A three-dimensional (3D) model of the human airway tree is proposed using a deterministic algorithm that can generate a branching duct system in an organ. The algorithm is based on two principles: 1) the amount of fluid delivery through a branch is proportional to the volume of the region it supplies; and 2) the terminal branches are arranged homogeneously within the organ. These principles define the basic process of branching: generation of the dimensions and directionality of two daughter branches is governed by the properties of the parent branch and the region the parent supplies. The algorithm is composed of nine basic rules and four complementary rules. When the contour of an organ and the position of the trunk are specified, branches are successively generated by the algorithm. Applied to the human lung, the algorithm generates an airway tree that consists of approximately 54,000 branches. Its morphometric characteristics are in good agreement with those reported in the literature. The algorithm and the 3D airway model are useful for studying the structure-function relationship in the lung.

By immunoperoxidase histochemical staining of formalin-fixed paraffin-embedded sections, the production of alpha-fetoprotein(AFP), albumin(ALB), transferrin(TF), alpha-1-antitrypsin(AAT), and human chorionic gonadotropin(HCG) was examined in 35 operatively resected stomach cancers with elevated serum AFP levels (higher than 20 ng/ml as determined by radioimmunoassay). Cells positive for AFP were found in 19 cases (54%). In 29 cases (83%), some tumor cells contained normal serum proteins (ALB, TF, or AAT). All 19 tumors with AFP-positive cells also stained positively for two or three kinds of normal serum proteins. In some cases, AFP and normal serum proteins were localized in the same cells. There were two cases in which metastatic tumors produced AFP, whereas the primary sites did not. In nine cases (26%), HCG was present in tumor cells and HCG- and AFP-positive cells were coexistent in six tumors. Histologic examination of AFP-producing stomach tumors revealed medullary or papillotubular arrangements with marked nuclear atypia and eosinophilic granular or clear cytoplasms containing no glycogen or mucin. Some tumors with medullary patterns resembled liver cell carcinomas. Concordant phenotypic expression of AFP and normal serum protein production appears to be a general feature of AFP-producing tumors such as liver cell carcinoma, yolk sac tumor, and stomach cancer.

Twenty-three patients with bone metastasis from gastric cancer which was resected during the ten years from 1970 through 1979 were investigated. The incidence was 1.2 per cent (23/1,945) and was higher in the younger patients. The main symptom was local bone pain. Change on the X-ray appeared a few months after complaints of pain. Consequently, the confirmation was delayed in most cases. All of the laboratory findings were not specific to bone metastasis. Referring to findings at the primary surgery for gastric cancer, this form of metastasis occurred in cases of a high involvement of regional lymph nodes and of a scirrhous type. The results of histological examination showed a high degree of lymphatic permeation in the submucosal layer. Poorly differentiated adenocarcinoma was readily identified. The lumbar and thoracic vertebra were the areas of frequent metastases. The metastasis occurred within two years after the gastric surgery, in most cases. Chemotherapy was ineffective and radiotherapy was effective for palliation of the bone pain. Prognosis was very poor and all but one patient died within a few months after confirmation of the metastasis.

A three-dimensional (3-D) model of the human pulmonary acinus, a gas exchange unit, is constructed with a labyrinthine algorithm generating branching ducts that fill a given space completely. Branching down to the third respiratory bronchioles is generated with the proposed algorithm. A subacinus, a region supplied by the last respiratory bronchiole, is approximated to be a set of cubic cells with a side dimension of 0.5 mm. The labyrinthine algorithm is used to determine a pathway through all cells only once, except at branching points with the smallest path lengths. In choosing each step of a pathway, random variables are used. Resulting labyrinths have equal mean path lengths and equal surface areas of inner walls. An alveolus can be generated by attaching alveolar septa, 0.25 mm long and 0.1 mm wide, to the inner walls. Total alveolar surface area and numbers of alveolar ducts, alveolar sacs, and alveoli in our 3-D acinar model are in good accordance with those reported in the literature.

We propose a method for designing the bronchial tree where the branching process is stochastic and the diameter (d) of a branch is determined by its flow rate (Q). We use two principles: the continuum equation for flow division and a power-law relationship between d and Q, given by Q approximately dn, where n is the diameter exponent. The value of n has been suggested to be approximately 3. We assume that flow is divided iteratively with a random variable for the flow-division ratio, defined as the ratio of flow in the branch to that in its parent branch. We show that the cumulative probability distribution function of Q, P(> Q) is proportional to Q-1. We analyzed prior morphometric airway data (O. G. Raabe, H. C. Yeh, H. M. Schum, and R. F. Phalen, Report No. LF-53, 1976) and found that the cumulative probability distribution function of diameters, P(> d), is proportional to d-n, which supports the validity of Q approximately dn since P(> Q) approximately Q-1. This allowed us to assign diameters to the segments of the flow-branching pattern. We modeled the bronchial trees of four mammals and found that their statistical features were in good accordance with the morphometric data. We conclude that our design method is appropriate for robust generation of bronchial tree models.