is
still a good deal of bone tissue left in the bones, enough to produce the
red blood cells.  Neat trivia (if you don't read the attached blurb):  A 
bird's bones are connected to the air sacs, so if a bird breaks a large enough
bone, it can actually breathe through it.

Super Complex -

Skeletal system. 

Many of the bones, including those in the skull, are pneumatized (filled
with air). Light, air-filled bones are an adaptation for flight. A bird's
skeleton comprises only about 5% of its total body weight (Brooke and
Birkhead, 1991).

The skeleton gives a bird protection, support, and movement. It's also a
site for calcium storage and the production of red blood cells. 

A bird's skeleton is made of bone. Many of the bones are fused or
modified for greater strength and rigidity in walking, jumping, running,
perching, and especially flying. 

The sternum, or breastbone, is more developed than in other
vertebrates. It has a large flattened plate, called a keel, for the
attachment of flight muscles. 

The wing attaches to the body via a sturdy pectoral girdle. In birds
the pectoral girdle is made of three bones, rather than two as in humans.
The furcula or "wish bone" is part of the pectoral girdle. 

The wrist bones of the wing are fused and elongated and only three
finger bones (digits) remain. 

The pelvis is long and has a forward opening to facilitate egg laying. 

The thigh bones are generally shortened and sturdy. The foot and
ankle bones are fused and elongated. 

The thigh is held close to the body and covered by feathers. The
visible backward bending leg joint corresponds to the ankle joint in humans.

Birds stand on their toes. 

Several vertebrae are fused except for those in the neck region. The
number of neck vertebrae for birds in general varies from 15 or fewer in
small birds with short necks to 20 or more in large birds with long necks.
More neck vertebrae means increased mobility of the head and neck.
California condors have 18 neck vertebrae (Mundy, 1992). 

The bird's large eyes are separately supported and protected by an
encircling ring of small, shinglelike bony plates called the sclerotic ring. 

A bird's flight muscles are red, not white, as in chickens or turkeys.
The coloration is due to the abundance of oxygen-carrying myoglobin, typical
of birds that are strong, long-distance flyers.  This means that less oxygen 
has to be supplied to the muscles.  A lower red blood count would not hinder a
bird.

The circulatory system is similar to those in other vertebrates. As in
mammals, birds have a four-chambered heart; however, a bird's heart is
proportionately larger and more powerful to help facilitate the spreading of 
oxygen faster and more efficiently.

Birds usually have higher metabolic rates than mammals and need larger,
more efficient hearts. 

Birds require large amounts of energy for flight, and need efficient
oxygen circulation in high altitudes. The highest flight recorded for a bird
was 11,274 m (37,000 ft.) when a Ruppell's griffon vulture collided into a
commercial airline over western Africa (Martin, 1987). 

Air enters the lungs from the nasal chambers and through the trachea. 

Unlike mammals, birds don't have a diaphragm. Instead, air moves into the
lungs by a complex system of nine air sacs and interconnecting tubes. 

The respiratory system behaves like a two-cycle pump. 

(1) During the first inspiration, air passes almost completely
into the posterior air sacs. 

In the first expiration, air moves into the lungs. 

On the second inspiration, air is drawn from the lungs into
the anterior air sacs. 

In the second expiration, air is exhaled to the outside.

To meet the rigorous demands of air consumption in flight, birds
have a highly efficient one-way air flow through the lungs and air sacs.
Mammals have a cul-de-sac system where old air in the lungs is mixed with
the new. 

Muscle movement of the ribs and sternum creates the vacuum needed
for air circulation in and out of the lungs and air sacs. 

Pneumatic bones are also connected to the air sacs. Scientists have
shown that birds can actually "breathe" through a few of the larger
pneumatic bones if they're broken.