## 1 Introduction  
Varcose veins of the lower limb are a common venous disease that disproportionately affects individuals who maintain a sedentary or physically demanding lifestyle. The primary etiology of the disease is the prolonged impairment of venous blood flow, resulting in blood accumulation and stasis within the veins and consequent venous reflux, increased venous pressure, and valve damage. Epidemiological studies conducted abroad have revealed an overall incidence rate of 29.5-39.0% among women and 10.4-23.0% among men [1]. As the disease is progressive, its initial clinical presentation is often insidious, with symptoms such as lower limb fatigue, heaviness, and ankle edema arising in the later stages. Left untreated, long-term blood stasis may cause skin pigmentation, venous ulcers, and thrombophlebitis, significantly impacting the patient's quality of life [2]. In the early stages of lower-limb varicose veins, patients may alleviate the condition and prevent further deterioration by wearing elastic stockings. However, surgical intervention becomes necessary as the condition worsens. Historically, high ligation and stripping of the great saphenous vein has been the primary surgical approach [3], involving suturing the vessels at their source and simultaneously stripping and removing the trunk vessels, along with the rest of the non-functional superficial veins. However, patients are at risk of infection and other complications due to the large surgical incision [4]. With the advancement of minimally invasive technology, treatment has shifted from open surgery to minimally invasive procedures that feature smaller incisions and faster recovery times. Currently, minimally invasive treatments include modified great saphenous vein high ligation and stripping, endovenous thermal ablation (EVTA), and injection sclerotherapy [5; 6]. While thermal ablation and other techniques have demonstrated their clinical effectiveness in treating varicose veins, they are not universally applicable. In particular, veins that are less than 3.5 mm in diameter and situated deep within the skin are not suitable for thermal ablation. Furthermore, minimally invasive procedures require experienced physicians to achieve high success rates, and there is a risk of distant thromboembolism or other potentially lethal complications [7; 8; 9; 10; 11]. As a result, the development of non-invasive methods for treating varicose veins in the lower extremities through in vitro closure is a desirable goal. In recent years, non-invasive therapies have become increasingly attractive for treating lower-limb varicose veins, with ultrasound-guided high-intensity focused Ultrasound (HIFU) therapy being a new focus [12; 13; 14; 15; 16]. HIFU technology is an effective non-invasive technique for precisely destroying deep target tissues. Its therapeutic principle is to concentrate energy at a focus using a concave HIFU probe, thereby producing a range of effects, including thermal, mechanical, and cavitation effects, that lead to precise tissue necrosis and vascular fibrosis. Some scholars have reported using HIFU in animal studies and clinical settings in a small number of patients to ablate varicose veins [17; 18]. In clinical trials, the therapy is accurately targeted to the vein of interest using ultrasound imaging guidance, with five successful cases reported. HIFU technology is an effective non-invasive technique for precisely destroying deep target tissues. In the abovementioned study, a conventional B-mode linear array probe was used to guide the focusing therapeutic probe. Due to the volume and weight limitation of the linear array imaging probe, the whole system often required the assistance of a mechanical arm to ensure accuracy [13]. Although handheld operation is more convenient for doctors to adjust the treatment plan during treatment, considering that the entire treatment cycle of focused ultrasound therapy for lower extremity veins is relatively long, holding such a large device for a long time puts a heavy burden on the doctor.