Hmmm. No one has replied as yet, so I did a search due to the fact that I'm not familiar with this particular problem.

First off, I'd suggest you make certain that's what you have because, although it does occur in the field, it sounds as if it's primarily a greenhouse problem. Beyond that, you didn't give adequate details to confirm, or not, the diagnosis.

You'd be wise to verify with a knowledgeable local source, perhaps your county's Extension Service or the personnel at a large, independent garden center.

Here's what I found at http://edis.ifas.ufl.edu/PG059

"Tomato Pith Necrosis (Pseudomonas corrugata)
Symptoms: This is a sporadic bacterial disease that was first reported in greenhouses in Europe, but has now been found in greenhouses in North America and in several field situations in Florida.

"Initial symptoms include chlorosis of young leaves, followed by wilting of plants. A brown discoloration of the surface of the lower stem may be evident. The most diagnostic characteristic is the appearance of a hollow or chambered ("laddered") pith in the lower stem evident when lower stems are cut open longitudinally. The intact pith tissue is often a dark brown color. Proliferation of adventitious roots is common.

"Cultural Controls: Little can be done for this disease once it appears in fields. It appears to be worse when nighttime temperatures are low, nitrogen fertilization is excessive, and humidity and rainfall are high."