A Stereoradiographic Technique and Its Application to the Evaluation of Lung Casts

Stereoradiographs have been used on occasion for three-dimensional recon struction and measurement of objects in radiology and radiotherapy. The lack of a good stereoradiographic technique has limited the nscs of stereoradio graphic exposures. In this paper, the principle of the double-image is out lined and a method of applying chis principle 10 stcrcoradiographic exposures is developed. A computer program has been developed from geometrical con siderations to analyze the stereobronchogram and to calculate the dimensions of the objects in question. The applications of this technique are discussed and its use in evaluating lung casts is dcscn"bcd.

cal details of the respiratory airways of man and experimental animals is essential to understand the deposition and ultimate toxicity of inhaled particles, and for physiological research. One approach to obtaining this information is to obtain casts of the airways and make detailed measurements o[ such anatomical parameters as diameters, lengths, and branching angles, all of which are needed to predict particle deposition! and in physiological research. During casting o[ the lung, however, the effects of either the density of t11e casting material and/or lack of restraint o[ the thorax and other organs imposed on the lung may change ainvay dimensions. This paper describes a stereoradiographic teclmique

Rupprecht.
which can be used to determine dimensions and locations on a stereoradiograph o[ any tllree-dimensional object. An example of tlle use of t11is method to investigate the artifacts of lung casts is presented.

Principle
The basic element of stereoscopic data reduction is a single point located in threedimensional space. Two or more points can be connected by line segments to form lines, angles, and branches as shown in Fig. L Such geometric forms have analogs in the tracheobronchial tree. 1£ the coordinates of the points are known in three-dimensional space in an arbitrary coordinate system, tlle length of a line connecting two points P 1 (x., y., zi) and P 2 (x., y., z 2 ) is (1) Other formulae can be derived to compute other parameters of interest such as brancltlng angles and inclination angles relative to gravity. For example, the branching angle P 2 P 1 P 8 (Fig. I)  if we know the locations of points P" P 2 , P,. and segment lengths calculated from equation (I).
The three-dimensional coordinates of each point of interest are calculated from the twodimensional coordinates of the radiograpltic film images of the point and from the threedimensional coordinates of each x-ray source in a common coordinate system. Figure I shows an object P 1 P 2 in three-dimensional space with its two images P 1 'P.' and P 1 "P 2 " corresponding to the two x-ray sources S' and s•. For an arbitrary point P (x, y, z) lying on the line connecting an x-ray source S (x.'. y. (2) where the supencript i refers to either (') or (") as appropriate. Equation (2) can be rearranged to give (4) selected for solving the overdetermined system (more equations than unknowns) is the least squares method.2 This method also allows a means for estimating the error associated with each point's coordinates.
In practice, the coordinates of an x-ray source relative to an arbitrary origin in the plane of the film are difficult to measure directly and precisely. To overcome this difficulty, t11e x-ray source coordinates were found indirectly by using at least two locator points above t11e film plane wit11 known coordinates Fie. 2. Schematic dia!P=' of a stereoradiographic positioning and filmholding device (for rodents or small objects). relative to a reference origin in the film plane. From their images on the film and their true coordinates, equations (3) and (4) are solved to find the x-ray source location. Four locator points are used, resulting in eight equations for three unknown coordinates (x, y, z) of the source. The eight equations form an overdetermined linear system which is solved by the least-squares method.

l\lethod and Experiment With Test Wire
A sd1ematic diagram of a stercoradiographic positioning and filmholding device is shown in ·Figure 2. The object is positioned on the top of plate A or C. The bottom side of plate A contains a rectangular metal wire grid pattern so that the film, when placed on plate B in contact with plate A, is directly beneath the grid whid1 forms a coordinate system on the film. The movable plate C is used for positioning the object at variable heights from the film to give higher mag· nification of the images if desired. Two x-ray source locator plates, D, each with two embedded metal locator points, E, are fixed to the two side walls. The locations of these four locator points are known precisely relative to an origin in the grid (xy) plane. A portable x-ray source is placed above the film at a distance of about 81 an. In making a stereoradiograpb, the x-ray source is moved horizontally about IO to 25 an for the second exposure.
Based on the geometric principles previously outlined, a computer program for stereographic data reduction was tested using radiographs of a metal object with a known configuration. The object was placed on the top of plate A, tl1e stereoradiograph was made, and the projected dimens!ons of the two images on the film were found by band measurement under IO.power comparator. These data were then processed with the computer program to provide computed lengths and angles of the object. These values showed excellent agreement with the known dimensions of the object (Table I).
E.~ample-Evaluation of lung casts. 'Vith the precision and validity of the stereoscopic method and computational tedmique established, experiments were performed involving the casting of rodent lungs to evaluate the Jung casts. The experiments were performed to visualize the d1anges in ainvay geometry during lung Cl.Sting. using an in situ Jung casting tedmique.s A powc!ered tantalum tedmique was used to obtain a good outline o[ the airways. 4 The animal subject was anesthetized with sodium pentobarbital and a trad1eostomy was performed. An endotrad1eal tube was tied into the trachea. A measured amount of tantalum powder (about 2.5 ,.m mean particle diameter) was introduced tluough the trad1ea using repeated pulses 0£ air to disperse tlie Ta powder into tl1e lung. This insuffiation ·"'as repeated until a good brond1ogram was obtained. The animal was placed in the stereoradiographic positioning and film· holding device and was prepared for lung casting by a saline replacement in situS with some modi .. fications for brond1ography. Two stereoradiograph pairs were taken, one after CO, washout (prior to saline infusion) and the other upon completion 0£ injecting tl1e casting material. During the filling process, additional stereobronchograms or monobronchograms were taken at pre- determined intervals (as each cubic centimeter of casting material was introduced into the lung) until the predetermined amount had been in· jeered. \Vhen a series of mono-brond1ograms was taken, the x-ray source Jocuion and the animal remained fixed so that bronchograms could be compared.
The three stages in the series of mono-hroncho-grams for in situ casting of rat lungs: A) before injection, B) after injection of 2 cml, and C) after injection of 7 anJ of silicone rubber are shown in Fig. 3. With in si1u casting, the airway lengths and bifurcation angles do not change appreciably (less than 53 overall). but the diameters of major bronchi increase about 153 during the injection of 2 cml of casting material. Further filling did not cause any additional increase in ain .. ·ay diameters.
A stereobronchogram was taken during the in situ experiment after filling a rat lung with CO,. A tracing of this stereobrond1ogrnm indicating the 1 segments and angles measured on both the radi~ graphic film and the finished cast are shown in Figs. 4 and 5, respectively. The data from these measurements were used as input to the computer program to calculate true dimensions of these seg· ments. 1\-Ieanwhile, these segments were identified in the lung cast, and direct hand measurements were made using a seven·power hand-held comparator. Considering the uncertainty involved in identifying the corresponding points between the finished c:ist and the stercoradiograph pairs, results of the dimensions of the airways before casting (calculated &om the stereobronchogram) and after casting (from the cast) ( Table 2) agree favorably with those seen in the monobrond1ogram series. Two segments measured and calculated from the stereobronchogrnm after injection of cast· ing material are also included in Table 2. Since the c:isting material moved the tantalum powder down during injection, most of the points identified  the sketch diagram of the points (segments and angles) being measured. These data further confirm that the main artifact is increasing the diameters of the major bronchi.

Discussion
In this paper, the principle of -the double image is outlined and a method of applying t11is principle in stereoradiographic exposures is developed. A test wire experiment is described and the results show the precision and validity of the technique.   (2) in describing the use of stereoradiograph pairs for measuring ainvay length and diameter in situ. Their procedure, however, required three e.'<posures for each measurement and the construction of a special frame for their x-ray source. This inconvenience caused them to use a two-dimensional approximation method in their e.'Cperimental data handling. The use of x-ray source locator points and a least-squares computing method requires only two exposures, or one simultaneous double exposure, and eliminates this difficulty. In addition, only two measurements from the radiograph are required for determining the location of each point (four measurements for calculating a segment length) rather than the three measurements for point determination in Hughes' method.
The stereoradiograph pair technique can be applied in various ways, such as to locate lung tumors or constricted ainvay segments and to quantitate the dtanges in major airways in a Ii ving animal during breathl:tg. In these cases, a pair of comparable x-ray sources has to be used with perfect synchronization in firing time and some modifications in locator points.
As an example of the application, lung casts of rodents were evaluated by this technique.