Fuzzy Contours Research Articles

Analysis Hybrid Approach for Multi-Objective Optimization-based segmentation of fuzzy contours in mammogram using artificial plant optimization algorithm

It is observed that importance is given to the identification of tumor in case of medical image diagnosis. It has been found that in women breast cancer is increasing and due to which it has an impact in the death rate also. In medical domain radiologist generally uses the computer aided detection methods (CAD ). Medical image often contains the noise and some fuzziness in the picture border so the identification of the tumor is having problem and it becomes challenging task. by Owing to the noise and fuzziness of the picture border, identifying tumors on mammograms is challenging. Even though Active contour is an effective method for the segmentation but It is having problem related to local minima. The proposed method is a hybrid which is consist of multi objective optimization and Gravitational search algorithm (GSA) used for segmentation after that results are given to an Artificial plant optimization algorithm (APOA). The operations involve in this process includes some subprocesses primarily contour initialization is done for ROI followed by segmentation through GSA and multi-objective optimization and then APOA is applied. To evaluate the results two different databases are used mini-MIAS and DDSM databases. Results are also compared with other research work carried out earlier. It is observed that our proposed method gives better output then other.

The role of ultrasound diagnostics in the management of patients with juvenile psoriatic arthritis

Psoriatic arthritis (PsA) is a chronic inflammatory disease of the peripheral joints, entheses, and spine joints, affecting 10–25% of patients with psoriasis. Early diagnosis of the disease is challenging due to the possible delayed skin and joint symptoms and signs. Before the advent of ultrasound examination, the diagnosis of joint diseases was limited only to the radiological method. The ultrasound diagnosis of joint diseases in children is not established and needs a more comprehensive study.
 Materials and methods. The study included 50 PsA patients aged 3 to 17 years. We performed an ultrasound examination of 178 various joints. Knee joints were involved in 46 children, hip joints in 24, ankle joints in 34, and interphalangeal joints in 10. The mean age at onset was 7.8 years (range 1.5 to 14 years). The mean duration of the disease was 4.7 years.
 Results. Homogeneous joint effusion was the most common finding in patients with juvenile PsA (JPsA) – 83%. The effusion heterogeneity (17%) was due to hyperechoic inclusions (fibrin) in anechoic content. Diffuse synovium thickening was found in 91% of the joints. In 12.3% of joints, cartilage thinning was observed (in patients with a disease duration of 5 years or more), with fuzzy contours in some cases and normal echostructure in others.
 Conclusion. Periarticular structures, most often ligaments and tendons, are also involved in JPsA. The inflammation progresses steadily, with the rate depending on disease activity. Joint ultrasound is a reliable and highly informative method of JPsA diagnosing. It can identify a wide range of joint abnormalities; moreover, the severity of ultrasound abnormalities correlates with the disease severity, enabling using this method for monitoring disease-modifying therapy and as a screening tool for detecting the early signs of arthritis in patients with psoriasis. Joint ultrasound helps to detect early abnormalities.

ULFAC-Net: Ultra-Lightweight Fully Asymmetric Convolutional Network for Skin Lesion Segmentation

Segmentation of skin lesions is a critical step in the process of skin lesion diagnosis. Such segmentation is challenging due to the irregular shape, fuzzy contours and severe noise interference in the skin lesion region. Existing deep learning-based skin lesion segmentation methods are usually computationally expensive, hindering their deployment in dermoscopic devices with poor computational power. To address these challenges, we propose an ultralightweight fully asymmetric convolutional network for skin lesion segmentation, called ULFAC-Net. we use a parallel asymmetric convolutional (PAC) module to extract features instead of the traditional square convolution, and innovatively propose a PAC module with dual attention (Att-PAC) to enhance the feature representation. Based on the PAC and Att-PAC modules, we further propose a lightweight textual information submodule. To balance the number of parameters and performance of the model, we also hand-design an asymmetric encoder-decoder architecture. In this paper, we validate the effectiveness and robustness of the proposed ULFAC-Net on four publicly available skin lesion segmentation datasets (ISIC2018, ISBI2017, ISIC2016 and PH2 datasets). The experimental results show that ULFAC-Net achieves competitive segmentation performance with only 0.842 million(0.842M) parameters and 3.71 gigabytes of floating point operations (GFLOPs) compared to other state-of-the-art methods.

Duplex Ultrasound in the Diagnosis of Liver Tumors

Objective: To investigate the diagnostic value of duplex ultrasound in the diagnosis of liver tumors. Method: The present study included 152 cases of liver tumors; there were 87 malignant and 65 benign tumors. Visualization of liver tumors was carried out of duplex ultrasound using a convex transducer in the frequency range of 2-5 MHz on Philips HD-11. The p-value <0.05 was regarded as having a significant difference. Results: The hepatocellular carcinoma was diagnosed in 29 cases, the cholangiocellular carcinoma – in 21 cases, the metastatic liver cancer – in 37 cases, the capillary hemangioma – in 39 cases and the cavernous hemangioma – in 26 cases, respectively. In 115 cases (P<0,001), liver tumors were localized in the right lobe, in 37 cases – in the left lobe. In 59 cases, the tumor morphology was regularly, in 93 cases – irregularly. In 74 cases, the tumor boundary edge was clearly, in 78 cases – unclearly. Acoustic halo at the edge of the tumors was observed in 27 cases, of which HCC in 19 (65.5 ± 8.8%) cases (P<0,001). Isoechoic lesions were registered in 19 cases of liver tumors, of which in 11 (52.4±10, 9%) cases of cholangicarcinoma – significantly (P<0.001) higher than the rest. Conclusions: Duplex ultrasound allows you to identify the malignant and benign liver tumors. The most significant ultrasonographic signs of malignancy of the formation are fuzzy contours, heterogeneous internal structure, hypoechogenicity and increased vascularization of the pathological formation

Successful living donor liver transplantation of the left lateral sector with simultaneous atypical resection of the S2 for focal nodular hyperplasia

The purpose of presenting a clinical observation. Description of a clinical observation of a successful atypical resection of focal nodular hyperplasia of the segment II of the liver to a relative donor, followed by transplantation of the left lateral sector of the liver to a one-year-old child with cirrhosis of the liver in the outcome of biliary atresia.General provisions. Patient Z., 29 years old, was examined as donor for related liver sector transplantation. The oval structure with fairly smooth contours, hyperechoic in the central parts and hypoechoic in the periphery, was found in the segment II during the ultrasound examination; assessment of blood flow was difficult due to acoustic interference. According to computed tomography, it was a weak hypervascular formation with fuzzy contours, accumulating contrast medium unevenly in the arterial phase, with visualization of a small hypodense area around, also accumulating contrast medium in the venous phase. According to magnetic resonance imaging, there is a zone of increased MR signal, with contrast enhancement uniformly accumulating contrast in the arterial phase. It was assumed that the patient had focal nodular liver hyperplasia. The patient underwent surgery, during which the left lateral sector of the liver was removed and a single-step atypical resection of the segment II was performed. Histological examination of the surgical material confirmed the presence of FNH. After excision and suturing of vascular structures in conditions of continued blood circulation, the left lateral sector was removed from the wound and implanted into the recipient in an orthotopic position. The postoperative period passed without complications. The donor and recipient were discharged from the hospital in a satisfactory condition on the planned date.Conclusion. This observation demonstrates the possibility of using a liver fragment as a transplant after resection of focal nodular hyperplasia.

Клініко-сонографічні особливості стеатозу підшлункової залози у дітей з надмірною вагою та ожирінням

Актуальність. Своєчасна діагностика стеатозу підшлункової залози (ПЗ) є необхідною умовою виявлення раннього метаболічного ризику та зниження захворюваності на хронічну гастроентерологічну патологію. Мета. Вивчення клініко-інструментальних особливостей стеатозу ПЗ у дітей із надмірною вагою та ожирінням. Матеріали та методи. У 53 дітей із функціональними розладами шлунково-кишкового тракту визначали наявність стеатозу ПЗ за допомогою ультразвукового дослідження. Розподіл за групами відбувся на основі наявності стеатозу ПЗ, ожиріння та надмірної ваги: 1 групу становили 24 пацієнти зі стеатозом ПЗ, ожирінням та надмірною вагою, 2 групу — 18 дітей з ожирінням і надмірною вагою без ознак стеатозу ПЗ, контрольну групу — 11 пацієнтів без стеатозу ПЗ, які мали нормальну вагу. Результати. Клінічна картина у дітей зі стеатозом ПЗ у більшості пацієнтів пояснювалась наявністю супутньої гастроентерологічної патології; 29,1 % хворих основної групи скаржились на біль у лівому підребер’ї. При аналізі диспептичних скарг слід відзначити, що пацієнти зі стеатозом ПЗ частіше скаржились на нудоту (58,3 %), метеоризм (45,8 %) проти пацієнтів, які мали нормальну вагу, однак значущість відмінностей не була достатньою. У пацієнтів 1 групи частіше виявлялась болісність при пальпації за ходом кишечника проти пацієнтів 2 групи. Болісність при пальпації в панкреатичних точках була вірогідно вищою у пацієнтів 1 групи (54,1 %) проти 3 групи. Підвищення ехогенності печінки в 2,4 раза частіше зустрічалось у пацієнтів 1 групи проти 2 групи та в 7 раз частіше, ніж у 3 групі. Зокрема, зміни зернистості печінки втричі частіше зустрічались у пацієнтів зі стеатозом ПЗ (p < 0,05), ніж у пацієнтів без стеатозу та з трофічними розладами, а також дітей, які мають нормальну вагу. Зміни ПЗ при її стеатозі проявлялись не лише змінами ехогенності, але й у майже половини пацієнтів (45,8 %) наявністю нечітких контурів органу, підвищенням зернистості (65,5 %). Об’єм і товщина стінки жовчного міхура були вірогідно вищими у групі дітей зі стеатозом ПЗ проти контрольної групи. Ознаки біліарного сладжу вдвічі частіше зустрічались у дітей зі стеатозом проти групи дітей без стеатозу та в 4 рази частіше, ніж у дітей, які мають нормальну вагу (43,87 % у 1 групі, 21 % у 2 групі та 9 % у 3 групі). Висновки. Клінічні та сонологічні зміни у пацієнтів зі стеатозом ПЗ свідчать про можливість запальних змін у паренхімі залози, що пов’язані із системним запаленням на фоні стеатозу та супутньою патологією органів шлунково-кишкового тракту.

Морфогенез енхондральних осередків окостеніння кісток пташенят спортивних голубів у ранньому постнатальному періоді онтогенезу

Racing pigeons are potential carriers of zooanthroponic diseases, since they can travel considerable distances during their flight. The study of the formation features of the pigeon skeleton’s hematopoietic function on different levels of its structural organization with the determination of the relationship between the growth and development of hematopoietic components and the processes of osteohistogenesis is necessary to understand the immunity of pigeons, especially during the early stages of their development when young animals are in the greatest risk of disease, especially during processes of osteogenesis and haematopoiesis in chicks. The bones of the axial and peripheral skeleton of one-day-old, 5-, 10-, 15-, 20-, and 25-day-old pigeons (n = 5) were examined. The presence and degree of development of dia- and epiphyseal ossification centers (EOCs), their relative area (RA) and X-ray density in the organs of universal hematopoiesis were determined on radiographs made on an x-Ray-TW-102 x-ray machine with an Alpha 4600 receiver using the MultiVox Dicom Viewer program. It was established that in day-old pigeons the rudiments of the studied bones are completely built by cartilaginous tissue, have low radiographic density, and fuzzy contours on radiographs. On the 10th day of life, the axial skeleton of pigeon cubs has formed EOCs of head and a tubercle on the 5th rib (third «true rib»), while in the bones of the peripheral skeleton there is an enchondral EOC of the diaphysis. The spongy and compact bone structure (BS) of the bones were fuzzy. The body of the rib and the epiphyses of the limbs’ tubular bones were cartilaginous. The X-ray density of the humerus at this age remains unchanged, and the tibial-metatarsal increases by 1.5 times, reaching 12 HU. In 15-day-old chicks, the RA of the EOC in the skeleton was moderately increased due to an increase in the RA of previously formed EOCs at the age of 10 days, the appearance of individual EOCs in the body of 5th rib, and in the tubular bones of the limbs, the enchondral EOCs of the proximal and distal epiphyses. In the diaphysis of the extremities tubular bones, a strip-like compact BS was clearly distinguished, and in the epiphyses, a small-sized spongy BS. The X-ray density of the bones almost doubled, reaching 19–21 HU. In 20-day-old pigeons, the processes of osteohistogenesis in the skeleton were almost completed, in the studied bones, all the main and additional EOCs were well expressed, their RA increased sharply. X-ray density of bones did not change. For 25-day-old pigeons in the skeleton, there was a slight increase in RA of the EOC, a process of complete synostosis of the bones was characteristic. From the moment of the appearance of the EOC in 10-day-old chicks until they reach the age of 25 days, the bones of the axial skeleton and the skeleton of the limbs were formed by 95–100% of BS, and their X-ray density was increased almost 2.5 times, reaching 19–26 HU.

Solitary Pulmonary nodule segmentation based on pyramid and improved grab cut

Background and objectiveAccurate segmentation of solitary pulmonary nodule of digital radiography image is essential for lesion appearance measurement and medical follow-up. However, the imaging characteristics of digital radiography, the inhomogeneity and fuzzy contours of nodules often lead to poor performances. This work aims to develop a segmentation framework that satisfies the requirements of accurate segmentation. MethodsIn this work, an interactive segmentation method which combined the enhanced total-variance pyramid and improved Grab cut was proposed to improve the performance of nodule segmentation. The edge-preserving multi-resolution pyramid structure did the rough segmentation on low resolution images, which provided contour nearby curves to initial the following accuracy segmentation and shortened the time of energy decreasing. With the multiscale information being incorporated to optimize the edge term and improve the appearance model, a novel Gibbs energy functional was constructed to extract the nodule in a proper scale. By introducing the multiscale processing and optimizing the energy terms, the proposed method could overcome the inhomogeneity and fuzzy contours. ResultsFor evaluation of the nodule segmentation, quantitative metrics such as precision, intersection over union, and dice similarity coefficient were introduced and compared in the experimental part. The proposed solitary pulmonary nodule segmentation method produced the results with mean values of precision 0.957, dice similarity coefficient 0.933, and intersection over union 0.891, respectively. And the corresponding standard deviation values were 0.041, 0.047, and 0.045. ConclusionsFrom the quantitative assessment and comparison in the experiments, the proposed method achieved a competitive performance in accuracy and stability, even in the cases with low contrast and fuzzy contours.

COVID-19 INTERSTITIAL PNEUMONIA (case report)

A clinical case of treatment of a 54-year-old man with several risk factors, including diabetes, obesity, hypertension, with moderate COVID-19 bilateral pneumonia is presented. His clinical symptoms and signs at presentation included combinations of fever, nonproductive cough, and shortness of breath. Initial chest radiograms faid to show any changes, but chest CT revealed ground glass opacities (GGOs) with fuzzy contours, parenchyma damage (27 %). He was treated according to the Guidelines for diagnosis and treatment of COVID-19 cases (the Order of Ministry of Health of Ukraine No. 762). After a 12-day treatment, the damaged area reduced to 5 % with fibrosis.

Clinical characteristics of mastocytoma in dogs

According to foreign researchers, mastocytoma is one of the most common (7-12 %) skin tumors in dogs. This neoplasia is caused by excessive proliferation of mast cells and characterized by a specific clinical course, unpredictable biological behavior and prognosis. Researches of clinical and morphological features of mastocytoma in geographical populations of Ukraine has not only scientific and general biological interest, but also important practical significance. The purpose of the research was to establish the frequency of spreading, the features of the clinical ostent and pathogenesis of cutaneous mastocytoma in dogs in conditions in Lviv and in the suburban zone of the regional center. The research was performed on dogs with skin tumors (n = 128), including 24 of them with mastocytoma, who came to the Department of Surgery and Clinic of Small Pets of Stepan Gzhytskyj LNUVMB during 2016–2020. The diagnosis on mastocytoma was verified by the results of physical examination and cytological examination of biopsy material of neoplasms. It was found that in the structure of oncological diseases of dogs the share of skin neoplasms was 32.16 %. Among animals with skin neoplasms, mastocytoma was diagnosed in 18.75 % of dogs aged 4 to 16 years. The highest incidence rates were found among animals aged 8 to 11 years; the median incidence was 9.5 years and fashion – 9 years. In terms of breeds, cutaneous mastocytoma was found in dogs of the breed: Rottweiler – 16.7 %, Sharpei – 12.5 %, Staffordshire Terrier – 12.5 %, Labrador – 8.3 %, Boxer – 8.3 %, Doberman – 8.3 %, chow-chow – 8.3 %. At the same time, the German Shepherd, Alabai, Spaniel, French Bulldog and Pug cases of the disease were isolated (4.2 %). Among sick animals, dogs accounted for 54.2 % and females for 45.8 %. It was found that in 41.7 % of the studied animals the rate of neoplasia was extremely rapid, because in 56.5 ± 1.91 days the tumors were doubled in size, which is evidence of significant aggressiveness of tumor growth. In 29.2 % of dogs the time of doubling the size of the primary tumor reached 122.1 ± 10.6 days, in 20.8 % of dogs the period of tumor development lasted for two years. In 8.3 % of dogs, the dynamics of neoplasia development is not clear. Sonography has shown that skin mastocytomas are usually visualized as heterogeneous, with uneven edges and fuzzy contours hypoechoic structures. Visualization of solid hypervascular foci with central type of vascularization, on the background of diffuse infiltration of neoplasia in the deeper layers of the skin and subcutaneous tissue, with a pronounced perinodular inflammatory reaction of the surrounding tissues is a sign of malignancy of the mastocytoma. The generalization of the neoplastic process in the internal organs was found, in particular the spleen, may indicate a predominance of the hematogenous route of metastasis of the mastocytoma. The obtained data complement and expand knowledge about the pathogenesis of mastocytoma in dogs, and also highlight the frequency of spreading and course features of this oncological pathology in a separate geographical population of Ukraine.

Multiparametric Ultrasound in the Diagnosis of Hepatocellular Carcinoma in Patients without Cirrhosis (Clinical Case)

Purpose: To demonstrate the capabilities of a complex of multiparametric ultrasound and MRI with intravenous contrast in the detection and characterization of atypical hepatocellular carcinoma with the example of a clinical case of a middle-aged patient without liver cirrhosis.Material and methods: Comprehensive study of medical history, outpatient records, results of clinical, laboratory, instrumental and morphological methods with independent retrospective analysis of the histological preparation of focal liver lesion.Results: Diagnostic search data are presented in a 48-year-old patient with hepatocellular carcinoma without signs of liver cirrhosis. The diagnosis required 1.5 months of examination in gastroenterological department, repeated review of the histological preparation by morphologists. The disease debuted with weakness after physical exertion, which was noted during a planned multiparameter abdomen ultrasound examination. During the study, multiple focal formations with uneven fuzzy contours, an inhomogeneous structure were visualized. Stiffness of the parenchyma in focal liver lesion is 108.29 kPa due to 2D-SWE. Further tactics consisted of hospitalization with further laboratory examination and abdomen MRI with intravenous contrast enhancement. Considering the results of instrumental examination, the patient was prescribed a puncture aspiration biopsy of focal liver lesion under ultrasound control followed by morphological verification.Conclusion: The presented clinical observation demonstrates the need of use an integrated approach in instrumental imaging methods in the diagnosis of atypical hepatocellular carcinoma.

Towards a Paradigm Shift in Governing Data Access and Related Intellectual Property Rights in Big Data and Health-Related Research

Big data is revolutionising the health care sector by making it easier to analyse large volumes of data. This enables health care providers to monitor individuals or systems in real time. However, the main concern with regard to big data in biomedicine is how to overcome the barriers to using such data for health-related research. The landscape of big data is still evolving and the law has not developed suitable principles for governing access to big data. This paper sketches the fuzzy contours of data ownership and related intellectual property rights to demonstrate that ownership is a concept that is ill-suited for governing rights in big data. The dawn of big data calls for an alternative normative framework. This framework must be capable of reconciling competing societal, individual and industries’ interests in the data with a view to ensuring fair access while minimising legal and ethical risks. Ultimately, the paper proposes a paradigm shift from ownership to custodianship in the governance of access and use of big data, particularly in international health-related research.

Mammographic mass segmentation using fuzzy contours

Background and Objective: Accurate mass segmentation in mammographic images is a critical requirement for computer-aided diagnosis systems since it allows accurate feature extraction and thus improves classification precision.Methods: In this paper, a novel automatic breast mass segmentation approach is presented. This approach consists of mainly three stages: contour initialization applied to a given region of interest; construction of fuzzy contours and estimation of fuzzy membership maps of different classes in the considered image; integration of these maps in the Chan–Vese model to get a fuzzy-energy based model that is used for final delineation of mass.Results: The proposed approach is evaluated using mass regions of interest extracted from the mini-MIAS database. The experimental results show that the proposed method achieves an average true positive rate of 91.12% with a precision of 88.08%.Conclusions: The achieved results show high accuracy in breast mass segmentation when compared to manually annotated ground truth and to other methods from the literature.

217 - Myelodysplastic Syndromes Dissected: Immunophenotypic Aberrant Stem Cells Predict Leukaemic Progression

Background and Objective: Accurate mass segmentation in mammographic images is a critical requirement for computer-aided diagnosis systems since it allows accurate feature extraction and thus improves classification precision.Methods: In this paper, a novel automatic breast mass segmentation approach is presented. This approach consists of mainly three stages: contour initialization applied to a given region of interest; construction of fuzzy contours and estimation of fuzzy membership maps of different classes in the considered image; integration of these maps in the Chan–Vese model to get a fuzzy-energy based model that is used for final delineation of mass.Results: The proposed approach is evaluated using mass regions of interest extracted from the mini-MIAS database. The experimental results show that the proposed method achieves an average true positive rate of 91.12% with a precision of 88.08%.Conclusions: The achieved results show high accuracy in breast mass segmentation when compared to manually annotated ground truth and to other methods from the literature.

Ultrasound Monitoring and Age Sonographic Characteristics of Community-Acquired Pneumonia in Children

The aim of the investigation was to study ultrasound semiotics of community-acquired pneumonias in children of different age, and its dynamics in the course of treatment. Materials and Methods. Pneumonia semiotics study and dynamic monitoring of the disease have been carried out on the basis of chest ultrasound of 154 children divided into 4 age groups: 14 infants (9.1%) from birth to 3 months; 60 children (39.0%) from 3 months to 3 years of age; 49 children (31.8%) from 4 to 7 years of age; 31 children (20.1%) from 7 to 18 years of age. During the hospital stay the children underwent ultrasound at least three times: on admission to determine pneumonia volume and localization; on day 3–5 or day 5–7 to assess the dynamics of sonographic picture and the necessity of etiotropic therapy change; before discharge to evaluate residual effects and determine the follow-up strategy. Ultrasound revealed zones of airness impairment of various size in the pulmonary tissue of all children. Pneumonia semiotics presented extensive and lobar forms of pneumonia. An extensive type occupies a segment or a lobe, and looks like a delta-shaped air-free area with fuzzy contours and heterogeneous structure, with an air echobronchogram, and occurs in children of older age. Lobar pneumonia presents small rounded subpleural infiltrate up to 15 mm with a homogeneous hypoechogenic structure, and is typical of newborns and younger children. The size and echostructure of apneumatic (air-free) area were the assessment criteria of pneumonia regression. Conclusion. Chest ultrasound is an informative radiologically safe technique for diagnosing and dynamic control of pneumonia in children of different age, which enables timely assessment of etiotropic therapy efficacy.

A statistical approach to investigate the formation of the solar system

A model describing a gravitational effect into a forming gravitating and rotating cosmological body based on the statistical theory has been proposed. In this model, the forming cosmological bodies are shown to have fuzzy contours and are represented by spheroidal forms. The proposed theory starts from the conception for forming a spheroidal body from a gas-dust protoplanetary nebula. The distribution functions together with the mass densities and gravitational field potentials for an immovable spheroidal body as well as rotating one have been derived. This work also considers problem of gravitational condensation of a gas-dust protoplanetary cloud with a view to protoplanet formation in its own gravitational field. It is known a protoplanetary system behavior can be described by Jeans’ equation in partial derivations relative to a distribution function. The paper derives a more general evolutional equation which generalizes the Jeans’ equation. Since the determination of gravitational potential (and mass density) is the main problem of statistical dynamics for protoplanetary system, then the work shows how this task of protoplanetary dynamics can be solved on the basis of the proposed spheroidal body theory. Within the framework of this theory, the distribution function of a specific angular momentum of a rotating uniformly spheroidal body has been found. As the specific angular momentums are averaged during a conglomeration process, the specific angular momentum of a protoplanet for a planetary system is found in this paper. The proposed theory is also applied to investigate formation of planets in our solar system. As a result, a new law for the solar system planetary distances (which generalizes the well-known Schmidt law) is derived in this paper. It has been shown that the new law gives a very good estimation of observable planetary distances in the solar system.